The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their volumes.

1 answer:

7 0

The ratio of the radii is 2:1, so the ratio of their surface areas is 4:1. The area of a sphere is defined by 4 * pi * r^2 

So if the radius of the first sphere is 2r, then it would be (2r)^2 = 4r^2 

The rest is the same. So the ratio of their surface areas would be 

4 * pi * 4r^2 divided by 
4 * pi * r^2 

or 4.

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Lola ride her bike for 7/10 of an hour on saturday and 3/5 of an hour on sunday. how much longer did she ride her bike on saturd

OverLord2011 [107]

3/5=6/10
7/10-6/10=1/10
1/10 or 6 minutes longer

6 0

4 years ago

Given the position of the particle, what the position(s) of the particle when it’s at rest

choli [55]

The position function of a particle is given by:

$X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t$

The velocity function is the derivative of the position:

$\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}$

The particle will be at rest when the velocity is 0, thus we solve the equation:

$2t^2-9t-18=0$

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

$t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Substituting:

$\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}$

We have two possible answers: