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Fynjy0 [20]
3 years ago
8

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

Mathematics
1 answer:
nydimaria [60]3 years ago
5 0

Volume of the cone = (1/3) pi r^2 h

h = 2r  so substituting for h:-

V = (1/3) pi r^2 * 2r

V = (2/3) pi r^3

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Abigail has $30.00 to buy groceries. She needs to buy some apples, some bananas, and 3 pounds of potatoes. Fuji apples are $1.79
maks197457 [2]

Answer:

30.00 – (1.79a + 0.36b + 2.99)

Step-by-step explanation:

you need to rest the amount of money pay.

6 0
3 years ago
How do you find a vector that is orthogonal to 5i + 12j ?
Rashid [163]
\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies  -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\

\bf \boxed{5i+12j}\implies 
\begin{array}{rllll}
\ \textless \ 5&,&12\ \textgreater \ \\
x&&y
\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}
\\\\\\
slope=\cfrac{12}{{{ 5}}}\qquad negative\implies  -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}
\\\\\\
\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}&#10;\\\\\\&#10;\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}&#10;\\\\\\&#10;\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}
4 0
4 years ago
Evaluate : f(x) = x^2 - 2x + 1 , x = 3
den301095 [7]

Answer:

4

Step-by-step explanation:

3^2=9

-2 times 3 = -6

9-6+1=4

8 0
3 years ago
15 POINTS
pochemuha
A shape with rotational symmetry means it looks the same after a rotation. The image at number 3 is the only one that has rotational symmetry so answer yes for 3 and no for 1 and 2 okay 
7 0
4 years ago
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How many cups are in 7 3/4 gallons?
Schach [20]

Answer:

124 us cups

Explanation:

6 0
3 years ago
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