Write an equation <br> the sum of two times a number and 5 is 11

Convert from rectangular to polar coordinates: note: choose rr and θθ such that rr is nonnegative and 0≤θ<2π0≤θ<2π (a)(9,0

DochEvi [55]

Answer:

Step-by-step explanation:

Convert rectangle (x , y) to polar coordinates ( r , θ)

$x=r \cos \theta, y= r \sin \theta$

$r=\sqrt{x^2+y^2} , \theta =tan^-^1 (\frac{y}{x} )$

a) converts (9, 0) to polar coordinates ( r , θ)

$r=\sqrt{x^2+y^2} \\\\=\sqrt{9^2+0} \\\\=9$

$\theta= \tan^-^1 (\frac{0}{9} )\\\\=0$

b) Convert $(18,\frac{18}{\sqrt{3} } )$ to polar coordinates ( r, θ)

$r = \sqrt{18^2+(\frac{18}{\sqrt{3} })^2 } \\\\=\sqrt{324+108} \\\\=\sqrt{432}$

$\frac{x}{y} \theta = \tan^-^1(\frac{\frac{18}{\sqrt{3} } }{18} )\\\\= \tan ^-^1(\frac{1}{\sqrt{3} } )\\\\= \frac{\pi}{6}$

c) converts (-5, 5) to polar coordinates ( r , θ)

$r =\sqrt{(-5)^2+(5)^2} \\\\=\sqrt{50} \\\\=5\sqrt{2}$

$\theta=\tan^-^1(\frac{5}{-5} )\\\\= \tan^-^1(-1)\\\\=\frac{3\pi}{4}$

d) converts (-1, √3) to polar coordinates ( r , θ)

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

$\theta=\tan^-^1(\frac{\sqrt{3} }{-1} )\\\=\tan^-^1(-\sqrt{3} )\\\\=\frac{2\pi}{3}$

$= \frac{2\pi}{\sqrt{3} }$

6 0

3 years ago

To fit between two windows, the width of a bookshelf must be no greater than 6 1/2feet. Mrs.aguilar purchases a bookshelf that i

MArishka [77]

I need points sorry

6 0

3 years ago

Mathematics help please!!!!!!!!!<br><br> what is -0.0833333333333 converted into a fraction?

VladimirAG [237]

Answer:

- 1/12

Step-by-step explanation:

Let -0.0833333 = x --- (1)

Multiply both sides by 10.

-0.833333 = 10x --- (2)

Subtract (2) from (1),

0.75 = -9x

-9x = $\frac{75}{100}$

= $\frac{3}{4}$

$x=-\frac{3}{36}$

$x=-\frac{1}{12}$

8 0

3 years ago

What is the equation of the line that passes through the point (-5, 7)<br> and has a slope of –1/5?

Snowcat [4.5K]

The equation is y = -1/5x + 6

8 0

3 years ago

The ammunition storage room has 10 feet between the floor and the ceiling. Each box of ammunition is 10 feet tall. Each crate of

KIM [24]

Answer:

the maximum number of crates that can be stacked between the floor and ceiling

$\frac{height \hspace{0.1cm} of \hspace{0.1cm} ammunition \hspace{0.1cm} box}{height \hspace{0.1cm} of \hspace{0.1cm} each \hspace{0.1cm} crate} = \frac{10 \hspace{0.1cm} feet}{12 \hspace{0.1cm} inches} = \frac{10 \times 12 \hspace{0.1cm} inches }{12 \hspace{0.1cm} inches} = 10 \hspace{0.1cm} crates$

where 1 foot = 12 inches. SO the answer is that a maximum of 10 crates can be stacked from floor to ceiling.

Step-by-step explanation:

i) the maximum number of crates that can be stacked between the floor and ceiling

$\frac{height \hspace{0.1cm} of \hspace{0.1cm} ammunition \hspace{0.1cm} box}{height \hspace{0.1cm} of \hspace{0.1cm} each \hspace{0.1cm} crate} = \frac{10 \hspace{0.1cm} feet}{12 \hspace{0.1cm} inches} = \frac{10 \times 12 \hspace{0.1cm} inches }{12 \hspace{0.1cm} inches} = 10 \hspace{0.1cm} crates$

where 1 foot = 12 inches

3 0

3 years ago

Write an equation the sum of two times a number and 5 is 11