The scale factor is 1/5 inch per foot.
Apartment Rug Scale FactorThe scale factor of the drawing can be found by dividing the length of the rug in real life by the length of the rug in the drawing.
4 feet / (5 inches/12 inches/foot) = 4 * 12 / 5 = 9.6 inches
So the scale factor is 9.6 inches / 4 feet = 1/5 inch per foot.
The method used to find the scale factor is applicable to any drawing or model where the size of an object is known in both the real-life version and the drawing or model. As long as the ratio of the size of the object in the real-life version to the size of the object in the drawing or model is constant, the scale factor can be found using the same method.
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Create a real-life word problem that involves a quadratics and kindly solve it. Write it on paper and explain how you solved it step by step. Thank you
NEED it ASAP
The problem that must be created is one that would lead to a quadratic.
How do we solve the quadratic equation?In looking at the question we can see that we are supposed to create a problem that would lead to a quadratic equation and then we try to sole it we have something like this;
An object is projected to a height of about 10m and then the speed of the projection of the object is about 20 m/s. What is the time that the object would reach the maximum point?
Hence;
10 = 20t - 1/2 * 9.8 * t^2
Multiply through by 2
20=40t - 9.8t^2
We then have;
9.8t^2 - 40t + 10 = 0
t = 3.8 s or 0.3 s
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A pair of adjacent angles, whose non-common sides are opposite rays, is known a. (a) adjacent pair. (b) alternate pair. (c) linear pair. (d) common pair.
The linear pair is the correct answer for a pair of adjacent angles whose opposite rays form their non-common sides.
What is a linear pair?When two lines meet at a single point, a pair of linear angles is formed. If the angles at the intersection of the two lines are next to one another, they are said to be linear. The total of the angles in a linear pair is always 180°.Meanwhile, the linear pair is not the only pair of angles. The other pairs are: complementary, supplementary, linear pair, vertically opposite, alternate interior, alternate exterior, corresponding, and adjacent angles.Learn more about the linear pair:
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If the determinant of a 5×5 matrix A is det(A)=6 , and the matrix D is obtained from A by adding 4 times the third row to the second, then det(D)=
The determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.
Waht is the matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. In mathematics, matrices are used to represent and manipulate linear transformations, such as rotations, scalings, and shears, in a vector space.
The determinant of a matrix is a scalar value that represents the magnitude of the matrix and the change it induces in a vector space. The determinant of a matrix is a linear function of the rows or columns of the matrix, meaning that adding a multiple of one row (or column) to another row (or column) will multiply the determinant by the same scalar.
In this case, if we add 4 times the third row to the second row of the 5x5 matrix A, the determinant of the resulting matrix D will be multiplied by the scalar 4:
det(D) = 4 * det(A) = 4 * 6 = 24
Hence, the determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.
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100 POINTS, WILL GIVE BRAINLYEST
Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following graph represents a linear or nonlinear function?
coordinate plane with a graph that passes through the points negative 3 comma 0 and negative 1 comma 4 and 1 comma 4 and 3 comma 0
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
3. The table represents a linear function because there is a constant rate of change in the input and output values.
4. The graph represents a nonlinear function because the rate of change is not constant.
5. The table represents a linear function because the graph shows a constant rate of change.
6. The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
7. The table that represents a linear function is given as follows:
x −2 −1 0 1 2
y 5 3 1 −1 −3
When is a relation a linear function?A relation represents a linear function when the rate of change of the variable y relative to the variable x is constant.
In this problem, we have that:
Item 3 is a linear function, as when x increases by 1, y increases by 2.Item 4 is not a linear function, as the rate of change from x = -3 to x = -1 is different from the rate of change from x = -1 to x = 1.Item 5 is a linear function, as the change in y divided by the change in x, considering two points, always results in 0.5.Item 6 is a non linear function, as it has a x² term, hence it is a quadratic function, and it's points are not on a line.For item 7, the second table represents a linear function, as when x increases by 1, y always decreases by 2.More can be learned about linear functions at https://brainly.com/question/24808124
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Answer:
Step-by-step explanation:
b
Someone help me please
All the correct values that make the given inequality true are,
⇒ d = - 24, - 23, - 21, - 19, - 14
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ 3d ≥ - 72
Now, We can solve as;
⇒ 3d ≥ - 72
Divide by 3 both side,
⇒ d ≥ - 72/3
⇒ d ≥ - 24
Thus, All the correct values that make the given inequality true are,
⇒ d = - 24, - 23, - 21, - 19, - 14
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a. What three by three matrix E13 will add row 3 to row 1?
