A cone has a height of 15 millimeters and a radius of 15 millimeters. What is its volume?

Mathematics

1 answer:

Alex787 [66]3 years ago

3 0

Answer:

10,597.50 cubic mm

Step-by-step explanation:

V(cone) = [3.14(h)(r²)] ÷ 3

= 3.14(15)(15²) ÷ 3

= 10,597.5

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If 30 percent of a certain number is 240 what is 50 percent the number

Ber [7]

Answer:

400

Step-by-step explanation:

0.30 * x = 240

x = 240/0.30 = 800

0.50 * 800 = 400

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4 years ago

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Suppose that f(5) = 1, f '(5) = 4, g(5) = −9, and g'(5) = 5. Find the following values.

stiv31 [10]

$\bf \begin{cases}
f(5)=1\qquad &f'(5)=4
\\\\
g(5)=-9\qquad &g'(x)=5
\end{cases}
\\\\

\begin{cases}
(f\cdot g)'(5)\impliedby \textit{product rule}
\\\\
\left( \frac{f}{g} \right)'(5)\impliedby \textit{quotient rule}
\end{cases}\\\\
-----------------------------\\\\
(f\cdot g)'(5)\implies f(x)\cdot g(x)\implies 
\begin{array}{llll}
f'(x)g(x)+f(x)g'(x)\\\\
x=5\\\\\
[4\cdot -9]+[1\cdot 5]
\end{array}
\\\\
-----------------------------\\\\
$

$\bf \left( \frac{f}{g} \right)'(5)\implies 
\begin{array}{llll}
\cfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\\\\
x=5\\\\
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3 years ago

Help me please, match the number to the letter

kenny6666 [7]

Answer: 1b 2c 3e? 4d 5a

<u>Step-by-step explanation:</u>

There are 2 items that need to be checked.

The midpoint of the coordinates is the center of the circle
The diameter of the coordinates is the diameter of the circle.

Midpoint:

$Midpoint = \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\1)\ \bigg(\dfrac{-4+2}{2},\dfrac{-1+10}{2}\bigg)=\bigg(\dfrac{-2}{2},\dfrac{9}{2}\bigg)=(-1, 4.5)\implies \text{equation b}\\\\\\2)\ \bigg(\dfrac{1+7}{2},\dfrac{3-10}{2}\bigg)=\bigg(\dfrac{8}{2},\dfrac{-7}{2}\bigg)=(4, -3.5)\implies \text{equation c}\\\\\\3)\ \bigg(\dfrac{4-8}{2},\dfrac{-2+6}{2}\bigg)=\bigg(\dfrac{-4}{2},\dfrac{4}{2}\bigg)=(-2,2 )\implies \text{none of the equations}$

$4)\ \bigg(\dfrac{6-4}{2},\dfrac{3-13}{2}\bigg)=\bigg(\dfrac{2}{2},\dfrac{-10}{2}\bigg)=(1, -5)\implies \text{equation d}\\\\\\5)\ \bigg(\dfrac{7-1}{2},\dfrac{5+8}{2}\bigg)=\bigg(\dfrac{6}{2},\dfrac{13}{2}\bigg)=(3, 6.5)\implies \text{equation a}$

Diameter:

distance between coordinates = 2√r² (from circle equation)

$\text{formula for coordinates is: }d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\1)\ \text{Coordinates: } d=\sqrt{(-4-2)^2+(-1-10)^2}=\sqrt{36+121}=12.5\\b)\ \text{Circle: }2\sqrt{39.25}=12.5\\\\\\2)\ \text{Coordinates: } d=\sqrt{(1-7)^2+(3+10)^2}=\sqrt{36+169}=14.3\\c)\ \text{Circle: }2\sqrt{51.25}=14.3\\\\\\4)\ \text{Coordinates: } d=\sqrt{(6+4)^2+(3+13)^2}=\sqrt{100+256}=18.9\\d)\ \text{Circle: }2\sqrt{89}=18.9$