-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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answers for Savvas Realize Math XL 4-5
Aurther have jump 0.50575 feet more to break the record.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
The high school jump record = 24 ft 5 1/4 inch
= 24 ft 21/4 inch = 24.4375 ft
and, Aurther jump is = 23.958 ft
So, Aurther have jump
= 24.46375 - 23.958
= 0.50575 feet more
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iven the following graph, what is the slope and y-intercept?
Answer:
slope: -3/2 y-intercept: -1
Answer: -32
Step-by-step explanation:
What numbers are in the range of S(n)?
find y' if x2 y2 = 10.
The derivative of the expression is y' = [tex]-\frac{-y}{x}[/tex].
What is derivative?
Differentiation refers to the method of determining the derivative. Anti-differentiation is the term for the opposite process. We'll calculate the derivative of the function y = f. (x). It represents the rate at which the value of y varies in relation to the change in the variable x. It is referred to as the "f" derivative with regard to the variable x.
Here the given expression is [tex]x^2y^2=10[/tex] then
=> f(x,y) = [tex]x^2y^2-10[/tex]
To find [tex]\frac{dy}{dx}[/tex] by using the formula [tex]\frac{dy}dx}=-\frac{f_x}{f_y}[/tex] and first find [tex]f_x , f_y[/tex]
Now ,
=> [tex]f_x =\frac{d}{dx}x^2y^2-10[/tex]
=> [tex]f_x=2xy^2[/tex]
Now,
=> [tex]f_y=\frac{d}{dy}x^2y^2-10[/tex]
=> [tex]f_y=2x^2y[/tex]
Now substitute into formula then
=> [tex]y' = -\frac{2xy^2}{2x^2y}[/tex]
=> y' = [tex]-\frac{-y}{x}[/tex]
Hence the derivative of the expression is y' = [tex]-\frac{-y}{x}[/tex].
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Suppose that a and b are nonzero vectors.
a) Under what circumstances is compa b=compb a
b) Under what circumstances is proja b=proj b a
Part (a) seems relatively simple but I'm having trouble with part (b). Thanks for any help!
a) Two vectors are proportional then compa b = compa a
b) Two vectors are parallel when proja b = proja a
A vector is a mathematical object with both magnitude and direction. In this problem, we have two vectors, a and b, which are assumed to be nonzero
(a) For two vectors a and b, the dot product (also known as the scalar product or inner product) is a scalar quantity that measures the extent to which the vectors are pointing in the same direction. The dot product of two vectors is defined as
=> compa b = ||a|| ||b|| cos(θ), where ||a|| and ||b|| are the magnitudes of the vectors and θ is the angle between them.
Hence,
=> compa b = compb a
if and only if the vectors are equal or parallel, meaning they have the same direction or are pointing in opposite directions.
(b) The projection of a vector onto another vector is the vector that points in the same direction as the second vector and has the same magnitude as the component of the first vector that lies in that direction. The projection of a vector a onto a vector b is given by
=> proja b = (compa b / compb b) b.
Since the dot product is commutative, it follows that
=> proja b = proj b
if and only if the vectors are equal.
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What comes after securing the string at point A and then setting the string length to be a little more than half of AB?
To mark the bisector of the AB make an arc above and below AB one from the point A and another arc from point B. Hence, option D is the answer.
What is a bisector?A line known as a bisector divides an angle or a line into two equally sized segments. A segment's midpoint is always contained in the segment's bisector. Based on the geometric shape that they bisect, there are two different sorts of bisectors.
Bisector of Line Segments (Perpendicular Bisector Theorem)
Bisector of angles (Triangle Bisector Theorem)
To mark the bisector of the AB make an arc above and below AB one from the point A and another arc from point B.
Hence, option D is the answer.
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Can an object with zero acceleration speed up?
Yes, an object can have zero velocity and immobile be accelerating together. While participating the object, you will find that the object will continue to move ahead for some time and then stops instantly.
Then the object will start to move in the reverse direction.
at all the velocity is constant, the acceleration is zero. For example, a car traveling at a constant 80 km/h in a straight line has nonzero velocity and zero acceleration.
