Due to ever-changing technology, a new xyz smartphone decreases in value 20% each year. (a) how much will this $1000 phone be worth in 2 years? (b) how long until it is worth less than 10% of it's original price?

10.3 years

Step-by-step explanation:

(a) Use the compound amount equation:  A = P(1 + rt), where, in this case,

P represents the original $1000 value and r is the rate of change.

Here, A = $1000(1 - 0.20)^2, or $1000(0.80)^2 = $640

the phone will be worth $640 after 2 years.

(b) "1/10 of its original price" would be (1/10)($1000) = $100.

Using the same equation:

$100 = $1000(0.80)^t

or:

1/10 = 0.80^t

Taking the natural log of both sides:

ln (1/10) = t ln 0.80, so that:

        -ln 10

t = = -2.3025 / (-0.2231)  =  10.3 years

       ln 0.80

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet