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3 years ago

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A dog is leashed to a point in the center of a large yard, so the area the dog is able of to explore is circular. The leash is 2

0 feet long (radius). What is the area of the region the dog is able to explore?

1 answer:

e-lub [12.9K]3 years ago

4 0

The formula for area is A=pi r^2 so you plug it in A=pi 20^2 = 1256.63 yd^2

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Step-by-step explanation:

x could be any value and make this equation true

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The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as

NISA [10]

$\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{W varies jointly as its width, squared heght and inversely with length}}{W=\cfrac{wh^2}{L}}$

$\bf \textit{now we also know that }~~ \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{3}\\ L=12\\ W=30 \end{cases}\implies 30=\cfrac{~~k\frac{1}{4}\left( \frac{1}{3} \right)^2~~}{12} \\\\\\ 360=\cfrac{k}{36}\implies 12960=k~\hfill \boxed{W=\cfrac{12960wh^2}{L}}$

$\bf \textit{when } \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{2}\\ L=12 \end{cases}\textit{ what is \underline{W}?}\qquad W=\cfrac{12960\left( \frac{1}{4} \right)\left(\frac{1}{2} \right)^2}{12} \\\\\\ W=1080\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies W=1080\cdot \cfrac{1}{16}\implies W=\cfrac{135}{2}\implies W=67\frac{1}{2}$

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4 years ago

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When 48 is factored, it factors to 4²×3. When you take the square root of that, you get 4√3.

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3 years ago

A sphere has a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the

faust18 [17]

Start with the given formula for the surface area of a sphere.

$S = 4 \pi r^2$

Now substitute 2x + 5 in for r, the radius.
Then simplify the expression and write it in standard form.

$S = 4 \pi (2x + 5)^2$

$S = 4 \pi (4x^2 + 20x + 25)$

$S = 16 \pi x^2 + 80 \pi x + 100 \pi$

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3 years ago

Jane Smith took out a loan for $40,000 to pay for her child's education. The loan would be repaid at the end of eight years in o

EleoNora [17]

Answer:

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Step-by-step explanation:

In order to solve this question we have to use the compound interest formula

A = P*(1+i)ˆn

A: final amount including principal

P: principal amount

i: interest per year

n: total number of years

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3 years ago