All categories

2 years ago

I need help with this last question !!!

Mathematics

1 answer:

Svetllana [295]2 years ago

3 0

So∠DHG = 7x-42, and since ∠FHC is directly opposite of it, it's the same value, 7x-42.

∠AGH should equal ∠CHF since they're both on parallel lines and line EF intersects them.

Therefore, ∠AGH =∠FHC:

3x-10=7x-42 (Subtract 7x and -10)

-4x=-32

x=8

∠DHG should be 8°

You might be interested in

rachel is trying to find deminsions of her new office. the office is 150 aquare feet(area+150ft2) the width of the office is 5 f

viva [34]

Answer:

Step-by-step explanation:

length =15 feet

width =10 feet

5 0

2 years ago

6% of what number is 24

Flura [38]

Answer:

4 i think, sorry if incorrect

Step-by-step explanation:

8 0

2 years ago

Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

2 years ago

3w + 6(w – 4) = 156, what does w equal?

RSB [31]

<h2>3w + 6 (w - 4) = 156</h2><h2 /><h2>3w + 6w - 24 = 156</h2><h2 /><h2>9w - 24 = 156</h2><h2 /><h2>9w = 180</h2><h2>÷9 ÷9 ← divide by 9 on both sides</h2><h2 /><h2> w = 20</h2>

3 0

2 years ago

What is the t-intercept of the line shown below?

larisa86 [58]

Answer:

the y intercept is 2

Step-by-step explanation:

its when the slope passes through the y-axis

6 0

2 years ago