The derivative of the equation 2y³ + xy - 6x + 3 at the point (1,1) is 0, and the second derivative is 13.
The derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x. This gives us:
[tex]\frac{dy}{dx} = \frac{x}{2y^2} - 5[/tex]
We can evaluate dy/dx at the point (1, 1) by substituting x = 1 and y = 1 into the equation for dy/dx and calculating the result. This gives us:
[tex]\frac{dy}{dx} = \frac{1}{2} - 6 = -5.5[/tex]
The second derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x twice. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2y^3}[/tex]
We can evaluate d2y/dx2 at the point (1, 1) by substituting x = 1 and y = 1 into the equation for d2y/dx2 and calculating the result. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2} = -0.5[/tex]
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How to calculate relative frequency percentage?
List the frequency's percentage. To do this, multiply your answer by 100 after dividing the frequency by the total number of results.
What is the relative frequency?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.
Two facts must be known in order to calculate the relative frequency:
1) the total number of occasions/trials
2) frequency count for a subgroup or category
Relative frequency = f/n
f = the number of times the data occurred in an observation.
n = total frequency.
The relative frequency percentage is f/n × 100%.
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Simplify. Express your answer using positive exponents. w^3 x w^5
[tex]w^8[/tex] is the expression using positive exponents.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
w³ x [tex]w^5[/tex]
= [tex]w^{3 + 5}[/tex]
= [tex]w^8[/tex]
Thus,
[tex]w^8[/tex] is the final expression.
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Determine whether the first vector is a linear combination of the other vectors.
(a) (-3, 3, 7); (1, -1, 2), (2, 1, 0), (-1, 2, 1)
(b) (-2, 11, 7); (1, -1, 0), (2, 1 , 4), (-2, 4, 1)
(c) (2, 7, 13); (1, 2, 3), (-1, 2, 4), (1, 6, 10)
7 = a × 2 + b × 0 + c × 1, 7 = a × 0 + b × 4 + c × 1, 13 = a × 3 + b × 4 + c × 10 are the first vector is a linear combination of the other vectors.
What do you mean by Linear combination?In linear algebra, a linear combination is an expression formed by multiplying each element of a set of vectors by a scalar (a real or complex number) and then adding the results. The scalars are called coefficients and the vectors are called terms.
A linear combination can be written as a sum of the form:
a1 × v1 + a2 × v2 + ... + an × vn
where a1, a2, ..., an are the coefficients and v1, v2, ..., vn are the vectors. The result of the linear combination is also a vector, which can be thought of as a combination of the original vectors, weighted by the coefficients.
Linear combinations are used in many applications, including solving systems of linear equations, finding eigenvectors and eigenvalues, and representing a vector as a combination of basis vectors in a vector space.
(a) To determine whether the first vector is a linear combination of the other vectors, we can write a system of equations and solve for the coefficients. If the coefficients exist and are unique, then the first vector is a linear combination of the other vectors. If the coefficients do not exist or are not unique, then the first vector is not a linear combination of the other vectors.
-3 = a × 1 + b × 2 + c × -1
3 = a × -1 + b × 1 + c × 2
7 = a × 2 + b × 0 + c × 1
We can solve this system of equations using methods such as Gaussian elimination or matrix inversion to obtain the coefficients: a = -2, b = -1, c = 4
Therefore, the first vector is a linear combination of the other vectors.
(b) Following the same procedure, we can write a system of equations and solve for the coefficients:
-2 = a × 1 + b × 2 + c × -2
11 = a × -1 + b × 1 + c × 4
7 = a × 0 + b × 4 + c × 1
We can solve this system of equations to obtain the coefficients: a = 3, b = -2, c = 2
Therefore, the first vector is a linear combination of the other vectors.
(c) Using the same procedure, we can write a system of equations and solve for the coefficients:
2 = a × 1 + b × -1 + c × 1
7 = a × 2 + b × 2 + c × 6
13 = a × 3 + b × 4 + c × 10
We can solve this system of equations, but it will have no solution, meaning the coefficients do not exist.
Therefore, the first vector is not a linear combination of the other vectors.
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For all the given vectors the first vector is a linear combination of the other vectors.
What do you mean by Linear combination?In linear algebra, a linear combination is an expression formed by multiplying each element of a set of vectors by a scalar (a real or complex number) and then adding the results. The scalars are called coefficients and the vectors are called terms.
