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4 years ago

It is math( help please

Mathematics

2 answers:

aleksandr82 [10.1K]4 years ago

8 0

Look at the picture.

It's a linear function.

A slope-point formula:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (1, 250) and (2, 300).

Substitute:

$m=\dfrac{300-250}{2-1}=\dfrac{50}{1}=50\\\\y-250=50(x-1)\\\\y-250=50x-50\qquad|+250\\\\y=50x+200$

Calculate the value of function for x = 12:

$y=50(12)+200=600+200=800$

<h3>Answer: 800</h3>

leva [86]4 years ago

7 0

After 12 months, Quynh will have saved $800

Simply follow the pattern shown on the graph.

Month 1: 250

Month 2: 300

Month 3: 350

Month 4: 400

Month 5: 450

Month 6: 500

Month 7: 550

Month 8: 600

Month 9: 650

Month 10: 700

Month 11: 750

Month 12: 800

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Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

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The cone equation gives

$z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2$

which means that the intersection of the cone and sphere occurs at

$x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92$

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We can parameterize the spherical cap in spherical coordinates by

$\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle$

where $0\le\theta\le2\pi$ and $0\le\varphi\le\dfrac\pi4$ , which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is $\dfrac3{\sqrt2}$ . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

$\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4$

Now the surface area of the cap is given by the surface integral,

$\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du$
$=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}$
$=18\pi\left(1-\dfrac1{\sqrt2}\right)$
$=9(2-\sqrt2)\pi$