Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B
is 200 feet. Angle A has a measure of 33°, and angle B has a measure of 63°. Find b.
2 answers:
A suitable solver will tell you instantly that the measure of b is 179.18 ft.
_____
If you want to do it yourself (meaning also with the aid of a calculator), you can use the Law of Sines. The given side is side "c", so you need the measure of angle C. That will be
180° -33° -63° = 84°
Then side "b" can be found from
b/sin(B) = c/sin(C)
b = c*sin(B)/sin(C)
b = (200 ft)*sin(63°)/sin(84°) ≈ 179.183 ft
_____
If you want to do it yourself (meaning also with the aid of a calculator), you can use the Law of Sines. The given side is side "c", so you need the measure of angle C. That will be
180° -33° -63° = 84°
Then side "b" can be found from
b/sin(B) = c/sin(C)
b = c*sin(B)/sin(C)
b = (200 ft)*sin(63°)/sin(84°) ≈ 179.183 ft
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Answer:
We accept the null hypothesis and conclude that voltage for these networks is 232 V.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 232 V
Sample mean, = 231.5 V
Sample size, n = 66
Sample standard deviation, s = 2.19 V
Alpha, α = 0.05
First, we design the null and the alternate hypothesis
We use Two-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We accept the null hypothesis and conclude that voltage for these networks is 232 V.
Answer:
(a)
(b)
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
Therefore, we have:
At point (12,30000)
Therefore:
(b)Revenue
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
Therefore:
- Optimal ticket price:$12
- Maximum Revenue:$360,000