A linear combination can be written as a sum of the form:
a1 × v1 + a2 × v2 + ... + an × vn
where a1, a2, ..., an are the coefficients and v1, v2, ..., vn are the vectors. The result of the linear combination is also a vector, which can be thought of as a combination of the original vectors, weighted by the coefficients.
Linear combinations are used in many applications, including solving systems of linear equations, finding eigenvectors and eigenvalues, and representing a vector as a combination of basis vectors in a vector space.
(a) To determine whether the first vector is a linear combination of the other vectors, we can write a system of equations and solve for the coefficients. If the coefficients exist and are unique, then the first vector is a linear combination of the other vectors. If the coefficients do not exist or are not unique, then the first vector is not a linear combination of the other vectors.
-3 = a × 1 + b × 2 + c × -1
3 = a × -1 + b × 1 + c × 2
7 = a × 2 + b × 0 + c × 1
We can solve this system of equations using methods such as Gaussian elimination or matrix inversion to obtain the coefficients: a = -2, b = -1, c = 4
Therefore, the first vector is a linear combination of the other vectors.
(b) Following the same procedure, we can write a system of equations and solve for the coefficients:
-2 = a × 1 + b × 2 + c × -2
11 = a × -1 + b × 1 + c × 4
7 = a × 0 + b × 4 + c × 1
We can solve this system of equations to obtain the coefficients: a = 3, b = -2, c = 2
Therefore, the first vector is a linear combination of the other vectors.
(c) Using the same procedure, we can write a system of equations and solve for the coefficients:
2 = a × 1 + b × -1 + c × 1
7 = a × 2 + b × 2 + c × 6
13 = a × 3 + b × 4 + c × 10
We can solve this system of equations, but it will have no solution, meaning the coefficients do not exist.
Therefore, the first vector is not a linear combination of the other vectors.
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the probability that concert tickets are available by telephone is 0.90. for the same event, the probability that tickets are available through a web site is 0.94. assume that these two ways to buy tickets are independent. what is the probability that someone who tries to buy tickets both through the internet and by the telephone will obtain at least one ticket? round your answer to four decimal places (e.g. 0.9876).
The probability that someone who tries to buy tickets both through the internet and by telephone will obtain at least one ticket is equal to 1 minus the probability that they won't obtain a ticket through either method.
The probability that they won't obtain a ticket through either method is equal to the product of the probabilities of not obtaining a ticket through each method, since the events are independent.
P(not obtaining a ticket through the internet) = 1 - 0.94 = 0.06P(not obtaining a ticket through telephone) = 1 - 0.90 = 0.10P(not obtaining a ticket through either method) = 0.06 * 0.10 = 0.006Therefore, the probability that someone who tries to buy tickets both through the internet and by the telephone will obtain at least one ticket is:
1 - 0.006 = 0.994 = 0.994 (rounded to four decimal places)
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Coefficient of x on 4(3x+5)
Coefficient of x on 4(3x+5) is 12
What is the co-efficient of a number?A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it.
To find the co-efficient of x in 4(3x+5)
Expand the bracket
4(3x+5) = 12x + 20
From 12x + 20
The co-efficient of x in 12, That is the number with the variable x
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Using the formula a(x+h)^2+k to solve 5x^2-3x-2=0 prove that the answer is 5(5x-3/10)^2-49/20
By Solving by factorization method of equation 5x² - 3x - 2 = 0
x = 1 , [tex]\frac{-2}{5}[/tex]
What is meant by Quadratic equations?The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.Quadratic equations include those that have the solutions 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. You can see from these examples that some quadratic equations don't contain the terms "c" and "bx."Given data :
Given equation is, 5x² - 3x - 2 = 0
Solving by factorization method,
5x² - 3x - 2 = 0
5x² - 5x + 2x - 2 = 0
( 5x + 2 ) ( x -*1 ) = 0
x = 1 , [tex]\frac{-2}{5}[/tex]
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Find the length is segment of FB?
The length of segment FB is given as follows:
FB = 4 in.
How to obtain the length of segment FB?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately, as similar triangles are formed.
The parallel segments in this problem are given as follows:
DF, EF and AB.
Hence the proportional side lengths are given as follows:
3 in and 4 in.6 in and GF.3 in and FB.Meaning that the length of segment FB is obtained as follows:
3/4 = 3/FB
FB = 4 in.
