All categories

3 years ago

Write the rectangular equation (x + 5)2 + y2 = 25 in polar form.

Mathematics

1 answer:

andrezito [222]3 years ago

8 0

Answer:

r = -10costheta

Step-by-step explanation:

Given the rectangular equation

(x + 5)² + y² = 25

in polar coordinate

x = rcos theta

y = rsin theta

Substitute into the expression

(rcos theta + 5)²+(rsin theta)² = 25

r²cos²theta + 10rcos theta +25 +r²sin²theta = 25

r²cos²theta+r²sin²theta+ 10rcos theta= 0

r²(cos²theta+sin²theta) + 10rcostheta = 0

r² + 10rcostheta = 0

r² = -10rcostheta

r = -10costheta

Hence the correct option is D

You might be interested in

The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect

ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

$Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}$

Now the points A(−3, 4) and B(7, 2)

$AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}$

$AB = \sqrt{(10)^{2} +(-2)^{2}}$

$AB = \sqrt{100+4}$

$AB = \sqrt{104}$

$AB = 2\sqrt{26}\units$

Thus

$CD= 2\sqrt{26}\units$

Now the points

A (−3, 4) , D (−4, −1)

$AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}$

$AD = \sqrt{(-1)^{2} +(-5)^{2}}$

$AD = \sqrt{1 + 25}$

$AD = \sqrt{26}\units$

Thus

$BC = \sqrt{26}\units$

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

$Length = 2\sqrt{26}\ units$

$Breadth = \sqrt{26}\ units$

$Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})$

$Perimeter\ of\ rectangle = 2(3\sqrt{26})$

$Perimeter\ of\ rectangle = 6\sqrt{26}$

$\sqrt{26} = 5.1 (Approx)$

$Perimeter\ of\ rectangle = 6\times 5.1$

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

8 0

3 years ago

Beatrice is purchasing yoga mats from an online store. Each mat costs $8.50, and there is a shipping charge of $12.50 for an ord

Lilit [14]

Answer:

A.7

Step-by-step explanation:

80 - 12.50 = 67.50

67.50 ÷ 8.50 = 7 with a remainder

=7 mats

4 0

3 years ago

What is the liability to equity ratio of chester? select: 1 2.84 1.61 .31 4.35?

stiv31 [10]

Answer:

1.61

Step-by-step explanation:

The liability to equity ratio measures the gearing risk or leverage of the company. It is a financial ratio which is calculated by dividing total liabilities of a company by its shareholders equity. It measure the degree to which a company is financing its operations with debt.

8 0

3 years ago

What is the awnser to (0.2 + 0.982) + 8 =

pogonyaev

Answer:

9.182

Step-by-step explanation:

0.2 + 0.982 = 1.182

1.182 + 8 = 9.182

7 0

3 years ago

-7y^2+3y-6y-(3y^2+4y+4)