If acceleration is 0, the velocity is not converted. If the velocity is constant (0 acceleration) then the object will continue needing slowing down or speeding up.
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Indigo's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y = 62 + 6x where y represents the expected quiz score and represents hours spent on homework that week. What is the meaning of the -value when y = 81
3.17 is the meaning of the x - value when y = 81. This equation can be solved using the concept of equation solving.
What is linear relationship?A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the type y = mx + b can both be used to represent linear connections. The quantity of hours worked in relation to income is an illustration of a linear connection. The independent variable would be the number of hours worked, and the dependent variable would be the amount of money made.
Linear relationship can be represented by the equation y = 62 + 6x where y represents the expected quiz score and x represents hours spent on homework that week.
when y = 81, then: y = 62 + 6x
or, 81 = 62 + 6x
or, 6x = 19
or, x = 3.17
3.17 is the meaning of the x - value when y = 81.
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PLEASE HELP HELP HELP HELP HELP HELP
Note that one advantage of the given Linear equation over the graph given above is that the whereas from the equation, we can immediately tell what the slope (m)is and what the y-intercept (b) is, this is not given in the above graph.
What is the Y-intercept and the slope as given in the above Linear Equation?Note that every linear equation takes the following form:
y = mx + b
Where:
the variable b denotes the y-intercept of the graph of the line; and variable m denotes the slope of the line.Since we have the given linear equation to be:
y = 6/1x + 100
m here = 6/1 or 6 which is the slope; while
b here = 100, that is the y-intercept.
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Part d
I m really confused
The expressions with powers are ( -7 )³ and [tex]3^{-2}[/tex]
What is an expression?
A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)
The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).
a) -7 is taken 3 times. so raise power as 3
( -7 )³
b) 1/(3²) = [tex]3^{-2}[/tex]
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what is fingers and multipliers
Answer: Fingering makes transistors which are connected in series, mulpliers create transistors which are connected in parallel.
Step-by-step explanation:
"Fingers" and "multipliers" are terms used in mathematics and specifically in multiplication to help perform calculations faster and with more accuracy.
"Fingers" is a method of multiplication that uses fingers on one's hand as a visual aid to keep track of numbers being multiplied. The method is often used by children who are learning how to perform basic multiplication, as it provides a concrete way of visualizing the problem. The student would put up a certain number of fingers on one hand to represent one of the numbers being multiplied, and then use the other hand to count the number of times that the first number is being multiplied.
"Multipliers" are a set of pre-memorized values that can be used to perform multiplication more quickly. These values are usually small, and when multiplied by 10, 100, 1000, and so on, give the result of more complex multiplication problems. For example, one common multiplier is 9, which can be used to quickly multiply any number between 90 and 99, such as 93 * 9 = 837. Knowing these multipliers is a key part of mental math and helps to perform calculations faster and with more accuracy.
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Find the solution to the differential equation dy/dt=y2(6+t), y=8 when t=1 .
The solution of the differential equation is [tex]y = (48/t - 6t)^{-1/2}.[/tex]
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives.
In this particular differential equation, the dependent variable is y and the independent variable is t. The equation states that the rate of change of y with respect to t is equal to
=> y²(6 + t).
To find the solution to this differential equation, we first need to separate the variables and integrate both sides.
This gives us an equation of the form
[tex]= > y = (C/t - 6t)^{-1/2}[/tex]
where C is an arbitrary constant.
To find the value of C, we use the initial condition y = 8 when t = 1. Plugging in these values, we find that
=> C = (8)² * 1 - 6 = 48.
So, the solution to the differential equation is
=> [tex]y = (48/t - 6t)^{-1/2}.[/tex]
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
The solution is Option C , Option D.
