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3 years ago

Compare the process of solving |x - 1 + 1 < 15 to that of solving 1x – 1| + 1 > 15.

Mathematics

1 answer:

Luden [163]3 years ago

8 0

Answer:

x-1+1<15; this gonna be x<15 and 1x-1+1>15 this is gonna be the same

Step-by-step explanation:

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Pls answer this with an explanation if you can

Sloan [31]

Answer:

300%

Step-by-step explanation:

$2.25 divided by $0.75 = 3 (new price divided by old price)

This means the price has gone up by 300% as $0.75= 100%

(I’m not sure I explained this very clearly, if you want me to rewrite it just say!)

6 0

3 years ago

Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

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

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

3 0

3 years ago

EASY MATH THAT I DON,T GET PLZ HELP QUICKLY<br>

jolli1 [7]

Answer:

Terms: 4

Degree: 3

Leading coeff: 7

Step-by-step explanation:

a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by division. 7x³+5x²-3x+1 would have 4 terms: 7x³, 5x², -3x, and 1

You already have the degree which is the highest power in a polynomial

The leading coefficent is the coefficient in the term with the highest power, in this case being 7.

hope this helps!

6 0

3 years ago

What is the surface area of the figure? Use 3.14 for π....PLEASE HELP....NEED HELP ASAP

raketka [301]

Answer:

Step-by-step explanation:

Always use your imaginary scissor:

Cut the above and below circle and the cylinder role it down-ways like a carpet and you will end up with two circles and a big rectangular.

Surface circle: 7 * 7 * 3,14 = 153.86

Surface carpet: 20 * circle exterior (or the length of the circle)= 20 * 2* 3.14 * 7

Results:

153, 86 * 2 (because we cut 2 circles from the cylinder) + 132,6 = 439.6

Answer: A

3 0

3 years ago

Read 2 more answers

Find the volume of the sphere. express your answer in term of Pie

IceJOKER [234]

Answer:

$\large\boxed{36\pi}$

Step-by-step explanation:

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

R - radius

We have R = 3 ?. Substitute

$V=\dfrac{4}{3}\pi(3^3)=\dfrac{4}{3}\pi(27)=(4)\pi(9)=36\pi$

If the radius is 30, then the volume is:

$V=\dfrac{4}{3}\pi(30^3)=\dfrac{4}{3}\pi(27,000)=(4)\pi(9,000)=36,000\pi$

If 30 is the length of diameter, then the radius R = 30 : 2 = 15.

Therefore the volume:

$V=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3,375)=(4)\pi(1,125)=4,500\pi$

3 0

3 years ago