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3 years ago

7x+3(-x+6)=42 Show all steps and properties used

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

4 0

Answer:

45/34

Step-by-step explanation:

7x+3(-x+6)=42

7x(-x+6)=42+3=45

-8x + 42x=45

34x=45

x=45/34

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Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 36.

rewona [7]

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed as:

$y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}$

Thus, the area of the surface is as follows:

$\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA$

$= \iint_D \sqrt{x^2 +y^2 +1 } \ dA$

$= \int^{2 \pi}_{0} \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr \ d \theta$

$=2 \pi \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr$

$= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0$

$= 2 \pi \times \dfrac{1}{3} \Bigg [ (37)^{3/2} - 1 \Bigg]$

$= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]$

3 0

2 years ago

Hello I don’t understand question 9 a and b. Please show working out.<br> Thanks

brilliants [131]

A) I would make the positive integer x and then form an equation.

x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6

Since the question asks for a positive integer the answer is 7.

B) two positive numbers x and y.

X - y = 3
x^2 + y^2 = 117

Use these simultaneous equations to figure out each number.

Rearrange the first equation

x = y + 3

Then substitute it into the second equation.

(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)

This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.

Use y to find x

x = y + 3
x = 6 + 3
x = 9

So the answers are x = 9 and y = 6.

3 0

2 years ago

A right triangle is shown below. What is cos EFD?<br> Will make BRAINLIEST

rjkz [21]

Are you looking for the length from E to F?

8 0

2 years ago

A rectangle has a perimeter of 204 feet. It's length is six feet longer than twice it's width. If L stands for the length of the

Ratling [72]

Answer:

L = 70

W = 32

Step-by-step explanation:

P = 2L + 2W

P 204 feet

W = x

L = 2x + 6

P = 2L + 2W

P = 2*(2x + 6) + 2*x

P = 4x + 12 + 2x

P = 6x + 12

But we know that P = 204 So 6x + 12 = 204

6x + 12 = 204 Subtract 12 from both sides

6x + 12 - 12 = 204 - 12 Collect like terms on the right

6x = 192 Divide by 6

x = 192/6

x = 32

Answer

W = 32

L = 2*W + 6

L = 2*32 + 6

L = 64 + 6

L = 70

7 0

3 years ago

How many gallons of a 80% antifreeze solution must be mixed with 100 gallons of 20% antifreeze to get a mixture that is 70% a

Blababa [14]

To Find :

How many gallons of a 80% antifreeze solution must be mixed with 100 gallons of 20% antifreeze to get a mixture that is 70% antifreeze.

Solution :

Let, x gallons of 80% antifreeze solution is required :

So,

$(x \times 80) + ( 100 \times 20 ) = (x + 100 )\times 70\\\\8x + 200 = 7( x + 100)\\\\x = 500$

Therefore, 500 gallons of 80% antifreeze solution is required.

6 0

2 years ago