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1 answer:
Problem 17, part A
i = simple interest = 900 dolars
p = principle = 1500 dollars
r = interest rate = 0.03 (decimal form of 3%)
t = time in years = unknown (leave it as t for now)
Plug in those values mentioned above and solve for t.
Simple interest formula
i = p*r*t
900 = 1500*0.03*t
900 = 45*t
900/45 = 45*t/45
20 = t
t = 20
Answer: 20 years
=============================================
Problem 17, part B
p = 1500
r = 0.03
t = 5 years
A = p+p*r*t
A = 1500+1500*0.03*5
A = 1500+225
A = 1725
Answer: 1725 dollars
=============================================
Problem 17, part C
Factor out the GCF p, then divide both sides by 1+rt
A = p+p*r*t
A = p*1+p*r*t
A = p*(1+rt)
A/(1+rt) = p*(1+rt)/(1+rt)
A/(1+rt) = p
p = A/(1+rt)
Answer: p = A/(1+rt)
The right side is the fraction of A all over the quantity (1+rt) which may be more readable if written like so
If you're going to write it in the way p = A/(1+rt) then don't forget to use parenthesis.
i = simple interest = 900 dolars
p = principle = 1500 dollars
r = interest rate = 0.03 (decimal form of 3%)
t = time in years = unknown (leave it as t for now)
Plug in those values mentioned above and solve for t.
Simple interest formula
i = p*r*t
900 = 1500*0.03*t
900 = 45*t
900/45 = 45*t/45
20 = t
t = 20
Answer: 20 years
=============================================
Problem 17, part B
p = 1500
r = 0.03
t = 5 years
A = p+p*r*t
A = 1500+1500*0.03*5
A = 1500+225
A = 1725
Answer: 1725 dollars
=============================================
Problem 17, part C
Factor out the GCF p, then divide both sides by 1+rt
A = p+p*r*t
A = p*1+p*r*t
A = p*(1+rt)
A/(1+rt) = p*(1+rt)/(1+rt)
A/(1+rt) = p
p = A/(1+rt)
Answer: p = A/(1+rt)
The right side is the fraction of A all over the quantity (1+rt) which may be more readable if written like so
If you're going to write it in the way p = A/(1+rt) then don't forget to use parenthesis.
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Step-by-step explanation:
First question:
You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.
The sine function can never equal 2, so there is no triangle in this case.
Answer: no triangle
Second question:
You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.
One triangle exists for sure. Now we see if there is a second one.
Now we look at the supplement of angle C.
m<C = 52.5°
supplement of angle C: m<C' = 180° - 52.5° = 127.5°
We add the measures of angles B and the supplement of angle C:
m<B + m<C' = 63° + 127.5° = 190.5°
Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.
Answer: one triangle