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3 years ago

How did the cold war begin?

1 answer:

5 0

Its started after World War 2 because after a lot of issues arose between the US and USSR. They had a mutual distrust with each other stemming from the way the US had perceived the USSR as an illegitimate part of the international community. The way the USSR perceived the US as people who intervened in everyone's business and had amounted weapons.

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Mark is interested in becoming a biomedical engineer or a journalist. Based on his research, he chose to pursue biomedical engin

Sveta_85 [38]

Answer: B. He is interested in designing machines that help people with disabilities

Explanation:

The options include:

A. He doesn’t enjoy solving problems by working as a team and using analytical skills.

B He is interested in designing machines that help people with disabilities.

C He enjoys writing, and he’s really good at it.

D He wants to get to know lots of different kinds of people around the world.

Biomedical engineers are the people who helps in the development of new devices and new equipment which will be used to improve the health of people.

In this case, since Mark chooses to pursue biomedical engineering, his reason will be because he's interested in designing machines that help people with disabilities.

8 0

3 years ago

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 $c=\frac\pi2$ .