Find an equation equivalent to r = 10 sin theta in rectangular coordinates.

r = 10sinθ

Is

x² + (y - 5)² = 25

in rectangular coordinates.

Step-by-step explanation:

To convert r = 10sinθ to rectangular coordinates,

First, note the following equivalents

r² = x² + y²

x = rcosθ

y = rsinθ

=> sinθ = y/r

Now, r = 10sinθ

Implies

r = 10 × y/r

Multiply both sides by r

r² = 10y

Since r² = x² + y², we have

x² + y² = 10y

Or

x² + y² - 10y = 0

Completing the square for y² - 10y, we have

x² + [y² -2(5)y + 5² - 5²] = 0

x² + (y - 5)² - 25 = 0

x² + (y - 5)² = 25

Centered at (0, 5) with radius 5

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: