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frez [133]
3 years ago
7

Please help me with this!!! Thanks!

Mathematics
1 answer:
kap26 [50]3 years ago
6 0

Answer:

3096

Step-by-step explanation:

So Carol gets 5/12 of the 40% so divide 860 by 5 to get 1/12 then multiply it by 12 to get 2064 which is 40% of the total money divide that by 4 to get 516 multiply that by 6 to get the amount Alexa received which is 60%

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Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

\rho = \sqrt{x^{2}+y^{2}+z^{2}}

\phi = cos^{-1}\frac{z}{\rho}

For angle θ:

  • If x > 0 and y > 0: \theta = tan^{-1}\frac{y}{x};
  • If x < 0: \theta = \pi + tan^{-1}\frac{y}{x};
  • If x > 0 and y < 0: \theta = 2\pi + tan^{-1}\frac{y}{x};

Calculating:

a) (4,2,-4)

\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}} = 6

\phi = cos^{-1}(\frac{-4}{6})

\phi = cos^{-1}(\frac{-2}{3})

For θ, choose 1st option:

\theta = tan^{-1}(\frac{2}{4})

\theta = tan^{-1}(\frac{1}{2})

b) (0,8,15)

\rho = \sqrt{0^{2}+8^{2}+(15)^{2}} = 17

\phi = cos^{-1}(\frac{15}{17})

\theta = tan^{-1}\frac{y}{x}

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = \frac{\pi}{2}

c) (√2,1,1)

\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}} = 2

\phi = cos^{-1}(\frac{1}{2})

\phi = \frac{\pi}{3}

\theta = tan^{-1}\frac{1}{\sqrt{2} }

d) (−2√3,−2,3)

\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}} = 5

\phi = cos^{-1}(\frac{3}{5})

Since x < 0, use 2nd option:

\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }

\theta = \pi + \frac{\pi}{6}

\theta = \frac{7\pi}{6}

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

r=\sqrt{x^{2}+y^{2}}

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

r=\sqrt{4^{2}+2^{2}} = \sqrt{20}

\theta = tan^{-1}\frac{1}{2}

z = -4

b) (0, 8, 15)

r=\sqrt{0^{2}+8^{2}} = 8

\theta = \frac{\pi}{2}

z = 15

c) (√2,1,1)

r=\sqrt{(\sqrt{2} )^{2}+1^{2}} = \sqrt{3}

\theta = \frac{\pi}{3}

z = 1

d) (−2√3,−2,3)

r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}} = 4

\theta = \frac{7\pi}{6}

z = 3

5 0
3 years ago
Which of the following expressions represents a function?
lora16 [44]
The correct answer is y=4x-1
4 0
3 years ago
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Hey! I'v been struggling with this question lately. Can someone just lend me a hand?
Dominik [7]
So, this problem is asking us to find the value of our variable u. 

How can you do this? By isolating the variable, or having only it on one side of the equals sign. 

Here's the step by step approach. It's just simple algebra and reverse order of operation (which is what you should do whenever you are solving for a variable).

\frac{u+88}{11} = 17

Multiply both sides by 11 to get rid of the 11 denominator.
u + 88 = 187

Then, subtract both sides by 88 to get u by itself.
u = 99

Therefore, u is equal to 99. 

6 0
3 years ago
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A box can hold 9 books. There are only 5 books in the box. What percentage of the box is full? 56% 80% 1.8% 44%
Doss [256]

Answer:

I do believe that the answer would be 56%

Step-by-step explanation:

Using estimation if the box is half full it would have 4.5 books in the box, if you add that extra book it would be around 56%

6 0
3 years ago
Help with 31 please
Goryan [66]

Answer:

C. 1/2 divided by 13

Step-by-step explanation:

You have to divide the 1/2 gallon between the 13 people...not the 13 people by the 1/2 gallon! Can you mark brainliest again??

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