The Tanners have received an $8000 gift from one of their parents to invest in their child’s college education. they estimate that they will need $20000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?

3.4%

Step-by-step explanation:

For given problem:

P=8000

n=2*12=24 compounding perods

A=12000

A/P=(1+i)^24

12000/8000=(1+i)^24

1.5=(1+i)^24

take log of both sides

log1.5=24log(1+i)

log1.5/24=log(1+i)

.007337=log(1+i)

10^(.007337)=1+i

1+i=1.017

i=1.017-1=.017 (interest rate per compounding period)

annual interest rate=2*.017=.034 or 3.4%

1010: 3030

is it i think

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81