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3 years ago

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Please help, i am stuck.

1 answer:

Alla [95]3 years ago

5 0

Answer:

Step-by-step explanation:

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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

How do I do number 7 please help me with

riadik2000 [5.3K]

There is a Khana Academy video that explains everything you have to do and it’s the same page that you’re on

3 0

3 years ago

Which point is on the graph of f(x) = 2*5^x

vodomira [7]

Answer:

Option B (1,10)

Step-by-step explanation:

we have

$f(x)=2(5^x)$

we know that

If a ordered pair is on the graph of f(x) then the ordered pair must satisfy the function f(x)

<u><em>Verify each case</em></u>

case A) (0,0)

For x=0

$f(x)=2(5^0)\\f(x)=2(1)=2$

Compare the value of f(x) with the y-coordinate of the ordered pair

$2\neq 0$

therefore

The ordered pair is not on the graph of f(x)

case B) (1,10)

For x=1

$f(x)=2(5^1)\\f(x)=2(5)=10$

Compare the value of f(x) with the y-coordinate of the ordered pair

$10=10$

therefore

The ordered pair is on the graph of f(x)

case C) (0,10)

For x=0

$f(x)=2(5^0)\\f(x)=2(1)=2$

Compare the value of f(x) with the y-coordinate of the ordered pair

$2\neq 10$

therefore

The ordered pair is not on the graph of f(x)

case D) (10,1)

For x=10

$f(x)=2(5^{10})\\f(x)=2(9,765,625)=19,531,250$

Compare the value of f(x) with the y-coordinate of the ordered pair

$19,531,250\neq 1$

therefore

The ordered pair is not on the graph of f(x)

7 0

3 years ago

the perimeter of an equilateral triangle equals 3 times the length of one side. write a function using 2 variables for this situ

ValentinkaMS [17]

I hope this helps you

4 0

3 years ago

Find the percent of increase.<br> Original number: 45 books<br> New number: 63 books

BARSIC [14]

Answer:

Step-by-step explanation:

first you multiply 45 by .40 you multiply by .40 because that is the percent increase.

45*.40=18

then you just add the 18 to 45 which get you 63.

answer:40%

7 0

3 years ago