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marusya05 [52]
3 years ago
15

The function A = 15x - x2, where x is the width in yards, gives the area A of a llama pen in square yards. Make a table using 1/

2 units from 0 to 10. Graph the function. Use your graph to answer the following question:
Which width gives the greatest area?
Which width gives the greatest area?
a.
6 yd
c.
8.5 yd
b.
7.5 yd
d.
10 yd
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
6 0

Answer:

The width which gives the greatest area is 7.5 yd

Step-by-step explanation:

This is an application of differential calculus. Given the area as a function of the width, we simply need to differentiate the function with respect to x and equate to zero which yields; 15-2x=0 since the slope of the graph is zero at the turning points. Solving for x yields, x=7.5 which indeed maximizes the area of the pen

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A value of two standard deviation from the mean is more likely to occur than a value three standard deviations from the mean
Anvisha [2.4K]

This is true. The closer to the mean that a value is, the more likely it is to occur.

In this case, two and three standard deviations away are both fairly unlikely, however, two is still more likely to occur than three.

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3 years ago
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What is the solution of the system? Use elimination.
sweet [91]

Answer:

The solutions to the system of the equations by the elimination method will be:

x=2,\:z=-1,\:y=2

Step-by-step explanation:

Given the system of the equations

2x\:+\:2y\:+z\:=\:7

-x-\:y\:+z\:=\:-5

x+3y-4z=12

solving the system of the equations by the elimination method

\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}

\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10

\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}

-2x-2y+2z=-10

+

\underline{2x+2y+z=7}

3z=-3

\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}

2x+6y-8z=24

-

\underline{2x+2y+z=7}

4y-9z=17

\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}

Rearranging the equations

\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}

solve 3z=-3 for z:

z=-1

\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1

solve  4y-9\left(-1\right)=17 for y:

4y-9\left(-1\right)=17

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y=2

\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2

solve 2x+2\cdot \:2-1=7 for x:

2x+2\cdot \:2-1=7

2x+3=7

2x=4

x=2

Therefore, the solutions to the system of the equations by the elimination method will be:

x=2,\:z=-1,\:y=2

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