Refer to the passage.

If point B is translated 5 units right and 3 units down, what are the coordinates of B'? A) (1, 3) B) (1, −3) C) (−1, 3) D) (3,

Blababa [14]

Answer:

(1, 3)

Explanation:

7 0

4 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

What is the highest level of classes you could take in middle school?

Anna11 [10]

Answer:

My sons middle school breaks the 7th grade kids in two groups for math. 3/5 of the classes are concidered accelerated. 2/5 are a "slower" pace. My son was placed in the accelerated class ( he had A's and B's last year) This year he is having a tough time in math. His confidence is down and he tells me that the teacher goes too fast. The teacher mentioned that we could swich him. I do not know what to do. in 8th grade the kids are in 3 groups. If he is placed in the lowest group now what will happen in the future. If he goes in with the low group will he be with a lot of behavior issue kids? I worry about his self esteem as well. Why would I want to switch him? He is frustrated with the pace and I find myself reteaching so that he can complete his homework. Is a lower grade in accelerated math better than a high grade in "slow" math.

I am told that:

Long term….it is unlikely a student can take Algebra in 8th grade if they are in math 2 in 7th. In that case, the student would take Algebra in high school.

Would love to hear some suggestions. Thanks

4 0

3 years ago

In the second and third sentences of the fifth paragraph (“He stops . . . gradual explanation”), the author presents a humorous

Elis [28]

Answer:

D. desire to surprise his friend and his friend’s failure to recognize him

Explanation:

Answer D

Correct. In these sentences, the author presents a humorous reversal that emerges from the ironic incongruity between the traveler’s plan to “overpower” his old friend with an excess of pleasure and the anticlimactic outcome of the surprise visit. As it turns out, the friend experiences no immediate pleasure from the visit because he fails to recognize the traveler and can only be made to remember him after the traveler gives a “gradual (in this context, methodical) explanation” of who he is.

7 0

3 years ago

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How much is the Bugatti Chiron Super Sport 300+ and how fast is it?

Sonja [21]

Answer:

Bugatti's new $3.9 million hypercar broke a world record for going over 300 miles per hour — now it's for sale. Bugatti is building 30 example of a souped-up version of its Chiron model — the Chiron Super Sport 300+, a version of which recently became the world's fastest production car, cracking the 300mph barrier.

Explanation:

3 0

4 years ago

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