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4 years ago

Please help i need to turn this in today

Advanced Placement (AP)

1 answer:

PilotLPTM [1.2K]4 years ago

5 0

<u>Claim 2:</u>

The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.

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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)

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

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

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3 years ago

Psychology: Which belief about attachment did Harlow's work with monkeys disprove?

Arisa [49]

Answer:

the first one

Explanation:

The whole theme of the monkey experiment was that the baby monkey would go towards the "mother" who was wrapped in a blanket and provided some form of comfort rather than the steel one who simply provided nourishment.

6 0

3 years ago

Bakit kaya may mga Pilipinong ninais na manirahan sa ibang bansa?

lana [24]

Answer:

Chutmarani kela..Tambul pan aur sadha

6 0

3 years ago

Read 2 more answers

On which part of the retina are the light rays from the object in the central vision landing?

Arisa [49]

Answer:

In nearsightedness (myopia), the light rays form an image in front of the retina. In farsightedness (hypermetropia), the rays focus behind the retina.

6 0

3 years ago

what material is formed by the implication of a water manufactured rock and a suppressed heating source

Allisa [31]

Hydraulic fracturing, informally referred to as “fracking” is an oil and gas development process that typically involves injecting water, sand, and chemicals under high pressure into a bedrock formation via a well

I hope that helps

4 0

4 years ago