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3 years ago

Describe, step by step, how we can map the field of a variable quantity

1 answer:

7 0

A variable quantity is a quantity that can assume any of a set of values, if you want to map them, you would have to determine the current value of the set.

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1. Slavery and serfdom were abolished in the 1860s in

Yanka [14]

B. I got the answer off of quizlet lol it helps a lot.

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3 years ago

AP CALC QUESTION!! WILL MARK BRAINLIEST (TWO QUESTIONS)

kodGreya [7K]

1. Using washers, the volume is given by the integral

$\displaystyle\pi\int_1^{e^2}((2+2)^2-(\ln x+2)^2)\,\mathrm dx$

$=\boxed{\displaystyle\pi\int_1^{e^2}(20+4\ln x-(\ln x)^2)\,\mathrm dx}$

We're using washers whose centers depend on the value of $x$ , hence we integrate with respect to

2. The area of the given region is given by the integral

$\displaystyle\int_0^2\sin^{-1}\frac x2\,\mathrm dx$

To compute the integral, first consider the substitution $u=\frac x2$ , or $2u=x$ so that $2\,\mathrm du=\mathrm dx$ . Then $x\to0\implies u\to0$ and $x\to2\implies u\to1$ , so the integral is equivalently

$\displaystyle2\int_0^1\sin^{-1}u\,\mathrm du$

Integrate by parts, taking

$f=\sin^{-1}u\implies\mathrm df=\dfrac{\mathrm du}{\sqrt{1-u^2}}$

$\mathrm dg=\mathrm du\implies g=u$

so that

$\displaystyle2\int_0^1\sin^{-1}u\,\mathrm du=2\left(u\sin^{-1}u\bigg|_0^1-\int_0^1\frac u{\sqrt{1-u^2}}\,\mathrm du\right)$

$\sin^{-1}0=0$ and $\sin^{-1}1=\frac\pi2$ , so the area is

$\displaystyle\pi-2\int_0^1\frac u{\sqrt{1-u^2}}\,\mathrm du$

For the remaining integral, substitute $w=1-u^2$ , so that $\mathrm dw=-2u\,\mathrm du$ . Then $u\to0\implies w\to1$ and $u\to1\implies w\to0$ :

$\displaystyle\pi-\int_0^1\frac{\mathrm dw}{\sqrt w}$

(notice that the integral is improper)

$\displaystyle\pi-\lim_{t\to0^+}2\sqrt w\bigg|_t^1$

$\displaystyle\pi-2\left(1-\lim_{t\to0^+}\sqrt t\right)=\boxed{\pi-2}$

8 0

3 years ago

Sino ang Unang Triyanggulo na nagtatag ng KKK? Please answer po

Kryger [21]

S hey there, hope you’re doing great. Can you please translate this into English unfortunately I do not understand what you were trying to say. No hate towards you happy Thanksgiving

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3 years ago

In which of the following sentences from "into the wild" is the author's tone evident?

Lady bird [3.3K]

Also like McCandless, Ruess was undeterred by physical discomfort; at times he seemed to welcome it

I hope this helps!

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3 years ago

The probability you win the game is 70%. What is the probability you don't win the game?

Sauron [17]

Answer: 30%

Explanation: If the probability you'll win is 70% and percentages can only reach up until 100% you subtract 70 from 100 and get 30. 100%-70%=30%

Hope this helped!

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3 years ago

Read 2 more answers