Find the polar coordinates of the points with cartesian coordinates (−x, y).

1 answer:

4 0

The relationship to go from Cartesian coordinates to polar coordinates is given by the following equations:

x = r * cos(theta)
y = r * sin(theta)

Since the coordinates we are given are just variables that can take <em>any </em>value, we'll have to work with that. Thankfully, that means we can just plug in these equations to get polar coordinates!

(-x, y) becomes
(-(r * cos(theta)), r * sin(theta))

You might be interested in

If Ryan gives 4/9 of his 36 cards to Josiah, how many cards does he give Josiah?

Tamiku [17]

Answer:

16 cards

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

There are 25 boxes of paper. each box has 789 pieces of paper. how many pieces of paper are in all?

nika2105 [10]

This is a pretty basic multiplication problem.

If one box has 789 pieces of paper in it and there are 25 boxes, you will simply multiply 789 x 25

789 x 25 = 19,725.

This shows that there are 19,725 pieces of paper in the 25 boxes of paper.

4 0

2 years ago

Read 2 more answers

A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is

Illusion [34]

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume $V$ of a solid pyramid can be given as:

$\displaystyle V = \frac{1}{3} \cdot b \cdot h$ ,

where

$b$ is the area of the base of the pyramid, and
$h$ is the height of the pyramid.

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be $x$ cm.

At the vertice of this pyramid, $x = 0$ and the length of a side of the square is also $0$ .
At the base of this pyramid, $x = 3$ and the length of a side of the square is $4$ cm.

As a result, the length of a side of the square will be

$\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x$ .

The area of the square will be

$\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}$ .

Integrate the area of the horizontal cross-section with respect to $x$

from the top of the pyramid, where $x = 0$ ,
to the base, where $x = 3$ .

$\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}$ .