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3 years ago

What is the slope of any parallel to the line 8x + 9y = 3 in the standard (x,y) coordinate plane?

Mathematics

1 answer:

iris [78.8K]3 years ago

8 0

Answer:y=−8x9+13 y = - 8 x 9 + 1 3 have the same slope of −89 .

Step-by-step explanation: Just do it.

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Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

Last spring, Bob built a rectangular pen for his pigs that measured 6 feet long and 4.5 feet wide. He wants to enlarge the pig p

Feliz [49]

A= h•w

6+2 = 8 feet long
4.5+1.5= 6 feet wide

8*6= 48 ft

Answer: 48 feet

3 0

3 years ago

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The perimeter of the rectangle below is 132 units. Find the length of side AB.

melisa1 [442]

Answer:

AB = 35

Step-by-step explanation:

For the value of variable z....;

;Perimetre = 132

; 132 = 2(4z + 3) + 2(5z)

; 132 = 8z + 6 + 10z

; 132 - 6 = 8z + 10z

; 126 = 18z

;the value of...z = 7

Therefore the value of length AB;

AB = 5z...then substitute the value of z into the length of AB

; AB = 5(7)

;AB = 35

5 0

3 years ago

Round 1/9 to the nearest 1/2

kifflom [539]

1. C

2. B

3. B

I hope this helped!

6 0

3 years ago

Help plz will mark brainliest

erik [133]

Answer:

hii there

the correct answer is option ( C ) to the right

Step-by-step explanation:

hope it helps

have a nice day : )

and sorry also

3 0

3 years ago

Read 2 more answers