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Oduvanchick [21]

2 years ago

10

Jane has a gift card with a balance of $100 She buys several t-shirts that cost $15 each After the purchases her gift card balan

ce is $10 Write an equation to help find out how many t-shirts Jane bought.

1 answer:

Arte-miy333 [17]2 years ago

3 0

The answer is 15n+10=100

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2. A sphere has surface area 16π. Find the radius of the sphere.

KiRa [710]

Answer:

The answer to your question is: 2.29 units

Step-by-step explanation:

Data

Volume = 16π

radius = ?

Formula

V = $\frac{4}{3}π r^{3}$

Process

16 π = $\frac{4}{3}π r^{3}$

$\frac{16(3)}{4} = r^{3}$

r³ = 12

r = 2.29

7 0

2 years ago

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2 years ago

What is the next figure in the pattern?

butalik [34]

Answer:

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Step-by-step explanation:

8 0

3 years ago

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A rectangular park has a width of 8/9 of a mile and a length 3/5 of a mile. Find the

Nesterboy [21]

Answer:0.53 miles

Step-by-step explanation:

4 0

3 years ago

A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

6 0

2 years ago