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When we add a displacement vector to another displacement vector, the result is: A) a velocity B) an acceleration C) another displacement D) a scalar
Vector is to scalar as displacement is to distance.
What is vector?A vector quantity has both magnitude and direction. A scalar quantity has only magnitude and no direction. Displacement is the measure of distance between initial and final points in a particular direction. Distance is length between initial and final points no matter the direction.
here, we have,
Displacement is to distance is as vector is to scalar because displacement is a vector quantity and and distance is scalar version of displacement. Of the other options speed is a scalar quantity and velocity is a vector quantity and none of them arranged in the form of vector is to scalar.
Therefore, Vector is to scalar as displacement is to distance.
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Find the value of c that makes DEF ~ XYZ
The value of x that makes triangles DEF ~ XYZ is -2. 25
How to determine the valueIt is important to note that perpendicular lines are equal to each other
From the triangles given, let us equate their perimeter one to another, we get;
8 + 10 + 3(x -1 ) = 7. 5 + 4 + x-1
expand the bracket
18 + 3x - 3 = 11. 5 + x - 1
collect like terms
3x - x = 10. 5 - 15
Add or subtract the collected like terms, we get;
2x = 4. 5
Now, make 'x' the subject from the equation
x = 4.5/2
Divide the values
x = -2. 25
Hence, the value is -2. 25
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log(f(n)) = o(log(g(n)))
When f(n) = o(g(n)), it is not necessary that log (f(n)) = o(log (g(n))) is proved using the limits.
Consider limits on both the sides,
lim(n→infinity) (log(f(n))/log(g(n)))
= lim n→infinity (1/(f(n)xln2)x f'(n)) / (1/(g(n) x(ln2)) x g'(n))
= lim n→infinity (g(n)/f(n) x f'(n)/g'(n))
lim n→infinity (g(n)/f(n)) = infinity
lim n→infinity (f'(n)/g'(n)) = 0
let f(n) = n, g(n) = n^2
lim n→ infinity (f(n)/g(n)) = lim n→ infinity (1/n)
= 0
f(n) = o(g(n))
In this condition
lim(n→infinity)(log(f(n))/log(g(n))) = lim n→infinity (n x 1/2n)
= 1
so it is not necessary that log (f(n)) = o(log (g(n))) when f(n) = o(g(n))
Hence proved.
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The complete question is :
Given f(n) = o(g(n)), show that it is not necessary that log (f(n)) = o(log (g(n)))
a+given+data+set+is+normally+distributed+with+a+mean+of+200+and+a+standard+deviation+of+5.+++which+two+values+does+95%+of+the+data+fall+between?
The data have a mean of 200 and a standard deviation of 5, with 95% of the data falling between 190 and 210.
Mean = 200
5 is the standard deviation.
10 divided by two standard deviations
Lower Boundary = Mean – Two SDs = 200 – 10 = 190
Upper Boundary = Mean + Two SDs, which is 200 + 10 = 210.
As a result, 190 through 210 should contain 95% of the data.
The data provided indicate that the data set's mean is 200 and its standard deviation is 5. Accordingly, the range of the data for 95% of the samples should be between 190 and 210, with 200 serving as the average. Due to the fact that for a set of data with a normally distributed distribution, around 95% of the values should be within two standard deviations of the mean, this is the case. Two standard deviations from the mean of 200 would be 190 and 210 since 5 is the standard deviation. As a result, these two figures should encompass 95% of the data.
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The complete question is
a+given+data+set+is+normally+distributed+with+a+mean+of+200+and+a+standard+deviation+of+5.+++which+two+values+does+95%+of+the+data+fall+between 190 and 210.
ill give brainlist if good
The correct solution is 24cm.
What is a property of similarity?
When two objects have the same shape but different sizes, they can be said to be comparable. This indicates that comparable shapes superimpose one another when amplified or demagnified. The term "Similarity" refers to this characteristic of like shapes.
Here, we have
Given: ∆ ABC ~ ∆ DEF
BC = 16cm
EF = 12cm
DE = 18cm
We have to find the correct solution.
By the property of similarity,
The corresponding sides are proportional.
So, AB/DE = BC/EF = AC/EF
AB/DE = BC/EF
x/18 = 16/12
x = 16×18/12
x = 24cm
Hence, the correct solution is 24cm.
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Calculate the approximate and exact doubling times for annual percentage increases of 5%, 10%, 15%, and 20%.
