9514 1404 393
Answer:
2 3/4 years
Step-by-step explanation:
The interest is given by the formula ...
I = Prt . . . . . . principal P at annual rate r for t years
Solving for t gives ...
t = I/(Pr)
t = 4167.90/(16840×0.09) = 2.75
The duration of the loan is 2 3/4 years.
Answer: b=4, c=2
Step-by-step explanation:
Since ΔXYZ and ΔVUW are congruent, we can set the sides equal to each other.
c+16=9c [subtract both sides by c]
16=8c [divide both sides by 8]
c=2
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10b=b+36 [subtract both sides by b]
9b=36 [divide both sides by 9]
b=4
Answer:
x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(2 x) = cos(x + 30 °)
Rewrite the right hand side using cos(θ) = sin(θ + π/2):
sin(2 x) = sin(30 ° + π/2 + x)
Take the inverse sine of both sides:
2 x = -30 ° + π/2 - x + 2 π n_1 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Add x to both sides:
3 x = -30 ° + π/2 + 2 π n_1 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Divide both sides by 3:
x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or 2 x = 30 ° + π/2 + x + 2 π n_2 for n_2 element Z
Subtract x from both sides:
Answer: x = -10 ° + π/6 + (2 π n_1)/3 for n_1 element Z
or x = 30 ° + π/2 + 2 π n_2 for n_2 element Z
Note that
- 12=2·2·<u>3</u>;
- 20=2·2·5;
- 36=2·2·<u>3</u>·3.
The common factors of these three numbers are 2, 2. Also numbers 12 and 36 have one more common factor <u>3</u>, then the least common multiple is
LCM(12,20,36)=2·2·<u>3</u>·5·3=180 sec=3 min (here first you write all common factors between all three numbers, then between two numbers and at last all remaining factors).
Answer: all three experiments will need to be checked after 3 minutes passed, then after 6 minutes passed, then after 9 minutes passed and so on.
