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:
The value of 
Step-by-step explanation:
Given that 
now to find from the given functions f(x) and f'x
let
Then put x=1 in above function we get
(from the table f(1)=3 and f(3)=6)
Therefore h(1)=6
Now to find h'(1)
Let
(since )
put x=1 in above function we get
(From the table 
and 
)
Therefore
First, we count how far reached the Nell:
3,5 * 16 = 56 miles
Secondly, we count how far reached the Kristin:
3,5 * 18 = 63 miles
Now we expect the difference in the distance between them:
63 - 56 = 7 miles
The results that Kristin about seven miles driven more than Nell.
Step-by-step explanation:
the sum of all angles in a triangle is always (ALWAYS !) 180°.
180 = 31 + 35 + x = 66 + x
x = 180 - 66 = 114°
