Two-fiths of a number is -12

HEYY I NEED HELP WITH AN AP CALC ASSIGNMENT ASAP

Vladimir79 [104]

CALCULATOR PART

1. The area of R + S is unsigned, meaning you want to find

$\displaystyle\int_a^b\left|f(x)-g(x)\right|\,\mathrm dx$

where $[a,b]$ is the interval between the leftmost and rightmost intersections of $f$ and $g$ .

First use your calculator to find these intersections:

$\cos x=\dfrac{x+1}3\implies x\approx-3.64,x\approx-1.86,x\approx0.889$

so that $a=-3.64$ and $b=0.889$ . Now compute the integral using your calculator:

$\displaystyle\int_a^b\left|f(x)-g(x)|\,\mathrm dx\approx1.662$

2. The volume, using the washer method, is given by the integral

$\displaystyle\pi\int_{-1.86}^{0.889}(|2-g(x)|^2-|2-f(x)|^2)\,\mathrm dx\approx12.078$

3. A circle of radius $r$ has area $\pi r^2$ ; a semicircle with the same radius thus has area $\frac{\pi r^2}2$ . Each cross section of this solid is a semicircle whose diameter is the vertical distance between $f(x)$ and $g(x)$ , or $|f(x)-g(x)|$ . In terms of the diameter $d=2r$ , the area of each semicircle would be $\frac{\pi d^2}8$ . Then the volume of the solid is

$\displaystyle\frac\pi8\int_{-3.64}^{-1.86}|f(x)-g(x)|^2\,\mathrm dx\approx0.0425$

NON-CALCULATOR PART

4. The mean value theorem says that for a function $F$ continuous on an interval $[a,b]$ and differentiable on $(a,b)$ , there is some $c\in(a,b)$ such that

$F'(c)=\dfrac{F(b)-F(a)}{b-a}$

If this $F$ happens to be an antiderivative of $f$ , then we end up with

$f(c)=\displaystyle\frac1{b-a}\int_a^bf(x)\,\mathrm dx$

$\cos x$ is continuous and differentiable everywhere, so the MVT applies. We have $F'(x)=f(x)=\cos x$ , so the MVT tells us there is some $c\in[0,\pi$ such that

$\cos c=\dfrac{\sin\pi-\sin0}{\pi-0}=0$

That is, the average value of $f(x)$ on $[0,\pi]$ is 0. The MVT says there is some $c$ in the interval such that the function takes on the average value itself; this happens for $c=\frac\pi2$ .

5. This question seems to be incomplete...

5 0

4 years ago

Identify two ways of demonstrating a complex understanding of an argument.

NNADVOKAT [17]

Answer:

Depends if it's leq or dbq

LEQ:

Use an event not related to the prompt and compare/contrast both events (Civil War and the Revolutionary War)
Explain both similarity or difference, continuity and change, cause and effect (depends on the prompt and what type it is)

DBQ:

I honestly don't know just pray your grader will be in a good mood.

6 0

3 years ago

Read 2 more answers

This news segment mentions visibility and kids wanting to see themselves in the media the

kumpel [21]

The question was split so i tried to understand it the best i could but i would say:

This news segments connects to our topic of diversity mainly because every kid doesn’t want to be in the media. And that’s why it’s diverse. Typical children like to play or run around for fun, but certain children have their motives and they find what they to do at an early age. Diversity is full of different passions and children are fully capable of having a passion at a young age.

7 0

3 years ago

The part of the spectrum that can be separated into rainbow-like colors is ...?

Rufina [12.5K]

Answer: Visible light spectrum.

Explanation: On the entire electromagnetic spectrum, the human eye can only detect and view the visible light spectrum which is what we, as humans, can separate into “rainbow-like colors.”

6 0

3 years ago

PKEASE HELP!!!!!!! what are a few reasons why the south seceded from the union

zvonat [6]

The scholars immediately disagreed over the causes of the war and they still disagree today.

Many maintain that the main cause of the was that the southern states desired to preserve the institution of slavery.

Others minimize slavery and point to other issues, taxation and principle of States' rights.

7 0

4 years ago