Answer:
The tip of the man shadow moves at the rate of 
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y = 
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
----(1)
We are given 
. Plug in the equation (1), we get
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
Answer:
g(-2) = -6
g(0) = 0
g(5) = 15
Step-by-step explanation:
For each of the evaluations, you have to plug in the number everywhere where there is an x
Answer:
Her usual rate is 0.8333 miles per hour.
Step-by-step explanation:
The velocity formula is given by:
In which d is the distance and t is the time.
She completed the first half of the walk 1 mi/h faster than usual
Her usual rate is v. 1mph faster is v + 1.
The second half of the walk 2 mi/h slower than the first half.
The first half is v + 1.
2mph slower is v + 1 - 2 = v - 1. Then
Total rate:
7.2 hours, and 6 miles. So
One half is v+1 and the other is v - 1. This is why each is multiplied by 0.5.
Her usual rate is 0.8333 miles per hour.
It was stated in the problem that a given volume of a is inversely proportional with the pressure of the system. It means that the as the volume increases, the pressure would decrease and as the volume decreases, the pressure would increase. We would express it as:
V α 1/P
To change it to an equality, we introduce a proportionality constant, k. We do as follows:
V = k/P
So, to determine what is asked, we need to first calculate for the value of k.
V = k/P
At V = 160 m^3 P = 108 cmHg
160 = k / (108)
k = 17280
Thus, at P = 87 cmHg
V = 17280 / 87
V = 198.62 m^3
