Answer:
The required expression would be
Step-by-step explanation:
Since, the amount formula is,
Where,
P = invested amount,
t = number of periods,
r = rate per period,
Given,
The invested amount at month 1, P = 4,
Number of periods from month 1 to month 4, t = 3
Amount at the end of fourth month, A = 256.
By substituting the values,
Hence, the amount of money at the end of t months.
9. 471.7 square units
10. 827.0 square units
<h3>Explanation:</h3>If you're going to have someone else solve your problem for you, it is much quicker and easier to use an appropriate computer or graphing calculator app. (See the attached.)
9. There are at least a couple of ways to approach this. The law of sines can be used to find the length of another side. Given two sides and the angle between them, a formula gives area.
<em>Law of Sines</em>
... a/sin(A) = c/sin(C)
Multiplying by sin(C) gives
... c = sin(C)·a/sin(A) = 19·sin(64°)/sin(20°) ≈ 49.9301
The angle between sides a and c is B, which has the value ...
... B = 180° -A -C = 180° -20° -64° = 96°
Then the area of the triangle is ...
... Area = (1/2)ac·sin(B) = (1/2)(19)(49.9301)(0.994522) ≈ 471.737 ≈ 471.7
10. Heron's formula will give the area of a triangle from its side lengths.
... s = (a+b+c)/2 = (51+38+45)/2 = 67
... Area = √(s(s-a)(s-b)(s-c)) = √(67·16·29·22) = √683936 ≈ 827.004 ≈ 827.0
