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3 years ago

Please help!!! will give brainliest find the value of x

Mathematics

1 answer:

kotykmax [81]3 years ago

6 0

Answer:

quick fyi! i dont recommend clicking on links there probably fake.

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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

3 years ago

If I have an equation in which x = pounds, and y = total cost, can I substitute quarts into the equation

Colt1911 [192]

Answer:

Yes, you can

Step-by-step explanation:

As a point of reference, assume the equation is:

$y = 5x$

Where

$y = total\ cost$

and

$x = pounds$

In standard unit of conversion:

$1\ pound = 0.4793\ quart$

So:

$x\ pounds = 0.4793x\ quart$

Substitute 0.4793x for x in $y = 5x$

$y = 5 * 0.4793x$

$y = 2.3965x$

The above equation is the equivalent of $y = 5x$ in quarts

<em>So, irrespective of what the equation is, you can always substitute quarts into the equation.</em>

8 0

3 years ago

MARKING BRAINLIEST!

Irina-Kira [14]

Answer: Felix has a job that pays 100 dollars an hour, If he makes 2500 dollars a week how many hours does he work each day.

100x = 2500

hope this helps mark me brainliest please

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Find the GCF of 42 and 63

Elanso [62]

Answer:

Step-by-step explanation:

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