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3 years ago

HELP ASAP!!! THE BEST ANSWER GETS BRAINLIST! (15 POINTS)

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

6 0

Don’t click on the link please

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Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and

Nadusha1986 [10]

Call the surface $S$ ; then the area of $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm d\mathbf S$

Parameterize the surface by

$\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}$

with $2\le u\le4$ and $0\le v\le2\pi$ . The surface element is given by

$\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$

So the area is

$\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8$

where $w=1+4u^2\implies\mathrm dw=8u\,\mathrm du$

$=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}$
$=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69$

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3 years ago

Calculus help! Using the mean value theorem!

marta [7]

$f$ is differentiable across its domain, so the MVT says there is some value of $c$ in the open interval $(a,b)$ such that

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

You have

$f(x)=Ax^2+Bx+C\implies f'(x)=2Ax+B$

so the equation above becomes

$2Ac+B=\dfrac{(Ab^2+Bb+C)-(Aa^2+Ba+C)}{b-a}$

Solve for $c$ .

$2Ac+B=\dfrac{A(b^2-a^2)+B(b-a)}{b-a}$
$2Ac+B=A(b+a)+B$
$2Ac=A(b+a)$
$c=\dfrac{b+a}2$

so $c$ is indeed the average of the endpoints, i.e. the midpoint.

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3 years ago

Find the slope please

Katarina [22]

Answer:

slope is $-\frac{3}{4}$

Step-by-step explanation:

1,-1 -3,2 are two points on the graph

the equation to find slope is $\frac{y_{1}- y_{2} }{x_{1}- x_{2} }$

so $\frac{2--1}{-3-1} = -\frac{3}{4}$

or you can count how many places it changed in the equation $\frac{rise}{run}$

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3 years ago

Which of the following represents the zeros of f(x) = x3 − 3x2 − 2x + 6?

Mrac [35]

D. {3, √ 2, -√ 2}.
The cubic factors- (x - 3)(x² - 2) = 0.

6 0

2 years ago

Read 2 more answers

What is the value of X? X= B=75 C=50 A=x Thank u! Sorry i'm dumb:(

murzikaleks [220]

Angels on a triangle is 180°
so you add 75 and 50 which gives you 125 then u take away that by 180 to find x
and that your answer
I'm going to let you work it out since its easy question

8 0

2 years ago