Brittany will be working full time this summer to save for her goal of having $10,000 by the time she's 21. Brittany has an account that will pay 3.5% interest, compounded monthly. She'll turn 17 at the end of the summer. About how much will Brittany have to deposit at the end of the summer so that her money can grow into $10,000 by the time she's 21?

the monthly balance will be $75,000

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west