Thank you for answering this question.

Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

3 years ago

What is the slope-intercept form of this equation?

kirill [66]

Answer:

y = -8x + 12

Step-by-step explanation:

Slope intercept form: y = mx + b

m ---> Slope & b ----> y-intercept

8x + y = 12

Subtract 8x from both sides

y = -8x + 12

5 0

3 years ago

Graph the line by plotting any two ordered pairs that satisfy the equation.

ollegr [7]

Answer:

(0,-4)

(3,0)

Step-by-step explanation:

Let start at the orgin.

This is a linear equation since the equation is in the form of

$y = mx + b$

where m is the slope and b is the y intercept.

Since we starting at the orgin, and b is our y intercept.

Our first point is

(0,-4).

since the slope is 4/3.

We would rise 4 from the y value and run 3 to the x value.

In other words, to find your second point, go up 4 units from the first point and move to the right 3 units.

So our next point is at

(3,0).

U can continously go up 4 units and move 3 units to the right to find other points.

6 0

3 years ago

A sprinkler is set to water the section of lawn represented by the shaded region in the circle below

Juli2301 [7.4K]

Answer:

We taking the same final exam

Step-by-step explanation:

I don’t know the answer that’s why I came here

6 0

2 years ago

Question partpointssubmissions usedverify that the divergence theorem is true for the vector field f on the region

maxonik [38]

$\nabla\cdot\mathbf f(x,y,z)=\dfrac{\partial(3x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(5xz)}{\partial z}=3+x+5x=3+6x$

By the divergence theorem, the flux across the boundary of the given region $\mathcal E$ is

$\displaystyle\iint_{\partial\mathcal E}\mathbf f(x,y,z)\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$
$=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(3+6x)\,\mathrm dx\,\mathrm dy\,\mathrm dz=72$

4 0

3 years ago