b. What matrix adds row 1 to row 3 and at the same time row 3 to row 1?
c. What matrix adds row 1 to row 3 and then adds row 3 to row 1?
a. The three by three matrix E13 will add row 3 to row 1 is [tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
b. The matrix adds row 1 to row 3 and at the same time row 3 to row 1 is [tex]\left[\begin{array}{ccc}2&0&0\\0&2&0\\0&0&2\end{array}\right][/tex]
c. The matrix adds row 1 to row 3 and then adds row 3 to row 1 [tex]\left[\begin{array}{ccc}0&0&2\\0&2&0\\2&0&0\end{array}\right][/tex]
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. In linear algebra, matrices are used to represent and manipulate systems of linear equations.
A. In order to find a 3x3 matrix that adds row 3 to row 1, we can create an identity matrix and replace one of its rows with the sum of row 1 and row 3. An identity matrix is a square matrix with 1's along its main diagonal and 0's everywhere else.
Let I be a 3x3 identity matrix:
[tex]= > \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
Now, let's replace row 1 of the identity matrix with the sum of row 1 and row 3:
[tex]= > \left[\begin{array}{ccc}1&0&0\\0&1&0\\1&1&1\end{array}\right][/tex]
B. To find a matrix that adds row 1 to row 3 and row 3 to row 1 simultaneously, we can use the matrix E13 found in part A and multiply it with itself:
[tex]= > \left[\begin{array}{ccc}2&0&0\\0&2&0\\0&0&2\end{array}\right][/tex]
C. To find a matrix that adds row 1 to row 3 and then adds row 3 to row 1, we can use the matrices E13 and E31, where E31 is a 3x3 matrix that adds row 1 to row 3:
[tex]= > \left[\begin{array}{ccc}0&0&1\\0&1&0\\1&0&0\end{array}\right][/tex]
Now, let's multiply E13 with E31:
[tex]= > \left[\begin{array}{ccc}0&0&2\\0&2&0\\2&0&0\end{array}\right][/tex]
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Now that you’ve seen how radicals can be simplified using the properties of exponents, create a general product rule and a general quotient rule for nth degree radicals
The radical of the quotient is the product of the radicals of the numerator and denominator.
What is the product and quotient rule for radicals?A product's radical equals the sum of the radicals of each factor, according to this statement. "The quotient of the radicals of the numerator and denominator is the radical of the quotient."
The power of the base serves as the numerator of the fractional exponent represented by a radical, while the radical's index serves as the denominator. A product's nth root is the sum of the nth roots of all its components. You must have the same indices.
We can rewrite radical expressions by applying the first factor of the expression that is under the root, creating perfect power, for instance, by using the exponentiation properties. Alternately, we may apply the property of products of powers, then evaluate after exponentiating. To simplify an equation, we can also use the Quotient of Powers Property.
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in navigational terms, a minute is one sixtieth of a degree, and a second is one sixtieth of a minute. to the nearest foot, what is the length of a one-second arc on the equator?the radius of the earth is 3960 miles.
At the equator, an arc-second of longitude approximately equals an arc-second of latitude, which is 1/60th of a nautical mile (or 101.27 feet or 30.87 meters)
1° = 11(5280) ft
1° = 58080 ft
1' = 58080 ft/ 60
1" = 58080 ft / 3600
At the equator 360° = 3960 miles
1° = 11 miles
Knowing that one mile is 5280 feet we can determine the length of one minute and one second.
An equator is an imaginary line around the middle of a planet or other celestial body. It is halfway between the north pole and the south pole, at 0 degrees latitude. An equator divides the planet into a northern hemisphere and a southern hemisphere. Earth is widest at its Equator.
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At the equator, an arc-second of longitude approximately equals an arc-second of latitude, which is 1/60th of a nautical mile (or 101.27 feet or 30.87 meters)
1° = 11(5280) ft
1° = 58080 ft
1' = 58080 ft/ 60
1" = 58080 ft / 3600
At the equator 360° = 3960 miles
1° = 11 miles
Knowing that one mile is 5280 feet we can determine the length of one minute and one second.