The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.
Approximate Doubling Time:
5% - 14 Years
10% - 7 Years
15% - 5 Years
20% - 4 Years
Exact Doubling Time:
5% - 14.2 Years
10% - 6.93 Years
15% - 4.77 Years
20% - 3.58 Years
Approximate doubling times are calculated by dividing 72 by the percentage rate of growth. This method assumes a consistent rate of growth, which is not always the case. The exact doubling time can be calculated by using the formula T=ln(2)/ln(1+r) where r is the rate of growth. This formula accounts for the compounding effect of the growth rate, which is not taken into account in the approximate calculation. For example, for a 5% annual growth rate, the approximate doubling time is 14 years, but the exact doubling time is 14.2 years. The exact doubling time calculation provides a more accurate estimate of how long it will take a given value to double.
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how to convert pennies to nickels dimes and pennis c
To convert pennies to nickels, dimes, and quarters, you need to divide the number of pennies by the value of each coin.
The value of a nickel is 5 cents, a dime is 10 cents, and a quarter is 25 cents.
Here's an example of how to convert 100 pennies to nickels, dimes, and quarters:
Nickels: 100 pennies / 5 cents/nickel = 20 nickels
Dimes: 100 pennies / 10 cents/dime = 10 dimes
Quarters: 100 pennies / 25 cents/quarter = 4 quarters
So, 100 pennies can be converted into 20 nickels, 10 dimes, and 4 quarters.
Correct Question :
How to convert pennies to nickels dimes and quarters?
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it is often useful to find the ___ of a polynomial in order to find its roots.
it is often useful to find the Factors of a polynomial in order to find its roots.
The opposite of multiplying, factoring is the process of expressing a polynomial as the product of two or more factors. To factor polynomials, we often combine the following identities or characteristics with various techniques. Ab + Ac = a(b + c) in the statistical distribution.
Because it is derived from the words poly-, which means "many," and -nominal, which in this context means "term," polynomial means "many terms." In mathematics, a polynomial is an expression with variables and coefficients that employs only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
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Please help me with math problem!! Will give brainliest!! :)
The powerline cable diagonal length is 61 feet.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Given:
Hypotenuse = x
Base = 50 feet
Perpendicular = 35 feet
Using Pythagoras theorem
H² = P² + B²
H² = 35² + 50²
H² = 1225 + 2500
H² = 3725
H= 61 feet
Hence, the diagonal length is 61 feet.
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i need help please
ill give 5 stars
The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF
What is a graph ?
Graph can be defined as visual representation of the data through the given ordered pairs .
First, you must find the y-value returned by the line in the graph for a time (x) of five minutes, and then use the deviation of 3º to conclude the range of the real temperature.
1. y- value at x = 5 min.
The trend line (blue line in the graph) passes through the point (5,15), which means that it predicts a temperature of 15ºF when the time (x) is 5 minutes, or five minutes after the freezer was turned on.
2. Actual temperature value
It is stated that the temperature was actually three degrees from what the trend line shows, that means that the actual temperature could be 3ºF more or 3ºF less than the predicted temperature of 15ºF.
Mathematically:
Temperature = 15ºF ± 3ºF
Temperature = 15ºF + 3ºF or 15ºF - 3ºF
Temperature = 18ºF or 12ºF
Therefore, The actual temperature after the freezer was on for five minutes could be 18ºF or 12ºF
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A circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees. What is the length of the arc?
The arc length of the circle will be 0.35 units.
What is the length of the arc of the circle?Using the formula Length of an Arc = r x θ, where is in radians, one can determine the arc length of a circle given its radius and central angle. Arc length is equal to Arc = θ × (π/180) × r, where r is the radius in degrees.
Given that a circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees.
The length of the arc of the circle will be calculated as:-
Arc = θ × (π/180) × r
Arc = 20 x (π/180) × 3
Arc = 0.35 units
Therefore, the arc length of the circle will be 0.35 units.
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The first term of an arithmetic sequence is 6. The common difference of sequence
is two-thirds the first term. Write the next three terms of the sequence.
this arithmetic sequence will be 10, 14, and 18.
What is arithmetic sequence?
There are two approaches to defining an arithmetic sequence. It is a "series where the differences between every two succeeding terms are identical" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The series where the common difference between any two next terms stays constant is known as the arithmetic sequence. Let's go through what a sequence is once again. A collection of numbers that follow a pattern is referred to as a sequence.