The inequality equation is x > 5
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the equation will be
Substituting the values in the equation , we get
-3 ( 2x - 5 ) < 5 ( 2 - x )
On simplifying the equation , we get
-3 ( 2x ) - 3 ( -5 ) < 10 - 5x
-6x + 15 < 10 - 5x
Adding 6x on both sides of the equation , we get
x + 10 > 15
Subtracting 10 on both sides of the equation , we get
x > 5
Hence , the inequality equation is x > 5
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The total surface area of a closed cylinder is 5000cm². Find the dimension of the radius that maximizes its volume and state the maximum volume.
The maximum volume of the cylinder is 27147.355 cm² at the maximum point.
What is volume of cylinder?
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. The substance could be a liquid amount or something else that can be evenly put into the cylinder.
The formula for the volume of the cylinder v = [tex]\pi r^2[/tex]h,
To find the maximum volume of the cylinder we apply the condition of maxima [tex]\frac{dv}{dr}[/tex] = 0.
Let r cm be the radius and h cm be the height of the closed cylinder.
Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]
5000 = [tex]2\pi r^{2} +2\pi rh[/tex]
h = [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex]............(1)
Volume of the cylinder v = [tex]\pi r^2h[/tex]
Substitute the value of h in the above equation
= [tex]\pi r^2[/tex] × [tex]\frac{5000-2\pi r^{2} }{2\pi rh}\\[/tex]
= [tex]\frac{r}{2}[/tex] × [tex]5000-2\pi r^2[/tex]
v = [tex]2500r-\pi x^{3}[/tex] ..............(2)
Now, for the maximum volume of the cylinder dv/dr= 0
[tex]\frac{d(2500r-\pi x^{3})}{dr}[/tex] =0
[tex]3\pi r^{2} =2500[/tex]
[tex]r^{2} =\frac{2500}{3\pi }[/tex]
r=[tex]\frac{50}{\sqrt{3\pi } }[/tex]
r= 27147.355
Hence, The maximum volume of the cylinder is 27147.355 at the maximum point r= [tex]\frac{50}{\sqrt{3\pi } }[/tex].
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Find the area of a rectangular garden with side length of 4x+11 and 2x+5
find the perimeter of the garden in the problem
The value of area of a rectangular garden is, (8x² + 42x + 55).
The perimeter of the garden is, (12x + 32).
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The side lengths of a rectangular garden are,
⇒ (4x + 11) and (2x + 5)
Now, We know that;
Area of rectangle = Length × Width
Thus, The value of area of a rectangular garden is,
⇒ Area = (4x + 11) × (2x + 5)
= (8x² + 20x + 22x + 55)
= (8x² + 42x + 55)
And, The perimeter of rectangle = 2 (Length + Width)
Thus, The perimeter of the garden is,
⇒ Perimeter = 2 (4x + 11 + 2x + 5)
= 2 (6x + 16)
= (12x + 32)
Thus, The value of area of a rectangular garden is, (8x² + 42x + 55).
And, The perimeter of the garden is, (12x + 32).
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Lucy sells jewelry that is painted either blue or green. She sold 65 pieces today. Eighty percent of the ones sold were blue. How many green pieces did she sell? Explain how you found your answer.
The total number of blue jewelry is 52, whereas the total number of green jewelry is 13.
what is percentage ?In algebra, a percentage is really a number any ratio that is presented as a part of 100. Often, the acronyms "percent growth.," "percentage points," and "personal computer" are utilized as well. But it is commonly indicated by the percent sign, "%." The % amount will have no dimensions. Percentages are essentially fractions when the denominator is 100. Can use percent sign (%) to indicate that perhaps a number is a percentages by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 respondents on a test (75/100). Divide the payment by the aggregate and multiply the results by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
given
80 percent of the jewelry in the equation is blue:
80/100 * 65 = 52.
Let the quantity of blue jewelry be x and the number of green jewelry be y.
20% of the jewelry is green, so
20/100 * 65, or 13
The total number of blue jewelry is 52, whereas the total number of green jewelry is 13.
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2113.58 = -0.33*x^2 63.78*x-968.15 solve for x
You can resolve the equation by completing the square. first, subtract 0.33 from both sides of the equation. Add 968.15/0.33 to both sides after that. The resulting equation will be x2 + 189.94 x = 2113.58. Divide both sides by 189.94, then multiply both sides by 0.5. To find x=-93.97, square root both sides of the equation.