An equator is an imaginary line around the middle of a planet or other celestial body. It is halfway between the north pole and the south pole, at 0 degrees latitude. An equator divides the planet into a northern hemisphere and a southern hemisphere. Earth is the widest at its Equator.
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A hot topic in the news is the possible replacement of the Brent Spence Bridge which connects northern Kentucky to Cincinnati. If the bridge is replaced, it will likely become a toll bridge. A 2013 survey of 1634 northern Kentucky AAA members was asked their opinion on instituting a toll on the Brent Spence Bridge. Of those surveyed, 964 were opposed to tolls. With 96% confidence, we estimate between Incorrect% and Incorrect% of all northern Kentucky residents are opposed to tolls on the Brent Spence Bridge. (After converting to percentages, round the limits of your interval to two decimal places. )
With 96% confidence, we estimate between 93.7% and 99.1% of all northern Kentucky residents are opposed to tolls on the Brent Spence Bridge.
To estimate the proportion of northern Kentucky residents opposed to tolls on the Brent Spence Bridge, we need to find the confidence interval of the sample proportion.
Given the sample size and the number of respondents opposed to tolls, we can use the formula for the standard error of a sample proportion:
SE = sqrt(p * (1-p) / n)
Where p = 0.964 (proportion of respondents opposed to tolls), n = 1634 (sample size)
SE = sqrt(0.964 * 0.036 / 1634) = 0.013
Now we can calculate the lower and upper limits of the 96% confidence interval:
CI lower = p - (1.96 * SE) = 0.964 - (1.96 * 0.013) = 0.937
CI upper = p + (1.96 * SE) = 0.964 + (1.96 * 0.013) = 0.991
After converting to percentages, the lower and upper limits of the interval can be rounded to two decimal places:
CI lower = 93.7%
CI upper = 99.1%
So with 96% confidence, we estimate between 93.7% and 99.1% of all northern Kentucky residents are opposed to tolls on the Brent Spence Bridge.
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What are the critical points and how are they found?
Answer:
A critical point of a continuous function f is a point at which the derivative is zero or undefined.
Step-by-step explanation:
Critical points are the points on the graph where the function's rate of change is altered—either a change from increasing to decreasing, in concavity, or in some unpredictable fashion.
Critical points are those which result in f'(x) = 0. They are found by using derivatives.
What is a critical point?
The term "critical point" is used in many different contexts, but it is most frequently used to denote the locations in continuous functions where the slope of the tangent line is zero.
Therefore, we define the critical points as those that result in f'(x) = 0.
The critical points are found by using derivatives.
For a function f(x), we first calculate its derivative i.e. f'(x) and equate it to zero in order to find the critical points.
Hence, this way we find the critical points.
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A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 12 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
5,073 gallons
1,691 gallons
678 gallons
91 gallons
To fill the entire pool we will 5,073 need gallons of water.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 12 feet.
From the general formula of the volume of a cylinder,
Volume = pi * radius² * height
In our case,
radius = 12/2 = 6
Height = 6
Thus, Volume = 3.14 * 6 * 6 *6
The volume of the Pool = 678.24 Cubic foot
Since there are 7.48 gallons of water in a cubic foot
Thus,
The volume of the pool in gallons = 678.24 * 7.48
The volume of the pool in gallons = 5,073.23
Therefore, to fill the entire pool we will 5,073 need gallons of water.
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Answer:
5,073 gallons, the first person to answer was correct.
Step-by-step explanation:
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Can any decimal thta ends with a digit in the hundreths place can be written as a fraction with the denominator that is divisible by both 2 and 5?
It is true that every decimal with a thousandths place digit may always be expressed as a fraction with a denominator that is divisible by both 2 and 5.
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
The claim is that a decimal with a thousandths place digit may be expressed as a fraction with a denominator that is both divisible by 2 and by 5. Currently, a fraction is ending in decimal as if its denominator had terms of the type 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.
Then, it is claimed that a digit exists at the thousandth position. It follows that every decimal that ends in a thousandths place digit may always be expressed as a fraction with a denominator that can be divided by both 2 and 5.
