Answer:
answer is down below
Step-by-step explanation:
4/10 0.4
<span>
Rate = 40/16 = 10/4 = 5/2 = 2.5 meters/second
Unit rate = ratio where denominator is 1 = 2.5/1 meters/second
</span>
Refer to the graph shown below. It confirms that points A, B and P are
collinear.
Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443
Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721
Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.
Answer: 2:1 ratio.
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
The answer is 42 because there are 10 adults and
M=4(10)+2
M=40+2
M=42