The first term of an arithmetic sequence is 6
common difference 2/3.
a2 = a+d = 6+4 =10
a3= a+8 =14
a4=a+12 =18
Hence this arithmetic sequence will be 10, 14, and 18.
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the quantity p(x = 1) is equal to
If the probability distribution of x is known, this probability can be calculated as the probability mass or density at x = 1. If the probability distribution is unknown, then p(x = 1) cannot be determined.
1. The quantity p(x = 1) is equal to the probability of x occurring when x = 1.
This statement is true. It means that the probability of an event x occurring is equal to the probability of x having the value of 1.
2. If the probability distribution of x is known, this probability can be calculated as the probability mass or density at x = 1.
This statement is also true. If the probability distribution of x is known, then the probability of x having the value of 1 can be calculated using the probability mass or density at x = 1.
3. If the probability distribution is unknown, then p(x = 1) cannot be determined.
This statement is also true. If the probability distribution of x is unknown, then the probability of x having the value of 1 cannot be determined.
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An annulus is the region between two concentric circles. The area of the annulus shown in the figure is R² - ².
R
(a) Factor this expression. (Factor your answer completely.)
I
The factor of the expression becomes:
π(R² - r²) = π(R + r) (R - r)
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It is possible to multiply, divide, add, or subtract in math. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, 10m + 5 is an expression including the terms 10m and 5 as well as m, the variable of the supplied expression, all separated by the arithmetic sign "+".
An annulus is the region between two concentric circles. The area of the annulus shown in the figure is πR² - πr²
= πR² - πr²
= π(R² - r²)
(R² - r²) is of the form (a² - b²)
where, a = R and b = r
As we know, (a² - b²) = a² - 2ab + b² = (a + b) (a - b)
so, (R² - r²) = (R + r) (R - r)
The polynomial factored completely is then:
π(R² - r²) = π(R + r) (R - r)
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There are 30 muffins in a tin. 14 of the muffins are iced, of which 6 contain raisins. 4 muffins are neither iced nor contain raisins. a) Draw a Venn diagram that shows the information above. b) Work out the probability that a muffin picked at random contains raisins. Give your answer as a fraction in its simplest form.
The probability that a muffin picked at random contains raisins is 3/5.
What is the probability that a muffin picked at random contains raisins?The probability that a muffin picked at random contains raisins is calculated as follows:
The number of muffins that are not frozen = 30 - 14
The number of muffins that are not frozen = 16
The number of muffins that are not frozen but contain raisins = 16 - 4
The number of muffins that are not frozen but contain raisins = 12
The total number of muffins that contain raisins = 12 + 6
The total number of muffins that contain raisins = 18
The probability that a muffin contains raisins, P(contain raisins) = 18/30
P(contain raisins) = 3/5
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Question 9 of 10
Pr(1+r)
In the monthly payment formula M
for r if the interest rate is 6. 3%?
(1+r) 1 what value would you put
O A. 0. 0063
B. 6. 3
C. 0. 00525
D. 0. 525
Submit
A. 0. 0063 is the correct answer.
What is the interest rate and give explanation?In the formula for monthly payment (M), the interest rate (r) is expressed as a decimal. To convert the interest rate of 6.3% to a decimal, we divide 6.3 by 100:6.3 ÷ 100 = 0.063So the value we would put for (1+r) in the formula would be:1 + 0.063 = 1.063Therefore, the correct answer is:(1+r) = 1.063So, option A (0.0063) is correct, option B (6.3) is incorrect, option C (0.00525) is incorrect, and option D (0.525) is incorrect.To learn more about interest rate refer:
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X=(5)
2((x)+y=10
2(5)+y=10
Given:-
[tex] \rm{x = \bold{ 5 }}[/tex][tex] \: [/tex]
now, put the value in eqⁿ
[tex] \rm{2(x)+y = 10}[/tex][tex] \: [/tex]
[tex] \rm{2(5)+y = 10}[/tex][tex] \: [/tex]
[tex] \rm{10+y = 10}[/tex][tex] \: [/tex]
[tex] \rm{y = 10-10}[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \rm \bold{ \red{y = 0}}}}[/tex][tex] \: [/tex]
hope it helps!:)
if a student scored 92, 76, and 79 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
The student's final grade in three significant digits is 247.
