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:
The ∆ given is an isosceles ∆ with a right angle measuring 90°, and two congruent angles measuring 45° each.
Using trigonometric ratio formula, we can find the lengths of the missing side as shown below:
Finding e:
hyp = 26
opp = e = ?
Plug in the values into the formula
Multiply both sides by 26
Since side e is of the same length with side f, therefore, the length of side f = 
3/4+2/3= 17/12
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
33 can be divided evenly by numbers other than one or itself