-0.33x^2 + 63.78x - 968.15 = 0
x2 + 189.94x = 2113.58 after subtracting -0.33 from both sides.
Multiply both sides by 189.94 to get 11.27 (x + 94.97).
To all sides, add 0.5: x + 94.97 + 0.5 = 11.77
Add up both sides and subtract 94.97: x + 0.5 = 11.77 - 94.97
Add 0.5 on either side to get the result: x = 11.27 - 94.97 x = -93.97
By completing the square, the equation -0.33x2 + 63.78x - 968.15 = 0 can be resolved. first, subtract 0.33 from both sides of the equation. As a result, the equation x2 + 189.94x = 2113.58 will be produced. Divide both sides by 189.94, then multiply both sides by 0.5. The outcome will be (x+94.97)2=2403.55. Square root both sides of the equation to finish. As a result, x + 0.5 = 11.27 - 94.97 will be obtained. The result of deducting 0.5 from both sides and then 94.97 from both sides is yield x = -93.97.
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I need this answer TODAY
A triangle has one side that measures x, and the other two sides each measure 4 Inches less than x. The perimeter is 19
Inches.
What is the measure of x?
5
3
9
2
Answer:3
Step-by-step explanation: the closest multiple of for is 16 then reminder 3
Answer:
9
Step-by-step explanation:
one side of a triangle =x
the other two sides measure = (x-4) each
perimeter = 19
therefore :
perimeter of a triangle = x + (x-4) + (x-4)
I.e = x+x+x-4-4=19
= 3x -8=19
= 3x = 19+8
3x=27
divide both sides by 3
x=9
Is 6.9meters per second faster than 0.95 meters per second ?
Answer:
Yes
Step-by-step explanation:
Yes, because 6.9 > 0.95
Answer:
Yes
Step-by-step explanation:
Yes....about 7 times faster because 6.9 >> .95 meters
Prove F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition
F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.
What is a Fibonacci sequence ?
The Fibonacci sequence is a number sequence in which each subsequent number is formed by adding the two numbers that came before it. The series is named after the Italian mathematician who devised it.
Fibonacci numbers are defined as follows:
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2) for n ≥ 2
Now, let's prove that F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using this definition:
F(n + 1) = F(n) + F(n - 1) (by definition)
F(n – 2) = F(n - 3) + F(n - 4) (by definition)
Adding these two equations, we get:
F(n + 1) + F(n – 2) = F(n) + F(n - 1) + F(n - 3) + F(n - 4)
Now, using the definition of F(n) = F(n-1) + F(n-2), we can substitute F(n-1) + F(n-2) for F(n):
F(n + 1) + F(n – 2) = F(n) + F(n) = 2F(n)
Therefore, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3, which is the desired result.
Hence, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.
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What does the "constant variance" assumption for Simple Linear Regression actually mean?
The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.
What is regression line?
A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.
The standard deviation and variance of the residuals are assumed to be constant for all values of independent variables in regression analysis under the concept of constant variance.
The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.
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Kiran is flying a kite. He gets tired, so he stakes the kite to the ground. The kite is on a string that is 12 feet long and makes a 50 degree angle. What is the height of the kite
The height of the kite is equal to 9.19 feet.
What is the law of sines?In Mathematics, the law of sines is sometimes referred to as sine rule and it can be modeled by this mathematical expression:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] or Sinθ = opposite/hypotenuse
What is the height of the kite?Since the reference angle lies between the ground and the string of the kite (hypotenuse), the side opposite the reference angle would be denoted by x and calculated as follows;
Sinθ = opposite/hypotenuse
Sin(50) = x/12
x = 12 × sin(50)
x = 12 × 0.7660
x = 9.19 feet.
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Which equation is equivalent to 12 3/x + 15 = 36?
O 3x + 15 = 3
O x + 15 = 9
O x + 15 = -6
O 3/x+ 15 = 24
The correct answer is option 4. The equation that is equivalent to 12 3/x + 15 = 36 is 3/x + 15 = 24.
