Answer:
Step-by-step explanation:
189² = 215² + 123² - 2(215)(123)cos x°
35,721 = 46,225 + 15,129 - 52,890 cos x°
35,721 = 61,354 - 52,890 cos x°
52,890 (cos x° ) = 25,633
cos x° = 25,633 ÷ 52,890 ≈ 0.4846
x° ≈ 61.01°
Answer:
6194.84
Step-by-step explanation:
Using the formula for calculating accumulated annuity amount
F = P × ([1 + I]^N - 1 )/I
Where P is the payment amount. I is equal to the interest (discount) rate and N number of duration
For 40 years,
X = 100[(1 + i)^40 + (1 + i)^36 + · · ·+ (1 + i)^4]
=[100 × (1+i)^4 × (1 - (1 + i)^40]/1 − (1 + i)^4
For 20 years,
Y = A(20) = 100[(1+i)^20+(1+i)^16+· · ·+(1+i)^4]
Using X = 5Y (5 times the accumulated amount in the account at the ned of 20 years) and using a difference of squares on the left side gives
1 + (1 + i)^20 = 5
so (1 + i)^20 = 4
so (1 + i)^4 = 4^0.2 = 1.319508
Hence X = [100 × (1 + i)^4 × (1 − (1 + i)^40)] / 1 − (1 + i)^4
= [100×1.3195×(1−4^2)] / 1−1.3195
X = 6194.84
Answer:
a.2s b.43.6m
Step-by-step explanation:
h(t)=−4.9t2+19.6t+24
24m = inittial possition
-4.9 t2= -1/2 g t2
19.6t= Vo t
as the initial velocity is positive, the ball is thrown up.
the maximum height of the ball is reached when the velocity is 0
V= Vo-gt=19.6m/s-9.8m/s2 t=0
t=19.6/9.8=2s
<u>it takes 2seconds for the ball to reach its maximum height</u>
h(t)=−4.9t2+19.6t+24
h(2)=-19.6m+39.2m+24=43.6m
<u>the maximum height of the ball is 43.6m</u>
Answer:
No solution.
Step-by-step explanation:
The range of the abs. val. function is [0, infinity). In other words, the output of this function is never negative. Thus, the equation you have posted has no solution.
10(2x)+x
21x is the original number
12x is the reversed number
24x is the reversed then doubled number
Set up an equation:
24x=21x+9
3x=9
x=3
The original number is 63 and the reversed number is 36, which then is 72 when doubled.