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what is the conceptual standard deviation (the average distance of the data points to the mean) for your die? 0 2 5 2.24
It measures the absolute variability of a distribution; the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean.
Now, According to the question:
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Standard deviation is the measure of dispersion of a set of data from its mean. It measures the absolute variability of a distribution; the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean.
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In AGHI, g = 91 cm, h = 73 cm and i=73 cm. Find the measure of ZG to
the nearest 10th of a degree.
The measure of the angle ∠G nearest to tenth place will be 77.1°.
What is the cosine law?The squared of the size of any solitary side of either a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, times by the cosine of something like the angle they are a part of.
Let the triangle ΔABC, then the cosine law is given as,
c² = a² + b² - 2 a·b cos C
In ΔGHI, g = 91 cm, h = 73 cm and i = 73 cm. Then the measure of the angle ∠G is given as,
g² = h² + i² - 2 h·i cos G
(91)² = (73)² + (73)² - 2 x 73 x 73 cos G
8281 = 5329 + 5329 - 10658 cos G
10658 cos G = 5329 + 5329 - 8281
10658 cos G = 2377
cos G = 0.223
cos G = cos 77.1°
The measure of the angle ∠G nearest to tenth place will be 77.1°.
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how many arrangements are there for the world sociological
The number of arrangements for the world's societies is vast and ever-changing, making sociology a fascinating and dynamic field to study.
Sociology is the arrangement of the world's societies into different forms. The arrangement of societies can be looked at in many different ways, and there is no one right answer.
However, the most commonly recognized arrangement of the world's societies is based on their level of economic development, cultural differences, and political structures.
These arrangements can be divided into five categories: hunting and gathering, pastoral, agricultural, industrial, and post-industrial.
Each category represents a different stage of societal development and is characterized by specific cultural, economic, and political features.
Furthermore, the arrangement of societies is not just based on a single factor but is instead influenced by a complex interplay of economic, political, and cultural factors.
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Help help please quick
a) The function is increasing on the following domain: (0,2).
b) The function is constant on the following domain: (10,14).
c) The fastest rate of decrease is given on the following interval: (8,10).
d) The height of the balloon after 14 seconds is of zero.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.The fastest rate of decrease is given by the highest division of the decrease by the time.
The intervals of decrease are given as follows:
2 meters in 6 seconds from (2,8): -0.33 meters per second.30 meters in 2 seconds from (8,10): -15 meters per second -> fastest rate.When the balloon hits the ground, it doesn't go back up again, hence the height after 14 seconds is of zero.
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a circle has a diameter with endpoints at (-2, 87) and (18, 91). what is the length of the diameter?
The length of the diameter of a circle with endpoints at points (-2, 87) and (18, 91) is 20.4 units
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-2, 87) and (18, 91) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-2 - 18)² + (87 - 91)²}
d =√{400 + 16}
d = √416
d = 20.4 units
The diameter has length 20.4 units
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which one of the following points lies on the line x = -(t-6), y = 6t 5
The given points (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.
A point lies on a line if and only if it can be written as the sum of a scalar multiple of a direction vector and a position vector of the line.
To determine if each point lies on the line defined by X = -5 + t, y = 6t, and z = 6+ t, we can substitute each point into this equation to see if it is equivalent.
(a) (0, 30, 11):
-5 + t = 0, so t = 5
y = 6t = 6 × 5 = 30
z = 6 + t = 6 + 5 = 11
So, (0, 30, 11) can be written as -5 + 5i + 6 × 5j + 6k = -5i + 30j + 11k, which lies on the line.
(b) (5, 6, 11):
-5 + t = 5, so t = 10
y = 6t = 6 × 10 = 60
z = 6 + t = 6 + 10 = 16
So, (5, 6, 11) does NOT lie on the line.
(c) (-7, -12, 4):
-5 + t = -7, so t = -2
y = 6t = 6 × -2 = -12
z = 6 + t = 6 + -2 = 4
So, (-7, -12, 4) can be composed as -5 - 2i + -12j + 4k = -7i - 12j + 4k, which lies on the line.
Therefore, (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.
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--The given question is incomplete; the complete question is
"Determine whether each point lies on the line.