To isolate x in the equation, we need to subtract 15 from both sides, which gives us 3/x = 9. Then, we need to multiply both sides by x, which gives us 3 = 9x. Finally, we divide both sides by 9 to get x = 1/3. This means that the value of x that makes the equation true is 1/3. To verify, we can plug this value back into the original equation and see if both sides are equal.
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y=4squared2 and on the table is 2,0,-1,-2,-3 i need those answers right now
The numeric values for the function y = 4x² are given as follows:
x = -3: y = 36.x = -2: y = 16.x = -1: y = 4.x = 0: y = 0.x = 2: y = 16.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function in this problem is given as follows:
y = 4x².
Hence, to obtain the numeric value at x = -3, we replace the lone instance of x by -3, hence:
y = 4(-3)² = 4 x 9 = 36.
The same procedure is applied to obtain the other numeric values.
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A cereal company packages there granola in cylindrical containers that have a diameter of 20 cm and a height of 17. 4 cm. Approximately how much granola will a container hold?
A. 348 cm^3
B. 5,464 cm^3
C. 174 cm^3
D. 3,140 cm^3
The approximate amount of granola that can be held in the container is B. 5,464 cm³.
The amount of granola held in the container can be calculated by finding the volume of cylinder. The formula to be used for volume calculation is -
V = πr²h, where V is volume of cylinder r is radius and h refers to height of cylinder.
Radius = diameter/2
Radius = 20/2
Radius = 10 cm
V = 22/7 × 10² × 17.4
Performing multiplication on Right Hand Side of the equation
V = 5464 cm³
Thus, the volume of the cylinder is 5464 cm³.
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An office supply store recently sold a black printer ink cartridge for $18.99 and a color printer ink cartridge for $22.99. At the start of a recent fall semester, a total of 36 of these cartridges was sold for a total of $723.64. How many of each type were purchased?
Answer:
Step-by-step explanation:
Let x be the number of black ink cartridges sold and y be the number of color ink cartridges sold. We know that:
x + y = 36 (total number of cartridges sold)
18.99x + 22.99y = 723.64 (total amount of money earned)
We can use the first equation to solve for one variable in terms of the other and substitute that expression into the second equation to get a single equation in one variable, which can then be solved. For example:
y = 36 - x
18.99x + 22.99(36 - x) = 723.64
18.99x + 827.64 - 22.99x = 723.64
-4x = -104
x = 26
So, 26 black cartridges were sold and 36 - 26 = 10 color cartridges were sold.
what is the probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele?
The probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.
To determine the probability that two grandchildren of a woman who are first cousins to one another will each inherit the dominant allele, we first need to understand the pattern of inheritance for dominant and recessive alleles.
Assuming the woman has two dominant alleles (D) and two recessive alleles (d), the probability of passing on a dominant allele to each grandchild is 1/2. For two first cousins to each inherit a dominant allele, we need both of their parents to pass on a dominant allele to them. The probability of both parents passing on a dominant allele is (1/2) * (1/2) = 1/4.
So, the probability of two first cousins each inheriting a dominant allele is 1/4 * 1/4 = 1/16. This means that there is a 1 in 16 chance that both first cousins will each inherit the dominant allele.
To summarize:
P(inheriting dominant allele) = 1/2
P(both parents passing on dominant allele) = 1/2 * 1/2 = 1/4
P(two first cousins each inheriting dominant allele) = 1/4 * 1/4 = 1/16
Therefore, the probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.
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The probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.
To determine the probability that two grandchildren of a woman who are first cousins to one another will each inherit the dominant allele, we first need to understand the pattern of inheritance for dominant and recessive alleles.
Assuming the woman has two dominant alleles (D) and two recessive alleles (d), the probability of passing on a dominant allele to each grandchild is 1/2. For two first cousins to each inherit a dominant allele, we need both of their parents to pass on a dominant allele to them. The probability of both parents passing on a dominant allele is (1/2) * (1/2) = 1/4.
