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3 years ago

Find the value of X

Mathematics

2 answers:

Basile [38]3 years ago

4 0

$x + 3x + 80 = 180 \\ 4x = 180 - 8 0 \\ 4x = 100 \\ x = \frac{100}{4} \\ x = 25 \: \: \:$

sweet [91]3 years ago

3 0

The sum of all the angles of the triangle is 180°.

80 + 3x + x = 180°

80 + 4x = 180°

4x = 180 - 80

4x = 100

x = 100/ 4

x= 25

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Find the volume of the ellipsoid x^2+y^2+9z^2=64

yuradex [85]

Parameterize the ellipsoid using the augmented spherical coordinates:

$\begin{cases}x=\frac18\rho\cos\theta\sin\varphi\\\\y=\frac18\rho\sin\theta\sin\varphi\\\\z=\frac38\rho\cos\varphi\end{cases}$

Then the Jacobian for the change of coordinates is

$\mathbf J=\dfrac{\partial(x,y,z)}{\partial(\rho,\theta,\varphi)}=\begin{bmatrix}\frac18\cos\theta\sin\varphi&-\frac18\rho\sin\theta\sin\varphi&\frac18\rho\cos\theta\cos\varphi\\\\\frac18\sin\theta\sin\varphi&\frac18\rho\cos\theta\sin\varphi&\frac18\rho\sin\theta\cos\varphi\\\frac38\cos\varphi&0&-\frac38\rho\sin\varphi\end{bmatrix}$

which has determinant

$\det\mathbf J=-\dfrac3{512}\rho^2\sin\varphi$

Then the volume of the ellipsoid is given by

$\displaystyle\iiint_E\mathrm dx\,\mathrm dy\,\mathrm dz=\iiint_E|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

where $E$ denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume

$\displaystyle\frac3{512}\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\dfrac\pi{128}$

4 0

3 years ago

Maury completed a bicycle race 1.5 hours faster than Vince at an average speed of 16 miles per hour. Vince completed the same ra

MAXImum [283]

Let the time taken by Vince to complete the race was x hours.
Maury completed the race 1.5 hours faster. This means Maury complete the race in (x - 1.5) hours.

Average Speed of Maury = 16 miles per hour
Average Speed of Vince = 12 miles per hour

Distance = Speed x Time.

For Maury:
Distance = 16(x - 1.5)

For Vince:
Distance = 12x

Since the distance covered by both was the same, we can equate the two equations as:

16(x - 1.5) = 12x
16x - 24 = 12x
4x = 24
x = 6
This means Vince complete the race in 6 hours.

Distance = Speed x Time = 12 x 6 = 72 miles

Thus, the total distance of the race was 72 miles.

3 0

3 years ago

(2 4/10+8 4/5)-3 1/5 equals what whole number

FromTheMoon [43]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

a trail is 5 miles long. carlos walks 2/3 of the trail and runs the rest. how many miles does carlos walk?

lana [24]

Answer:

as 1 mile = 1.609 km

so 5miles = 8.045 km

so 2/3 of the trail = 2/3 × 8.045 = 5.3633333 (ans)

Hope it helps

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%28a%29%20%7B%20-%20%28b%29%7D%5E%7B2%7D%20" id="TexFormula1" title="(a) { - (b)}^{2} " alt="(

Cloud [144]

Answer:

a - b2

Step-by-step explanation:

STEP 1 :

Trying to factor as a Difference of Squares:

1.1 Factoring: a-b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : a1 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares

Final result :

a - b2

HOPE THIS HELPS!

PLEASE MARK BRAINLIEST! :)

7 0

2 years ago

Find the value of X ​

Find the value of X