Sam has $40. He buys a book for $12.99 and a puzzle for $15.49.
2 answers:
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Option D: is the x-coordinate
Explanation:
It is given that the coordinates of the line segment are A(3,2) and B(6,11).
Since, the line is partitioned by the point C by the ratio AC : BC = 2 : 3
The distance between the x-coordinates is 3 units.
To determine the value of the x-coordinate for point C, let us divide the value of x-coordinate from the ratio divided by the sum of ratio.
The value of x-coordinate from the ratio is 2.
Sum of the ratio is 2 +3 = 5
Thus,
The x - coordinate = value of x-coordinate from the ratio / Sum of ratio = 2/5
Substituting the values, we have,
The x - coordinate of the Point C =
Thus, Option D is the correct answer.
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