there are 7 verticles on this triangular prism
Answer:
59.2 m
Step-by-step explanation:
The tangent of the angle of elevation will be the ratio of pole height to distance from the pole:
tan(2α) = h/10
tan(α) = h/70
The double-angle formula for tangents tells us ...
tan(2α) = 2tan(α)/(1 -tan(α)²)
Multiplying by the denominator and substituting from above, we get ...
(1 -(h/70)²)(h/10) = 2(h/70)
7(1 -(h/70)²) = 2 . . . . . . . . multiply by 70/h
1 - 2/7 = (h/70)² . . . . . . . . divide by 7, subtract 2/7-(h/70)²; next: square root
h = 70√(5/7) ≈ 59.2 . . . . meters
The height of the top of the pole is about 59.2 meters above the observer.
In order to find each of those values, we need to replace x in the appropriate function with the entry given for that function.
Part a
Replace x with 3 in the expression 3x+2:
Part b
Replace x with -2 in the expression 3x+2:
Part c
Replace x with -1 in the expression x²+x+1:
Part d
Replace x with 3 in the expression x²+x+1:
Part e
Replace x with a-2 in the expression 3x+2:
Part f
Replace x with a-2 in the expression x²+x+1:
Answer:
6.42 %
Step-by-step explanation:
Formula FV = PV ( 1 + i)^n i = periodic interest in decimal
FV = future value PV = present value
n = periods ( years in this case)
3412.23 = 2500 ( 1 + i)^5
3412.23/2500 = (1+i)^5
1.364892 = (1+i)^5
1.0641 = 1+ i
i = .0642 or 6.42 %