Answer:
x + y = 41
x - y = 13
------------------
2x = 54..............We divide 2 such that
x = 27
Then we plug 27 into the equation such that
27 + y = 54.................Subtract 27 to get
y = 14
Step-by-step explanation:
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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
Answer:
Step-by-step explanation:
<u>Given inequality:</u>
<u>Since b is negative, when multiplied by b, the inequality changes to opposite direction:</u>
If the probability of even is 1/4 that is a quarter. A quarter of 120 is 120/4= 30 times
