What is the slope of the line? -2 1/2 1 2

Given the function below, what value will result in f(x)=10? f(x)=1/2x+8

nignag [31]

10 = 1/2x + 8
2 = 1/2x
X = 4

5 0

3 years ago

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The area of a rectangular front yard is, 180 square feet find the length of the front yard if the width is 15 feet

VMariaS [17]

Area = length x width
180 = L x 15
L = 180/15
Length = 12 feet

6 0

2 years ago

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1.The plate, including the bound

rjkz [21]

Answer:

We have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . and the hottest value is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

Step-by-step explanation:

We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.

The temperature equation is:

$T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x$

Let's take the partials derivatives.

$T_{x}(x,y)=2x-\frac{3}{2}=0$

$T_{y}(x,y)=4y=0$

So, we can find the critical point (x,y) of T(x,y).

$2x-\frac{3}{2}=0$

$x=\frac{3}{4}$

$4y=0$

$y=0$

The critical point is (3/4,0) so the temperature at this point is: $T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})$

$T(\frac{3}{4},0)=-\frac{9}{16}$

Now, we need to evaluate the boundary condition.

$x^{2}+y^{2}=1$

We can solve this equation for y and evaluate this value in the temperature.

$y=\pm \sqrt{1-x^{2}}$

$T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x$

$T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2$

Now, let's find the critical point again, as we did above.

$T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0$

$x=-\frac{3}{4}$

Evaluating T(x,y) at this point, we have:

$T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2$

$T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$

Now, we can see that at point (3/4,0) we have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . On the other hand, at the point $-(3/4),\frac{\sqrt{7}}{4})$ we have the hottest value of temperature, it is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

I hope it helps you!

4 0

2 years ago

Find the value of the expression. (6.885−0.365)÷2+1.44.

EleoNora [17]

Answer:

4.7

Step-by-step explanation: I bet your family tree is a cactus because everyone on it is a pain/your like the first slice of bread everyone touches you but nobody wants you

4 0

3 years ago

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What is the simplified form of the following expression? 4/7^3

timofeeve [1]

If your question is :
$\frac{4}{7^3}$

Then the answer is:
$\frac{4}{7*7*7} = \frac{4}{343}$

If your question is:
$(\frac{4}{7}) ^{3}$

Then the answer is:
$\frac{4*4*4}{7*7*7} = \frac{64}{343}$

6 0

3 years ago

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What is the slope of the line?-21/212