Solution :
Given :
The height of the person is 5 foot.
The height of the lamppost is 12 foot.
Speed of the person away from the lamppost = 4 ft/s
Let the distance of the tip of the shadow of the perosn to the pole at t seconds after the person started walking away from the pole be d(t).
By similarity of the triangles, we see that
.................(i)
Here x is the distance from the person to the tip of the shadow. As it is given the speed of the person is 4 ft/s, then the distance of the person from the pole 4t. So we have,
x = d - 4t .............(ii)
Putting (ii) in (i) and solving for d is
d(t) = 6.85 t
So now if we derive d(t), we will get the wanted rate of the tip of the shadow.
∴ d'(t) = 6.85 ft/s
55
Explanation: the triangle is equal to 180, 35 plus 90 is 125 and 180-125= 55.
7^2 x 3.14 = 154 inches^2
This should be relatively easy, since most of us have learned and used the formula for the volume of a sphere: V = (4/3)* pi* r^3.
Just combine (4/3)pi into a single value, k, which results in V = kr^3.
Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