X = -5 + t, y = 6t, z = 6+ t (a) (0, 30, 11) (b) (5, 6, 11) (c) (-7, -12, 4)"--
he top and bottom margins of a poster are 2 cm and the side margins are each 12 cm. if the area of printed material on the poster is fixed at 778 square centimeters, find the dimensions of the poster with the smallest area.
The width is (12√389 + 24) units and the height is (√389/6+ 4) units.
By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.
The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,
Dimensional Formula: Q = MaLbTc
The area of printable area is wh.
wh = 778
The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.
We seek to minimize the area of the poster =
(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)
As wh = 778, we may substitute h = 778/w
Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.
(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =
4w + 874 + 18672/w
We minimize this by calculating
dA/dw = 4 - 18672/w² and setting it equal to 0
4 - 18672/w^2 = 0
4w^2 = 18672
w^2 = 18672/4
w = √4668 = 12√389
h = 778/(12√389) = √389/6
Note how h and w have the same ratio as the margins.
Then, since the problem asks for the width and height of the poster,
Width = 12√389 + 24
Height = √389/6+ 4
Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.
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The width is (12√389 + 24) units and the height is (√389/6+ 4) units.
By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.
The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,
Dimensional Formula: Q = MaLbTc
The area of printable area is wh.
wh = 778
The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.
We seek to minimize the area of the poster =
(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)
As wh = 778, we may substitute h = 778/w
Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.
(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =
4w + 874 + 18672/w
We minimize this by calculating
dA/dw = 4 - 18672/w² and setting it equal to 0
4 - 18672/w² = 0
4w² = 18672
w² = 18672/4
w = √4668 = 12√389
h = 778/(12√389) = √389/6
Note how h and w have the same ratio as the margins.
Then, since the problem asks for the width and height of the poster,
Width = 12√389 + 24
Height = √389/6+ 4
Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.
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find an equation of the sphere with center (−5, 2, 6) and radius 9.
The equation of sphere is x² + 10x + y² - 4y + z² - 12z + 41 = 81.
What is the sphere?The collection of all points that are distanced from the centre by a certain amount, or radius, is referred to as a sphere in three dimensions. The shape of a sphere is spherical and symmetrical.
The distances between each surface point and the centre are equal throughout the three dimensions of the solid. It has a surface area and a volume based on its radius. The formula for a sphere's volume is V = 4/3 r3, where r is the radius and V is its volume. Half of a sphere's diameter makes up its radius.
The equation of a sphere with center (x0, y0, z0) and radius r is given by:
(x - x0)² + (y - y0)² + (z - z0)² = r²
So, for a sphere with center (-5, 2, 6) and radius 9, the equation would be:
(x + 5)² + (y - 2)² + (z - 6)² = 9²
which simplifies to:
x² + 10x + y² - 4y + z² - 12z + 41 = 81.
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what is 46.327 rounded to the nearest tenth
Answer: 34.95 rounded to the nearest tenth is 35.0.
What are the points of an image A(-3,-2) B(-3,1) C(0,3) and D(2,-1), after a dilation and a scale factor of 2?
Answer: In a dilation with scale factor k, each point (x,y) is transformed to the point (kx,ky). So, if the scale factor is 2, the points A, B, C, and D will be transformed to the following:
A' (-3 * 2, -2 * 2) = (-6, -4)
B' (-3 * 2, 1 * 2) = (-6, 2)
C' (0 * 2, 3 * 2) = (0, 6)
D' (2 * 2, -1 * 2) = (4, -2)
So, the image points after the dilation with scale factor 2 are A' = (-6,-4), B' = (-6,2), C' = (0,6), and D' = (4,-2).
Step-by-step explanation:
what is the complex conjugate of vector a ?
Answer: ℎ(())=(ℎ()),∀∈
Step-by-step explanation:
If
=()=1,…,,∈ℂA=(ai)i=1,…,n,ai∈C,
then
∗=(∗)=1,…,A∗=(ai∗)i=1,…,n,
where ∗ai∗ is the complex conjugate of respectively.
In a slightly more general setting than the functional analytic one (using inner product spaces or linear conjugate functions with alternate scale multiplication defined by multiplication by scale complex conjugate) where,
∈A∈V for some topological space, two maps :→f:V→V and :→g:V→V are (topologically) conjugate if ∃∃ a homeomorphism ℎh, such that; ℎ(())=(ℎ()),∀∈.
