Help me plz! I need the answer...
1 answer:
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Answer:
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost=2046.16 cents
Step-by-step explanation:
Given that a rectangular box with a volume of 684 ft³.
The base and the top of the rectangular box is square in shape
Let the length and width of the rectangular box be x.
[since the base is square in shape, length=width]
and the height of the rectangular box be h.
The volume of rectangular box is = Length ×width × height
=(x²h) ft³
(1)
The area of the base and top of rectangular box is = x² ft²
The surface area of the sides= 2(length+width) height
=2(x+x)h
=4xh ft²
The total cost to construct the rectangular box is
=[(x²×20)+(x²×15)+(4xh×1.5)] cents
=(20x²+15x²+6xh) cents
=(25x²+6xh) cents
Total cost= C(x).
C(x) is in cents.
∴C(x)=25x²+6xh
Putting
Differentiating with respect to x
To find minimum cost, we set C'(x)=0
ft.
Putting the value x in equation (1) we get
≈36.23 ft.
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents
=2046.16 cents
Answer:
It would look like the picture I attached at the bottom.
Step-by-step explanation:
We know that the slope is -3 and the y intercept is (0,4) (plugging in 0 for x will get you that point), and then you can just graph an equation like you normally would, using rise/run to go down 3 units for every one unit you go right, and plugging in easy x values to check your work.
It gets a little tricky because the question then adds the inequality, and we see that y is now less than <em>or equal to </em>the original equation.
Since it is less than, we can shade all the values below the graph.
(Also, you should probably note for future reference that if it was just less than, the shading would look the same while the graph itself would be dotted because the values on the line are nor included in the solution set).
Desmos is a great website to use if you're having trouble graphing in the future :)
