Using the law of cosines and sines, the measure of angle B is: 38.4°.
<h3>What is the Law of Cosines and Sines?</h3>
Law of cosines is: c = √[a² + b² ﹣ 2ab(cos C)]
Law of sines is: sin A/a = sin B/b = sin C/c
Use the law of cosines to find c:
c = √[12² + 18² ﹣ 2(12)(18)(cos 117)]
c ≈ 25.8
Use the law of sines to find angle B:
sin B/b = sin C/c
sin B/18 = sin 117/25.8
sin B = (sin 117 × 18)/25.8
sin B = 0.6216
B = sin^(-1)(0.6216)
B = 38.4°
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C = $5.85
$5.85 = 0.35t + 0.6
-.6 -.6
$5.25 = 0.35t
------- --------
.35 .35
15 = t
15 minutes
Answer:
6/5 or 1.2
Step-by-step explanation:
First, you need to multiply the length by how much the width is of the length, which is 2/3, so you multiply 1 4/5 by 2/3 and you get 6/5. If you want the decimal form, then the answer will be 1.2.
Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.
