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3 years ago

HELP ASAP!!

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

7 0

Answer:

The answer for -7x + 8 - 4x - 9 is 1. -11x-1

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Find the value of x and y of the equilateral triangle. I need it ASAP

katrin2010 [14]

Answer:

x=12, y=30

Step-by-step explanation:

to find x:

in a equilateral triangle, all three sides are congruent, so:

4x-4=3x+8

x-4=8

x=12

to find y:

in an equilateral triangle, all the angles are 60°, so:

2y=60

y=30°

7 0

3 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

3 years ago

Use the diagram to copy and complete the statement. (#12, 14, 16)

Sergio [31]

11 is the biggest and the 22

8 0

4 years ago

The length of an equilateral triangle is increased by 5 cm. The perimeter of the new triangle is 72 cm. What is the side length

Igoryamba

Answer:

19cm

Step-by-step explanation:

An equilateral triangle is a triangle where the length of the 3 sides are the same.

the perimeter is the sum of the 3 sides

for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15

let x = unknown length of side

length after increase = x + 5

(x + 5) x 3 = 72

divide both sides of the equation by 3

x + 5 = 24

subtract 5 from both sides of the equation

x = 24 - 5 = 19cm

6 0

3 years ago

Triangles R S T and X Y T are congruent. Triangle R S T is reflected across a line and then rotated at point T to form triangle

vredina [299]

Answer:

C. Yes, ΔRST can be reflected across the line containing RT and then rotated about T so that S is mapped to Y.

Step-by-step explanation:

Rigid transformations are processes that can be applied to change the orientation or size of a given object, while its shape is maintained. Examples are; rotation, reflection, dilation and translation.

To map ΔRST to ΔXYT, the rigid transformations required are; reflection and rotation. ΔRST can be reflected across the line containing RT and then rotated about T so that S is mapped to Y.

Therefore, option C is correct from the given question.

6 0

4 years ago

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