Answer:
26 ft square by 13 ft high
Step-by-step explanation:
The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...
2·(8788 ft^3) = (26 ft)^3
The square bottom of the tank is 26 ft square, and its height is 13 ft.
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<em>Solution using derivatives</em>
If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...
x^2 + 4x(8788/x^2) = x^2 +35152/x
The derivative of this is zero when area is minimized:
2x -35152/x^2 = 0
x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576
x = 26
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As the attached graph shows, a graphing calculator can also provide the solution.
Answer:
A. 5 ft, 4 ft, 3 ft
Step-by-step explanation:
When you use the Pythagorean theorem with the numbers of the first choice, you find that these could be the sides of a right triangle:
3² + 4² = 9 + 16 = 25 = 5²
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You have found the correct answer at this point.
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If you want to check, you can examine the other choices:
C: 6² +10² = 136 ≠ 11²
B: 2² +4² = 20 ≠ 6²
D: 5² +10² = 125 ≠ 15²
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<em>Comment on 3-4-5 triangle</em>
As you can see from the above, side measures of 3, 4, and 5 will form a right triangle. This is the smallest set of integers that will do so. It is also the ratios of the only set of side lengths in arithmetic progression that will do so.
This latter fact can help you rule out choices B and D in this problem, because each of those has sides in the progression 1 : 2 : 3.
(3, 4, 5) triangles come up often in algebra and geometry problems. This is a useful "Pythagorean triple" to remember.
Answer:
Answer: x= -6 and y= -7
Step-by-step explanation:
Substitute 2x+5 for y in y=3x+11:
y=3x+11
2x+5=3x+11
2x+5+−3x=3x+11+−3x(Add -3x to both sides)
−x+5=11
−x+5+−5=11+−5(Add -5 to both sides)
−x=6
−x−1=6−1(Divide both sides by -1)
x=−6
Step: Substitute −6 for x in y=2x+5:
y=2x+5
y=(2)(−6)+5
y=−7(Simplify both sides of the equation)
-Source: MathPapa
Answer:
50/50. there is no outside force that decides otherwise
