Answer:
Step-by-step explanation:
If $10,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
a)6 years
b)12 years
c)18 years
***
compound interest formula: A=P(1+r/n)^nt, P=initial investment, r=interest rate, n=number of compounding periods per year, A=amt after t-years.
For given problem:
P=10000
r=.02
n=2
t=6, 12, 18
..
A(6)=10000(1+.02/2)^2*6
A(6)=10000(1.01)^12=11,268.25
A(12)=10000(1.01)^24=12,697.35
A(18)=10000(1.01)^36=14,307.69
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There are 3 right triangles.
Long leg short leg hypotenuse
Large ? ? 32+18 = 50 m
Medium 32 m x ?
Small x 18 m ?
Similar triangles: small & medium
short leg / long leg
x/32 = 18/x
x*x = 18 * 32
x² = 576
√x² = √576
x = 24
Long leg short leg hypotenuse
Large ? → 40 m ? 32+18 = 50 m
Medium 32 m 24 m ? → 40 m
Small 24 m 18 m ? → 30 m
solve hypotenuse of medium and small using Pythagorean theorem.
32² + 24² = c²
1024 + 576 = c²
1600 = c²
√1600 = √c²
40 = c
24² + 18² = c²
576 + 324 = c²
900 = c²
√900 = √c²
30 = c
Solve for the long leg of the large right triangle using ratio and proportion
medium and large: long leg / hypotenuse
32/40 = x/50
32*50 = 40 * x
1600 = 40x
1600/40 = x
40 = x
<span>
</span><span>A. How far is the spot on the beach from the parking lot? 24 meters
B. How far will he have to walk from the parking lot to get to the refreshment stand? 40 meters
</span>
Answer:
768
Step-by-step explanation:
