Remember that transformation between Cartesian and polar system are:
x=r*cos(α)
y=r*sin(α)
From this we can conclude that:
r=√(x^2 + y^2)
Using trigonometry transformations we can write:
r=sin(2α) = 2sin(α)cos(α)
Now we can multiply both sides with r^2:
r^3 = 2(r*sin(α))*(r*cos(α))
Now using some replacements we can write:
(x^2 + y^2)^(3/2) = 2*x*y
Answer:
x = - 33
Step-by-step explanation:
Given
(x + 6) = - 18
Multiply both sides by 3 to clear the fraction
2(x + 6) = - 54 ( divide both sides by 2 )
x + 6 = - 27 ( subtract 6 from both sides )
x = - 33
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Given Information
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Adrian can run 3/4 mile in 1 morning.
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Find how long he needs to run 1 mile
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3/4 miles = 1 morning
[ Divide by 3/4 on both side ]
3/4 ÷ 3/4 miles = 1 ÷ 3/4
1 miles = 4/3 morning
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Find how long he needs to take to run 3 miles
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1 miles = 4/3 morning
[ multiply by 3 through ]
3 miles = 4/3 x 3
3 miles = 4 mornings
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Answer : 4 mornings
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Answer:
2,744 feet³
Step-by-step explanation:
Volume = Length * Width* Hight
A cube has all the sides equal in measure so Length and Width and Hight are equal and are given in the picture to be 14 feet.
V = 14 *14*14 = 2,744 cubic feet
X - 2y = -24
x - y = 4
Isolate x in the first equation by adding 2y to both sides.
x = -24 + 2y
Now plug in this value of x into the second equation.
(-24 + 2y) - y = 4
Solve. Combine all like terms, 2y - y.
-24 + y = 4
Add 24 to both sides to isolate y.
y = 28
Now plug y back into the first equation to find x.
x - 2(28) = -24
x - 56 = -24
Add 56 to both sides to isolate x.
x = 32
The solution is (32, 28).