What is 15x-8=14x+13

Find all polar coordinates of point P where P = ordered pair 3 comma negative pi divided by 3 .

jek_recluse [69]

Answer:

The all polar coordinates of P are:

(3 , -π/3) , (3 , 5π/3) , (-3 , 2π/3) , (-3 , -4π/3)

Step-by-step explanation:

* Lets study the polar coordinates of a point

- In polar coordinates there is an infinite number of coordinates

for a given point.

- The polar coordinates of a point (x , y) is (r , θ), where

r = √ ( x2 + y2 )

θ = tan-1 ( y / x )

# Ex: the following four points are all coordinates for the same point.

* (5 , π/3) = (5 , −5π/3) = (−5 , 4π/3) =(−5 , −2π/3)

- These four points only represent the coordinates of the point without

rotating more than once

- So the point (r,θ) can be represented by any of the following

coordinate pairs (r , θ + 2π n) and (−r , θ + (2n + 1) π), where n is

any integer.

* Now lets solve the problem

∵ P = (3 , -π/3)

∵ (r , θ + 2πn)

∴ r = 3 an d Ф = -π/3

- let n = 1

∴ P = (3 , -π/3 + 2π)

∴ P = (3 , 5π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = 0

∴ P = (-3 , -π/3 + (2×0 + 1) π)

∴ P = (-3 , -π/3 + (0 + 1) π)

∴ P = (-3 , -π/3 + π)

∴ P = (-3 , 2π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = -1

∴ P = (-3 , -π/3 + (2(-1) + 1) π)

∴ P = (-3 , -π/3 + (-2 + 1) π)

∴ P = (-3 , -π/3 + -π) = (-3 , -4π/3)

∴ P = (-3 , -4π/3)

5 0

2 years ago

Henry invested $59,000 in an account paying an interest rate of 2% compounded quarterly. Assuming no deposits or withdrawals are

AfilCa [17]

Answer:

Step-by-step explanation:

$A=P(1+r/4)^{(4t)}\\ \\ A=P(1+.02/4)^{(4t)}\\ \\ A=59000(1.005)^{4(20)}\\ \\ A=\$ 87929.98$

5 0

3 years ago

Click the picture for the question please help!!!

sesenic [268]

Answer:

297.33 m

Step-by-step explanation:

3 0

3 years ago

What is the surface area of the net of this 3-dimensional figure?

zhenek [66]

Answer:

3 multiply by 6 multiply by 5

= 90 cm²

6 0

1 year ago

Read 2 more answers

Use theorem 7. 4. 2 to evaluate the given laplace transform. do not evaluate the convolution integral before transforming. (writ

irga5000 [103]

With convolution theorem the equation is proved.

According to the statement

we have given that the equation and we have to evaluate with the convolution theorem.

Then for this purpose, we know that the

A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.

And the given equation is solved with this given integral.

So, According to this theorem the equation becomes the

$\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).$

Then after solving, it become and with theorem it says that the

$\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .$

Hence by this way the given equation with convolution theorem is proved.

So, With convolution theorem the equation is proved.

Learn more about convolution theorem here

brainly.com/question/15409558

#SPJ4

3 0

1 year ago