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3 years ago

Using point-slope form, write an equation of the line that passes through (2,-1) and has a slope of -5

Mathematics

1 answer:

expeople1 [14]3 years ago

5 0

Y – y1 = m(x – x1)

y-(-1)=-5(x-2)

Y+1=-5(x-2)

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Central Middle School sold 50 tickets for one night of the school play. Student tickets sold for $2 each and adult tickets sold

Andru [333]

35 $3 tickets and 15 $2 tickets

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2 years ago

The base of a solid is the region in the first quadrant bounded above by the line y = 5, below by y = sin−1(x), and to the right

Arturiano [62]

Each cross section is a square with side length equal to the vertical distance between the curves $y=5$ and $y=\sin^{-1}x$ , with $0\le x\le1$ , or $5-\sin^{-1}x$ . Then each section has an area of $(5-\sin^{-1}x)^2$ , so the volume of this solid is

$\displaystyle\int_0^1(5-\sin^{-1}x)^2\,\mathrm dx=\boxed{33-5\pi+\frac{\pi^2}4}$

For computing the integral, consider the substitution

$u=5-\sin^{-1}x\implies x=\sin(5-u)\implies\mathrm dx=-\cos(5-u)\,\mathrm du$

Then the integral becomes

$\displaystyle\int_5^{5-\pi/2}u^2(-\cos(5-u))\,\mathrm du$

$=\displaystyle\int_{5-\pi/2}^5u^2\cos(u-5)\,\mathrm du$

Integrate by parts twice; for the first round, take

$f=u^2\implies\mathrm df=2u\,\mathrm du$

$\mathrm dg=\cos(u-5)\,\mathrm du\implies g=\sin(u-5)$

$\implies\displaystyle u^2\sin(u-5)\bigg|_{5-\pi/2}^5-2\int_{5-\pi/2}^5u\sin(u-5)\,\mathrm du$

For the second round, take

$f=u\implies\mathrm df=\mathrm du$

$\mathrm dg=-\sin(u-5)\,\mathrm du\implies g=\cos(u-5)$

$\implies\displaystyle\bigg(u^2\sin(u-5)+u\cos(u-5)\bigg)\bigg|_{5-\pi/2}^5-\int_{5-\pi/2}^5\cos(u-5)\,\mathrm du$

and the rest is trivial.

8 0

3 years ago

The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:

Lera25 [3.4K]

Pick any two points on the line and find the slope.

I chose the points (0,35) and (1,105).

The speed of the motorboat is 70 miles per hour.
Hope this helps!!!!

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3 years ago

Read 2 more answers

I need help (3/4)x+2=(3/8)x-4

bezimeni [28]

Answer:

x = -16

Step-by-step explantion:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

(・∀・(・∀・(・∀・*)

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2 years ago

A tissue box shaped like a rectangular prism. The box is 2.3 feet wide, 4 feet long and 6 feet tall. what is the volume of the t

Taya2010 [7]

Multiply 2.3 x 4 x 6 and u shall get yer answer.

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3 years ago