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2 years ago

A rectangle is twice as long as it is wide. Its area is 72 square units. Find the length of each side. System of equations

Mathematics

1 answer:

liraira [26]2 years ago

6 0

Answer:

L = 12

W = 6

Step-by-step explanation:

W = 2L

A = L * W

A = 72

72 = L * 2L

72 = 3L

24 = L (you have to divide by 2)

L = 12

W = 6

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Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

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Let $z=-\sqrt3+i$ . Then

$|z|=\sqrt{(-\sqrt3)^2+1^2}=2$

$z$ lies in the second quadrant, so

$\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6$

So we have

$z=2e^{i5\pi/6}$

and the fourth roots of $z$ are

$2^{1/4}e^{i(5\pi/6+k\pi)/4}$

where $k\in\{0,1,2,3\}$ . In particular, they are

$2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}$

$2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}$

$2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}$

$2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}$

7 0

3 years ago

Given the formula PV = nRT , solve for the variable T

aleksley [76]

T=PV/Rn you just divide both sides by Rn

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3 years ago

Suppose that y varies directly with x and y=12 when x=-2. what is when x=-6?

dlinn [17]

Y=4

How?
When they say directly you should multiply the x and y together. You would get -24, now using that number divide -24 by the new x(-6) you would get 4.

4 0

3 years ago

Read 2 more answers

What is the graph of y=-(x-2)^3-5

natulia [17]

When x=0,
y=-(0-2)^3-5
y=3

When y=0,
(x-2)^3=5
x-2= +/- 5^1/3
x= +/- 5^1/3 +2
x= 3.70997 or x=0.29002

To find the turning point at y, substitute the information that you have found above.

y=-(3.70997-2)^3-5
y=-9.99994

Find the mid-point next as mid-point is also the turning point.

(3.70997+0.29002)÷2=1.999995

Hence, Turning point is (1.999995, 9.99994)

Plot a graph using turning point, y value and the 2-x values.

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3 years ago

X=2y+7 3x−2y=3 solve by substitution

vazorg [7]

Answer: x= -2

Step-by-step explanation:

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3 years ago