Write the point-slope form for a line that passes through (2,7) and has a slope of 1/2

Mathematics

1 answer:

maks197457 [2]3 years ago

6 0

Answer: y - 7 = 1/2 ( x - 2 )

I hope you got a good grade on your assignment!! ^w^

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A hemisphere has an area of 256 pi cm^2. What is its volume?

Amanda [17]

$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
\\\\\\
\textit{a hemisphere is half that}\\\\
A=\cfrac{4\pi r^2}{2}\implies A=2\pi r^2
\end{array}\qquad r=radius
\\\\\\
\textit{now, we know the area is }256\pi \implies 256\pi =2\pi r^2
\\\\\\
\cfrac{256\pi }{2\pi }=r^2\implies \sqrt{128}=r\implies \boxed{8\sqrt{2}=r}
\\\\
-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad r=radius
\\\\\\
\textit{a hemisphere is half that}\\\\
V=\cfrac{\frac{4}{3}\pi r^3}{2}\implies V=\cfrac{\frac{4\pi r^3}{3}}{\frac{2}{1}}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}
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V=\cfrac{2\pi r^3}{3}
\\\\\\
\textit{now, we know the radius is }8\sqrt{2}\implies V=\cfrac{2\pi (8\sqrt{2})^3}{3}
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V=\cfrac{2\pi (8^3\sqrt{2^3})}{3}\implies V=\cfrac{2\pi \cdot 512\cdot 2\sqrt{2}}{3}
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Answer: rational

Step-by-step explanation:

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Multiply: (3x + 2)(4x - 7)

svetoff [14.1K]

When you are doing distribution with this problem you are going to get your answer of....
D) 12x^2 - 13x - 14

Steps:
Simplify...
<span>(3x + 2)(4x - 7)
= (3x + 2) (4x + -7)
= (3x)(4x) + (3x)(-7) + (2)(4x) + (2)(-7)

= 12x^2 - 21x + 8x - 14
=12x^2 - 13x -14</span>

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4 years ago