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3 years ago

What is the slope of a line that is parallel to the line y = 3/4x + 2?

Mathematics

1 answer:

alexandr402 [8]3 years ago

5 0

3/4
when it’s parallel it has the same slope!

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zepelin [54]

Answer: A/The LINE graph

Step-by-step explanation:

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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

Y = -4/3x − 1<br> y = 1/3x + 4

Tom [10]

Answer:

x = -3, y =3

Step-by-step explanation:

y = -4/3x - 1

y = 1/3x + 4 -------> 4y = 4/3x + 16

Adding the first equation and the new second equation together:

5y = 15 ------> y = 3

Plug y = 3 into one of the original equations:

3 = 1/3x + 4

-1 = 1/3x

x = -3

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3 years ago

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butalik [34]

Answer: 1,341 3/4

Step-by-step explanation:

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3 years ago

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How many of each type of box is it carrying?

CaHeK987 [17]

Answer:

Number of large boxes: 55

Number of small boxes:65

Step-by-step explanation:

Let be "l" the number of large boxes and "s" the number of small boxes.

Set up a system of equations:

$\left \{ {{l+s=120} \atop {60l+30s=5250}} \right.$

Use the methof of elimination. Mulitply the first equation by -60 and add both equations. Then solve for "s":

$\left \{ {{-60l-60s=-7200} \atop {60l+30s=5250}} \right.\\.........................\\-30s=-1950\\s=65$

Substitute s=65 into any of the original equations and solve for "l":

$l+65=120\\l=55$

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3 years ago

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