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Pavlova-9 [17]
3 years ago
5

What does happiness really means​

Advanced Placement (AP)
2 answers:
Zinaida [17]3 years ago
8 0
Happiness means you can smile without being forced too, you can go to bed without crying and can wake up and get ready for the day. Now remember only you are capable of your feelings you cant live in the past. The past is just memories and you overthink by thinking of the future. Don’t think of the future think of were you are rn think of you present think to yourself “why am I not doing anything with my life” and the reason dude is cause your living in the past and past causes nothing but pain.
Vladimir79 [104]3 years ago
3 0

Answer:

So, happiness is the state of feeling or showing pleasure or contentment. Happiness is a state, not a trait; in other words, it isn’t a long-lasting, permanent feature or personality trait, but a more fleeting, changeable state. Happiness is equated with feeling pleasure or contentment, meaning that happiness is not to be confused with joy, ecstasy, bliss, or other more intense feelings. Happiness can be either feeling or showing, meaning that happiness is not necessarily an internal or external experience, but can be both.

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HEYY I NEED HELP WITH AN AP CALC ASSIGNMENT ASAP
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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.

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