So, the probability of two first cousins each inheriting a dominant allele is 1/4 * 1/4 = 1/16. This means that there is a 1 in 16 chance that both first cousins will each inherit the dominant allele.
To summarize:
P(inheriting dominant allele) = 1/2
P(both parents passing on dominant allele) = 1/2 * 1/2 = 1/4
P(two first cousins each inheriting dominant allele) = 1/4 * 1/4 = 1/16
Therefore, the probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.
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A scientist decreases the temperature of a liquid
from 1:00 p. M. Until 10:00 p. M. • The
temperature of the liquid is 14. 7°C at 1:00 p. M.
• The temperature of the liquid is -6. 8 C° at
10:00 p. M.
The average decrease in the temperature of the
liquid is approximately how many degrees Celsius
per hour?
The average decrease in temperature of the liquid from 1:00 p.m. to 10:00 p.m. is approximately 0.8°C per hour.
The concept used in this calculation is average rate of change. The average rate of change is the change in a quantity (in this case, temperature) over a certain time period (in this case, 9 hours), expressed as a ratio or per unit of time. In this calculation, we are finding the average decrease in temperature per hour.
To find the average decrease, we need to find the difference between the starting temperature (14.7°C) and the final temperature (-6.8°C), and then divide by the number of hours that passed, which is 9 hours.
Therefore:
(14.7°C - (-6.8°C)) / 9 hours = 21.5°C / 9 hours = 2.39°C per hour
Rounding to the nearest whole number, we have:
2.39°C per hour ≈ 2.4°C per hour = 0.8°C per hour.
So, The average decrease in temperature of the liquid from 1:00 p.m. to 10:00 p.m. is approximately 0.8°C per hour.
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The average rate of change is the idea used in this calculation. The change in a number (in this case, temperature) over a predetermined amount of time (in this case, 9 hours), expressed as a ratio or per unit of time, is known as the average rate of change. We are calculating the average temperature drop per hour in this computation.
We must calculate the difference between the initial temperature (14.7°C) and the final temperature (-6.8°C) and divide it by the number of hours that elapsed, which is 9 hours, to determine the average decrease.
Therefore:
(14.7°C - (-6.8°C)) / 9 hours = 21.5°C / 9 hours = 2.39°C per hour
Rounding to the nearest whole number, we have:
2.39°C per hour ≈ 2.4°C per hour = 0.8°C per hour.
Boubacar is driving on a long road trip. He created the graph below to represent the of gas left in his tank. What is the meaning of the point ? Time ()
of gas in the tank after .
The change in the number of of gas in the tank for every one additional .
How long it takes Boubacar to run out of gas.
The number of of gas initially in the tank.
The meaning of the point (1,10) on the graph of the function is given as follows:
10 gallons of gas in the tank after one hour.
How to interpret the point?All the points in the graph of a function have the format presented as follows:
(x,y).
In which:
x is the input variable.y is the output variable relative to the input variable x.For this problem, the input and output variables are given as follows:
Input: number of hours.Output: number of gallons of gases in the tank.Hence the interpretation of point (1,10) is that there are 10 gallons of gas in the tank after one hour.
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Khalid said : If the egg is not broken, then you did not drop it.
If the egg is boiled, then it will not break.
Ahmed said : Therefore, If you drop a boiled egg , then it will not break.
Adel said : Therefore, If egg is not boiled or you drop it, then it will break.
Use truth table to show whether, Ahmed or Adel conclusion is valid or not.
Neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.
The truth table would look like this:
Egg broken? Egg boiled? Khalid's statement Ahmed's conclusion Adel's conclusion
No No True False False
No Yes False True False
Yes No True False True
Yes Yes False False False
From the truth table, we can see that Ahmed's conclusion is only true in one case (when the egg is boiled and not dropped), but false in two cases (when the egg is not boiled or when it is dropped). Adel's conclusion is only false in one case (when the egg is boiled and not dropped), but true in two cases (when the egg is not boiled or when it is dropped).
So, neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.
Therefore, Neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.
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