First, we plug in the numbers.
$40 = P(4%)(2)
4% = 0.04
40 = P * 0.04 * 2
Divide each side by 2
20 = P * 0.04
Divide by 0.04
P = 500
Lets check it!
500 * 0.04 * 2 = 40
500 * 0.04 = 20
20 * 2 = 40
40 = 40
Answer: A) none of the equations are identities
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Part 1
Plug in theta = 0
sin(theta+pi/2) - cos(theta+pi/6) = 2*cos(theta) - sin(theta)
sin(0+pi/2) - cos(0+pi/6) = 2*cos(0) - sin(0)
1 - sqrt(3)/2 = 2*1 - 0
0.13 = 2
which is a false equation
So we do not have an identity in equation 1.
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Part 2
Plug in theta = 0
sin(theta+pi/6) + cos(theta+pi/3) = (sqrt(2)/3)*sin(theta) + 2*cos(theta)
sin(0+pi/6) + cos(0+pi/3) = (sqrt(2)/3)*sin(0) + 2*cos(0)
1/2 + 1/2 = 0 + 2
1 = 2
which is also false
This is not an identity either.
Answer:
a) -45, <u>-43.5, -42, -40.5</u>, -39. f(n) = -45 + 1.5(n-1)
b) -34, 3, 40, 77. f(n) = -34 + 37(n-1)
Step-by-step explanation:
The explicit formula for an arithmetic formula can be defined as: f(n) = f(1) + d(n-1).
Where n is the number, and d is the common difference.
Answer: 15.44 m
Step-by-step explanation:
We can think this as two triangle rectangles.
In both cases, the adjacent cathetus is 120m.
When the angle is 32°, the opposite cathetus will be the height of the cliff.
When the angle is 37°, the opposite cathetus will be the heigth of the cliff plus the height of the flagpole.
Then we need to compute both of them and calculate the difference.
We can use the trigonometric relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
in this case we have:
Tan(32°) = (height of the cliff)/(120m)
Tan(32°)*120m = height of the cliff = 74.98m
Now we can use the other angle to compute:
Tan(37°) = (heigth of the cliff + heigth of the flagpole)/120m
Tan(37°)*120m = heigth of the cliff + heigth of the flagpole = 90.42m
Then the height of the flagpole will be:
H = 90.42m - 74.98m = 15.44 m
Last answer. 288. Modifying above 8 with bar