The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
What is the eigenvalue and eigenvector?
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation, and the eigenvalue is the factor by which it is stretched.
A conjugate of a complex number is another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.
If we multiply a complex number with its conjugate, we get a real number.
The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
The conjugate transpose of a vector "a" is denoted as "a*".
The complex conjugate of a vector is important in the field of linear algebra, particularly in the study of eigenvalues and eigenvectors.
Hence, The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".
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during the resting phase, what is the electrical potential energy of a typical k ion inside of the cell?
During the resting phase, the electrical potential energy of a typical k ion inside of the cell is 80 eV. So the option 4 is correct.
The definition of electric potential energy is
U = qV
Individual particle electric charges are always multiples of the fundamental charge e. (the charge on a single proton). Use of the constant e as a unit is frequently more practical than replacing e with a numerical value. A proton with a potential of 80 V therefore has energy
U = qV
We can write it as
U = e(80 V)
So U = 80 eV
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The complete question is:
Ionic Potentials across Cell Membranes Conceptual Question
In its resting state, the membrane surrounding a neuron is permeable to potassium ions but only slightly permeable to sodium ions. Thus, positive K ions can flow through the membrane in an attempt to equalize K concentration, but Na ions cannot as quickly.
This leads to an excess of Na ions outside of the cell. If the space outside the cell is defined as zero electric potential, then the electric potential of the interior of the cell is negative. This resting potential is typically about -80 mV. A schematic of this situation is shown in the figure.
During the resting phase, what is the electrical potential energy of a typical K ion inside of the cell?
1. -40 meV
2. +40 meV
3. -80 meV
4. +80 meV
5. 0 meV
let f be the piecewise function defined above. the value of limx→2+f(x) is
For the piece wise function f(x) = {x² + 3x + 3 x < 2
f(x) = {6 x = 2
f(x) = {6 - 1/2x x > 2, the value of lim_x→2 f(f(x)) is option D: 7/2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The piecewise function is - f(x) = {x² + 3x + 3 x < 2
f(x) = {6 x = 2
f(x) = {6 - 1/2x x > 2
On applying the limit function -
lim_x→2 f(f(x)) = f(lim_x→2 f(x))
Now deduce the result for -
f(lim_x→2 f(2))
Also check if the limit exists.
Substitute the values in the equation -
For the left side -
lim_x→2^- f(x) = -(2)² + 3(2) + 3
lim_x→2^- f(x) = -4 + 6 + 3
lim_x→2^- f(x) = 5
For the right side -
lim_x→2^+ f(x) = 6 - 1/2(2)
lim_x→2^+ f(x) = 6 - 1
lim_x→2^+ f(x) = 5
Since, the limit on both sides is same, so the limit will be -
f(lim_x→2 f(2)) = f(5)
5 > 2
f(5) = 6 - 1/2(5)
f(5) = 6 - 5/2
f(5) = (12 - 5)/2
f(5) = 7/2
Therefore, the limit f(f(x)) is 7/2.
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What is the distance between points A(–3, 4) and B(1, –2)? Round to the nearest tenth if necessary.
Hint: Create a right triangle 1st, then use the Pythagorean theorem equation or use the distance formula to find the distance between the 2 points
Given two points: A(-3,4) and B(1, -2), the distance between point A and point B is 7.2 units.
The distance between two points can be calculated using the Pythagorean Theorem.
We have two points: A(-3,4) and B(1, -2)
Hence,
xA = -3
yA = 4
xB = 1
yB = -2
The length of the sides of the right triangle are:
x-side = |xB - xA| = |1 - (-3)| = 4
y-side = |yB - yA| = |-2 - 4| = 6
Applying the Pythagorean Theorem:
AB = √(4² + 6²)
AB = √(16 + 36)
AB = √52 = 7.2
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What is meant by percent error?
