Can someone help me this is my last question on this assignment
2 answers:
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Answer:
(a)Therefore the volume of the box is 361.19 cubic ft.
(b)Therefore the volume of the box is 361.19 cubic ft.
Step-by-step explanation:
Given that,
Squares with sides length x are cut out from of each corner of a rectangular piece of cardboard measuring 23 ft and 13 ft.
Now the length of the box is =(23-2x) ft
The width of the box is =(13-2x) ft
The height of the box is= x
The volume of the box is = Length×width×Height
=(23-2x)(13-2x)x cubic ft
= 299x-72x²+4x³ cubic ft
Let,
V=299x-72x²+4x³
Differentiating with respect to x
V'= 299-144x+12x²
Again differentiating with respect to x
V''= -144+24x
To find the maximum volume, we set V'=0
∴299-144x+12x²=0
Applying quadratic formula , here a=12,b= -144 and c=299
For x= 9.33 , the width of the box will negative which is impossible.
So, x= 2.67
So, at x=2.67, the volume of the box will be maximum.
Therefore the volume of the box is
=(299x-72x²+4x³) cubic ft
=361.19 cubic ft
(b)
The value of s will same with the value of x
so the volume of the box also remains same.
Therefore the volume of the box is 361.19 cubic ft
Answer:
1.92%
Step-by-step explanation:
The probability for first case, picking a queen out of deck, will be:
as there will be 4 queens in a deck, one of each suit.
For the second pick, the probability of picking a diamond card, will be:
here the total will remain 52 as he has replaced the first card and not kept it aside and there will be 13 cards in diamond suit (including the three face cards).
Thus the net probability for both cases will be:
Thus total probability for the combined two cases will be 1.92%