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3 years ago

Which of the following is true of two algorithms designed to solve the same problem?

Advanced Placement (AP)

1 answer:

Rufina [12.5K]3 years ago

5 0

ねなちゃんのツイートばかりにrかなのである。

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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)

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

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

8 0

3 years ago

The zone of proximal development is the difference between what the learner knows and what the learner is capable of __________.

MariettaO [177]

Answer

The zone of proximal development is the difference between what the learner knows and what the learner is capable of understanding with the help from a peer.

Explanation

The zone of proximal development (ZPD) is the range of abilities a learner can perform with assistance and what he or she can do without help. Potential development of an individual as determined by his independent problem solving abilities compared to problem solving under guidance of a peer will show the person’s zone of proximal development.

7 0

4 years ago

Flauer [41]

Answer:

its honesty!!

Explanation:

its honestly because she isn't taking the money that would've been used to trick a customer :)

8 0

2 years ago

Explain Sigmund Freud’s view of personality. In your response, discuss the conscious mind, the subconscious mind, the id, the eg

oee [108]

Answer:

According to Sigmund Freud, human personality is complex and has more than a single component. In his famous psychoanalytic theory, Freud states that personality is composed of three elements known as the id, the ego, and the superego. These elements work together to create complex human behaviors. Freud believed that the id, ego, and superego are in constant conflict and that adult personality and behavior are rooted in the results of these internal struggles throughout childhood.

Hope this helps:)

6 0

3 years ago

Read 2 more answers

What is the sample space of a die (dice)?

Aleksandr-060686 [28]

Yes the answer is dice

3 0

3 years ago