Answer:
62.8 km per min
Step-by-step explanation:
Let the diagram of this situation is shown below,
In which
is the angle made by light to the straight line joining the lighthouse and P,
∵ Light makes 4 revolutions per minute.
Also, 1 revolution =
radians
So, the change in angle with respect to t ( time ),

Let x be the distance of beam from P,

Differentiating with respect to x,



If x = 1 km,



Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min
Answer:
a If we make the parent function 2sqrt(x) then we translate to the left 4 units and up 5 units
Step-by-step explanation:
y = sqrt(4x+16) +5
y = sqrt(4 (x+4)) +5
y = sqrt(4) sqrt(x+4) +5
y =2sqrt(x+4) +5
f(x) = sqrt(x) this is the parent function
g(x) = sqrt(x+4) This moves it to the left 4 units
h(x) = 2 sqrt (x+4) This stretches it by 2 in the y direction
j(x) = 2 sqrt(x+4) +5 This moves it up by 5 units
y = 2sqrt(x+4) +5
This is to the left 4 units, stretched 2 units in the y direction and up 5 units
If we make the parent function 2sqrt(x) then we translate to the left 4 units and up 5 units
Answer:
12, 5, 1 1/2, -12, -19
Step-by-step explanation:
hope this helped!
Answer:
We conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 25.4 minutes
Sample mean,
= 22.1 minutes
Sample size, n = 15
Alpha, α = 0.10
Sample standard deviation, s = 5.3 minutes
First, we design the null and the alternate hypothesis
We use one-tailed t(left) test to perform this hypothesis.
Formula:
Putting all the values, we have

Now,
Since,
We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Thus, there is enough evidence to conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.