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3 years ago

Allen runs 8 miles in 3 hours at a steady pace. How long does it take him to run 3 miles?

1 answer:

8 0

We know that she runs 8 miles in 3 hours and we have to find how much time it takes to run 3 miles.
Let time be x and now lets put in the numeric form.
$\frac{8}{3}$ = $\frac{3}{x}$
now cross multiplying each other so we get
8 * x = 3 * 3
8x = 9 { dividing both sides by 8 }
x = 9/8
or
x = 1.125 hrs.

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a

Elodia [21]

We have been given that a sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. We are asked to find the volume of the sphere.

We know that height of sphere is equal to its radius. This means that $r=h$ .

$\text{Volume of sphere}=\frac{4}{3}\pi r^3$

$\text{Volume of cylinder}=\pi r^2 h$

Using $r=h$ , we will get:

$\text{Volume of cylinder}=\pi r^2\cdot r$

$\text{Volume of cylinder}=\pi r^3$

Upon comparing volume of sphere and volume of cylinder, we can see that volume of sphere is $\frac{4}{3}$ times volume of cylinder.

$\pi r^3=21$

$\frac{4}{3}\pi r^3=\frac{4}{3}\cdot 21$

$\frac{4}{3}\pi r^3=4\cdot 7$

$\frac{4}{3}\pi r^3=28$

Therefore, the volume of the sphere would be 28 cubic meters.

4 0

3 years ago

Read 2 more answers

Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and c= 81,000 km. Assume the cen

elena-14-01-66 [18.8K]

Answer:

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$

Step-by-step explanation:

the transverse axis is horizontal.

so its a horizontal hyperbola

Center is the origin so center is (0,0)

Equation of horizontal hyperbola is

$\frac{x^2}{a^2} - \frac{y^2}{b^2} =1$

Given a= 55000 and c= 81000

c^2 = a^2 + b^2

81000^2 = 55000^2 + b^2

subtract 55000^2 on both sides

b = sqrt(81000^2 - 55000^2)= 59464.27

now plug in the values

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$

7 0

3 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$