The main rules that we use here are :
i)
for nonnegative values a and b.
ii)
.
Thus, first 'decompose' the numbers in the radicals into prime factors:
.
By rule (i) we write:
.
We can collect these terms as follows:
, and by rule (ii) we have:
Answer:
.
If the diameter is 10.5 then the radius is 5.25.
This is because the radius of a diameter is half the diameter.
So
10.5/2
= 5.25
Therefore the radius is 5.25
Answer: Using the proportions between the segments, the area of the triangles are:
1. Area of triangle ADC is 25 in^2.
2. Area of triangle BDC is 15 in^2.
3. Area of triangle CDE is 12 in^2.
Please, see the attached files.
Thanks.
Answer: The velocity of the ball is 108.8 ft/s downwards.
Step-by-step explanation:
When the ball is dropped, the only force acting on the ball will be the gravitational force. Then the acceleration of the ball will be the gravitational acceleration, that is something like:
g = 32 ft/s^2
To get the velocity equation we need to integrate over time, to get:
v(t) = (32ft/s^2)*t + v0
where v0 is the initial velocity of the ball. (t = 0s is when the ball is dropped)
Because it is dropped, the initial velocity is equal to zero, then we get:
v(t) = (32ft/s^2)*t
Which is the same equation that we can see in the hint.
Now we want to find the velocity 3.4 seconds after the ball is dropped, then we just replace t by 3.4s, then we get:
v(3.4s) = (32ft/s^2)*3.4s = 108.8 ft/s
The velocity of the ball is 108.8 ft/s downwards.
