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3 years ago

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

Mathematics

1 answer:

uranmaximum [27]3 years ago

4 0

Answer:

volume of sphere = 113.14inches³ or

36πinces³

Step-by-step explanation:

given the radius of a sphere = 3inches

volume of the sphere = ?

π = 3.14v 0r 22/7

recall, the formula for finding the volume of a sphere is given to be = 4/3 πr³

so,

volume of sphere = 4/3 πr³

volume of sphere = 4/3 × 22/7 × ( 3)³

volume of sphere = 4/3 × 22/7 × 27

volume of sphere = (4 × 22 × 9)/7

volume of sphere = 113.14inches³ or 36πinces³

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Which of the following functions has the steepest slope?

Nonamiya [84]

The one with the steepest slope would be the equation that will have the highest value of m regardless of the sign. From the choices, I believe the correct answer is option C. It is <span>y=-4x+1 that has the steepest slope where m is equal to -4, the negative would indicate the direction of the slope.</span>

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3 years ago

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

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3 years ago

What are the coordinates of the midpoint of the segment whose endpoints are (-4,6) and (-8,-2)

umka2103 [35]

The formula to find the midpoint of a segment is ((x1 + x2)/2,),(y1 + y2)/2).

The x coordinate of the first point is -4, and the x coordinate of the second point is -8. The y coordinate of the first point is 6, and the y coordinate of the second point is -2. Now, we can plug these into our formula.

((-4 + (-8))/2), (6 + (-2))/2)) = (-12/2), (4/2) = (-6, 2)

So, (-6, 2) is the midpoint of the segment.

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3 years ago

Solve by elimination <br> 5x-y=12 <br> 3x+2y=2

Ber [7]

(2)5x-y=12
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3 years ago

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Simplify (2*4)−1.

EastWind [94]

The simplification form of the number expression (2⁴)⁻¹ is 1/2⁴ option (B) one over two raised to the fourth power is correct.

<h3>What is an integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

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Thus, the simplification form of the number expression (2⁴)⁻¹ is 1/2⁴ option (B) one over two raised to the fourth power is correct.

Learn more about the integer exponent here:

brainly.com/question/4533599

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