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3 years ago

Calculate the volume of a prism with:

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

3 0

The answer is C hope it helps

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A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius Each o th

zysi [14]

A regular polygon is drawn in a circle so that each vertex is on the circle

Each of the central angles has a measure of 40

360 / 40 = 9

so the polygon has 9 sides

Answer is the second option

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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

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

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3 years ago

A right rectangular prism has a volume of 6x3 - 3x2 - 45x.

USPshnik [31]

Answer:

Step-by-step explanation:

6x^3 - 3x^2 - 45x = 3x(2x^2-x-15) = 3x((2x+5)(x-3)

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3 years ago

Sam made 6 identical necklaces, each having beads and a pendant. the total cost of the beads and pendants for all 6 necklaces wa

Marizza181 [45]

Since six necklaces all together costs 31.80 to make, I divided 31.80 by 6 and got 5.3. That means that to make one necklace, they'd spend $5.30. The beads alone for 1 necklace cost $2.70, so I subtracted that from the $5.30.

Answer: Each pendant costs $2.60

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3 years ago

HELP PLEASE!! Victoria and Jennifer walk at a different averagr speed. Victoris walks at an average speed of 1 1/5 miles in 1/2

Zanzabum

Answer:

Jennifer

4/15 mph

Step-by-step explanation:

First, we find the two speeds in miles per hour.

Victoria:

1 1/5 mile per 1/2 hour = (1 1/5 mile)/(1/2 hour) = 2 2/5 mph = 2.4 mph

Jennifer:

2/3 mile per 1/4 hour = (2/3 mile)/(1/4 hour) = 8/3 mph = 2 2/3 mph

2 2/3 mph > 2 2/5 mph, so Jennifer's speed is greater.

The difference in speeds in mph is:

2 2/3 - 2 2/5 = 2 10/15 - 2 6/15 = 4/15

5 0

2 years ago

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