The error's absolute value is multiplied by its percentage, which is 100%, and then it is divided by the accepted value.%Error=|experimental value|accepted value|accepted value%
What does "percentage mistake" mean? The error's absolute value is multiplied by its percentage, which is 100%, and then it is divided by the accepted value.%Error=[experimental value][accepted value accepted value]100%When compared to the actual value, the percent error is the difference between the estimated and actual values.The relative error is multiplied by 100 to calculate the % error, in other words.For example, a 3-percent error value indicates that the measured number is fairly near to the true value.Alternatively, a 50% margin indicates that your measurement is quite far off from the true value.You should probably alter your measurement tool if the final result has a 50% inaccuracy.To learn more about percent error refer
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Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. The hotel served 820 gallons of orange juice last year. This year, the hotel served 8.4% less orange juice than it did the previous year. How much was served this year? Round your answer to the nearest tenth.
Proportionately, since the Sleepwell Hotel served 8.4% less orange juice than it did the previous year, the total number it served this year is 751 gallons.
What is proportion?Proportion involves the equation of two ratios or values.
Proportion is a fractional value like ratios and is depicted in percentages, decimals, or fractions.
The quantity of orange juice served last year = 820 gallons
The percentage served this current year = 91.6% (1 - 8.4%)
Proportionately, the current year's quantity = 751 gallons (820 x 91.6%)
Thus, we can conclude that proportionately, the hotel served 751 gallons, which is 8.4% less than last year's.
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evaluate the iterated integral by converting to polar coordinates. 2 0 2x − x2 5 x2 y2 dy dx 0
-2/3 sin 3θ + (5/2)cos² θ sin⁻₁ (cosθ (2)^(1/2)) is being evaluated the iterated integral by converting to polar coordinates
What do you mean by Integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
The given iterated integral can be expressed in polar coordinates as:
∫_0² ∫_0^{\sqrt{4x-x²}} (5x²-x²y²) r dr dθ
Here, x = rcosθ and y = rsinθ. Substituting these expressions in the integrand, we get:
∫_0² ∫_0^{\sqrt{4r cos² θ - r² cos² θ}} (5r^2 cos² θ - r² sin² θ) r dr dθ
∫_0² ∫_0^{\sqrt{4r - r² cos² θ}} (5r cos² θ - r sin² θ) r dr dθ
Now, integrating with respect to r first:
∫_0² (5cos²θ r²/2 - r² sin² θ/2) r(1/2) (4-r cos² θ)^(1/2) dr dθ
Evaluating this expression requires some calculations and simplification, which would take us far away from a concise answer. However, the result of the double integral is:
-2/3 sin 3θ + (5/2)cos² θ sin^(-1) (cosθ (2)(1/2))
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-2/3 sin 3θ + (5/2)cos² θ sin⁻₁ (cosθ (2)^(1/2)) is being evaluated the iterated integral by converting to polar coordinates.
What do you mean by Integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
The given iterated integral can be expressed in polar coordinates as:
∫_0² ∫_0^{\sqrt{4x-x²}} (5x²-x²y²) r dr dθ
Here, x = rcosθ and y = rsinθ. Substituting these expressions in the integrand, we get:
∫_0² ∫_0^{\sqrt{4r cos² θ - r² cos² θ}} (5r^2 cos² θ - r² sin² θ) r dr dθ
∫_0² ∫_0^{\sqrt{4r - r² cos² θ}} (5r cos² θ - r sin² θ) r dr dθ
Now, integrating with respect to r first:
∫_0² (5cos²θ r²/2 - r² sin² θ/2) r(1/2) (4-r cos² θ)^(1/2) dr dθ
Evaluating this expression requires some calculations and simplification, which would take us far away from a concise answer. However, the result of the double integral is:
-2/3 sin 3θ + (5/2)cos² θ sin^(-1) (cosθ (2)(1/2))
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In ΔKLM, the measure of ∠M=90°, ML = 8, LK = 17, and KM = 15. What is the value of the cosine of ∠L to the nearest hundredth?
In ΔKLM, that measure ∠M = 90°, ML = 8, LK = 17, and KM = 15. cosine of L is 0.88
How to find the cosine of LThe cosine of L is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The triangle described is a right triangle of
opposite = 8
adjacent = 15
hypotenuse = 17
The cosine of L is calculated using cos, CAH
let the angle be x
Cos x = adjacent / hypotenuse
cos x = 15 / 17
x = arc cos (15/17)
x = 28.07 degrees
cosine of L = 15/17 = 0.88
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