Significant Figures refer to the number of important single digits from 0 to 9 in the coefficient of the expression that conveys the message accurately. These significant figures help engineers or scientists in asserting the quantity of any measurement, length, volume, or mass. For example, 453 has three significant figures.
The two main applications to understand significant figures are - Precision and Accuracy. Let's learn how these two terms play an important role in real-life situations when it comes to the concept of significant figures.
Precision - The closeness between two or more quantities to each other under the same condition is called precision. In precision, the level of measurement when repeated gives the same result and the individual measurement agrees to each other.
Accuracy - The closeness between the measurement and the accurate number is called accuracy. Accuracy helps in providing consistent results with no error along with accuracy in the result.
The final grade of the student would be equal to the sum of the grades obtained in the quizzes, exams, and final.
So, the total grades = 92 + 76+ 79 = 247
Calculating this to three significant digits, we get 247.
Thus, the student's final grade in three significant digits is 247.
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find the length of the given curve: where .
The length of the curve is [5, 3].
A curve is a continuous and smooth function that can be represented in a three-dimensional space. The length of a curve is a measure of the distance between two points on the curve.
The curve r(t) = (-4t, -sin(t), -cos(t)) is a parameterized curve, where t is the parameter that defines the position of a point on the curve.
Here we need to find the length of this curve, we need to calculate the distance between two points on the curve for different values of t.
In order to find the length of the curve, we use the formula for the length of a vector, which is
=> √(x² + y² + z²),
where x, y, and z are the components of the vector.
In this case, the vector is the difference between two points on the curve. The length of the curve is then found by integrating the length of the vector over the interval [5, 3].
Complete Question:
Find the length of the given curve: r(t)=(−4t,−1sint,−1cost)where−5≤t≤3.
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solve the following differential equation. compare to computer solutions and reconcile differences. yy′−2y2 cot x = sin xcos x
ysinx=x ² sinx+c where c is the constant of integration is the value of the differential equation.
Any equation containing one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable)
dy/dx +ycotx=2x+x ² cotx is of the form dy/dx+Py=Q where P=cotx and Q=2x+x ² cotx
The solution is y×I.F=∫Q×I.Fdx+c
⇒ysinx=2∫xsinxdx+∫x² cosxdx
Consider ∫x² cosxdx
Take u=x ² ⇒du=2xdx and dv=cosxdx⇒v=sinx
∫x² cosxdx = x² sinx−2∫xsinxdx
∴ysinx=x ² sinx+c where c is the constant of integration.
Thus, ysinx=x ² sinx+c where c is the constant of integration is the value of the differential equation.
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What are the multiples of 5?
The multiples of 5 are completely divisible by 5. The multiples of 5 are 5, 10, 15, 20, etc.
What is multiple?
Manifold is the fundamental definition of multiple. A multiple in mathematics refers to the outcome of multiplying two numbers together.
The first 5 multiples of 5 are 5, 10, 15, 20, and 25. These can be written as:
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25
5 × 6 = 30
5 × 7 = 35
5 × 8 = 40
5 × 9 = 45
5 × 10 = 50
The number whose unit digit is either 0 or 5 is a multiple of 5.
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Convert each of the following to a common fraction: in a sequence way.
According to the above, the fractions numbers would be: 0.8 = 4/5, 2.34 = 117/50, and 1.25 = 5/4.
How to write decimals as fractions?To convert a decimal to a fraction, we must write the decimal number as a numerator and its place value as the denominator. Also, if there is a number to the left of the decimal point, we leave that number as an integer. According to the above, the fractional numbers would be:
0,8 = 8/10 = 4/52,34 = 234/100 = 117/501,25 = 125/100 = 25/20 = 5/4Those fractions are simplified.
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You decide to launch an internet start-up for a new communication app you created. You find a
venture capitalist who gives you a one time gift of $5,000,000 to start your company.
Unfortunately it turns out you are a horrible businessman and you lose 7% of that start up cash
every quarter. How much of your original money will you have after 8 quarters?
The requried amount of original money will we have after 8 quarters is $2,200,000.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The amount of money we lose every quarter is
= $5,000,000 × 7%
= $350,000.
After 8 quarters, the total amount of money we lose would be
= $350,000 × 8
= $2,800,000.
So, after 8 quarters we would have
= $5,000,000 - $2,800,000
= $2,200,000
Thus, the requried amount of original money will we have with after 8 quarters is $2,200,000.
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