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Veseljchak [2.6K]

3 years ago

9

Michelle wishes to build a square pool in her backyard. She has saved enough to build a pool with the area of 150 square feet. W

hat is the length of each side of her pool? (Recall that the area of a square is 2003-04-01-00-00_files/i0200000.jpg, where l is the length of a single side).

1 answer:

frozen [14]3 years ago

7 0

When it comes to finding the area of spaces, you must determine its shape. In this case, the shape of the pool is a square. From there, we will use the formula to find the area of a square.

Area = (side)^2

Since the square of the square's side is its total area, then if vice versa, we have to find the square root of the area to find the length. Thus,

Length = √150 = 5√6 = 12.25 ft

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Draw a line tangent to the circle at the point (0, 4). Write an equation for this tangent line. Explain your work.PLEASE HELP

kirill [66]

Answer:

y = 1/4x + 4

Step-by-step explanation:

5 0

2 years ago

Ray Cupple bought a basic car costing $26,500.00, with options costing $725.00. There is a 6% sales tax in his state and a combi

Alenkinab [10]

Given:
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option:    <u>     725</u>
total    27,225
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5 0

3 years ago

Read 2 more answers

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

Combine Like Terms: 9a + 6(10a+1) <br> 69a+1 <br> 75a <br> 30a+3<br> 69a+6

Oliga [24]

Answer:

69a+6

Step-by-step explanation:

Distribute the 6 over the (10a+1) then you get 60a+6. Add the 9a to the 60 giving u 69a then you have the 6 left over making the answer 69a+6

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2 years ago

Mary read a book that had 4200 pages last summer. If it took her 35 days to finish the book. How many pages did she read per day

kari74 [83]

120 Pages.....................

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3 years ago