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:

Step-by-step explanation:
Step 1
List the length of the wingspan of the five butterflies

Step 2:
The two butterflies with the shortest wingspan has a wing length of
inches each.
Step 3:
Total length of the wingspan of the two butterflies with the shortest wingspan
= 
Final answer:
= 
We know that
[scale factor]=1/2
[dilated area of circle]=[original area of circle]*[scale factor]²
so
[dilated area of circle]=[original area of circle]*[1/2]²
[dilated area of circle]=[original area of circle]*[1/4]
therefore
the answer is
<span>The area will be 1/4 the original</span>
Answer:
5
Step-by-step explanation:
6 x 3 = 18
90 / 18 = 5