Lauren has a points card for a movie theater.

Mathematics

2 answers:

mash [69]3 years ago

8 0

The answer is 5.5x+60=104

Lesechka [4]3 years ago

5 0

Multiply points per visit x number of visits, using x for the number of visits:

5.5x

Add that to the points she already has:

5.5x + 60

This needs to equal a total of 104 points:

5.5x + 60 = 104

Now solve for x

5.5x + 60 = 104

Subtract 60 from both sides

5.5x = 44

Divide both sides by 5.5

X = 8

She needs 8 more visits

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I need help rn please

nirvana33 [79]

Hello!

$\large\boxed{\text{ slope = -3}}$

Use the slope formula to solve for the slope of the line (m):

$m = \frac{y^{2} -y^{1} }{x^{2} -x^{1} }$

We can plug in the points (0, 4) and (1, 1) to solve:

$m = \frac{1-4}{1-0}= \frac{-3}{1} = -3$

Therefore, the slope of the line is -3.

8 0

3 years ago

Use spherical coordinates. evaluate (9 − x2 − y2) dv, where h is the solid hemisphere x2 + y2 + z2 ≤ 4, z ≥ 0.

avanturin [10]

In spherical coordinates, we have

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}$

which gives volume element

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

and so the triple integral is given by

$\displaystyle\iiint_H(9-x^2-y^2)\,\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9-\rho^2\sin^2\varphi)\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$
$=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9\rho^2\sin\varphi-\rho^4\sin^3\varphi)\,\mathrm d\rho\,\mathrm d\varphi$
$=\dfrac{592\pi}{15}$