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3 years ago

Julio is putting a rectangular pool in his backyard. The length of

Mathematics

1 answer:

IrinaVladis [17]3 years ago

8 0

Answer: 17

Step-by-step explanation: Luckly, this question is multiple choice meaning that we could try all the solutions going backwords. We will start from 10. Since the length is 7 feet more than the width, we will do 10 - 7 to find the width. That gives you 3 and perimiter means we have to add up all the sides. 3 + 10 + 3 + 10 = 26 and 54 does not equal 54. Now we will do 17. 17 - 7 gives you 10. So, 17 + 10 + 17 + 10 = 54. 54 = 54 so your answer will be 17.

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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

4 years ago

Which statement can you use to conclude that RSTW is a parallelogram

Romashka [77]

It is answer choice a

3 0

3 years ago

Find the measure of this angle in degrees.

Fantom [35]

Answer:

10 degrees

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

In triangle ABC, point D is the centroid, and BD = 6. Find BE.

pshichka [43]

Given:

In triangle ABC, point D is the centroid, and BD = 6.

To find:

The measure of side BE.

Solution:

We know that the centroid divides each median in 2:1.

In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.

Let BD and DE are 2x and x respectively.

We have, BD = 6 units.

$2x=6$

$x=\dfrac{6}{2}$

$x=3$

Now,

$BE=BD+DE$

$BE=6+x$

$BE=6+3$

$BE=9$

Therefore, the measure of side BE is 9 units.

6 0

3 years ago

If the graph is reflected across the y-axis, what will be the equation of the new graph?

Bumek [7]

Answer:

$\displaystyle b)y = { 3}^{ - x} + 1$

Step-by-step explanation:

we are given a exponential function

$\displaystyle y = {3}^{x} + 1$

we want to figure out the equation of the new graph reflected across the y-axis

remember that,

$\rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x,y)$

let y be $3^x+1$ so,

$\rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x, {3}^{ - x} + 1 )$

hence,

the equation of the new graph

$\displaystyle y = { 3}^{ - x} + 1$

5 0

3 years ago

Read 2 more answers