A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.

The equation of the parabola is (x + 4)² = -16(y + 1)

Step-by-step explanation:

The standard form of the equation of the parabola is (x - h)²  = 4p(y - k), where

∵ The focus at (-4, -5)

∴ h = -4

∴ k + p = -5 ⇒ (1)

∵ The directrix at y = 3

∴ k - p = 3 ⇒ (2)

→ Add equations (1) and (2) to find k

∴ 2k = -2

→ Divide both sides by 2 to find k

∴ k = -1

→ Substitute it in equation (1) to find p

∵  -1 + p = -5

→ Add both sides by 1

∴ -1 + 1 + p = -5 + 1

∴ p = -4

→ Substitute the values of h, k, and p in the formula above

∵ (x - -4)² = 4(-4)(y - -1)

∴ (x + 4)² = -16(y + 1)

∴ The equation of the parabola is (x + 4)² = -16(y + 1)

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)