Answer:
it's A
Step-by-step explanation:
1) To make a rectangular box you need to cut squares from the four corners of the rectangular sheet.
2) Call x the length of the sides of the squares cut off.
3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)
4) The height of the box will be x
5) The volume of the box will be the area of the base times the height:
Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x
6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>
d (volume) / dx = 12x^2 - 84x + 104 = 0
7) Solve the quadratic equation 12x^2 - 84x + 104 = 0
=> 4(3x^2 - 21x + 26) = 0
=> 3x^2 - 21x + 26 = 0
=> 3 (x^2 - 7x) + 26 = 0
=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0
=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0
=> 3 (x - 7/2)^2 = 3*49/4 - 26
=> (x -7/2)^2 = (49/4 - 26/3)
=> x = 7/2 +/- √(49/4 - 26/3)
x = 7/2 + √3.583 and x = 7/2 - √3.583
x = 5.393 and x = 1.607
=> Volume =
1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning
2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer
Answer: 75.27 in^3
I hope this helps you
xy=-6 y=-6/x
2y-x=8
-x+2.-6/x=8
-x^2-12=8x
x^2+8x+12=0
(x+6). (x+2)=0
x+6=0 x=-6
x+2=0 x=-2
x=-6 -6.y=-6 y=1
x=-2 -2.y=-6 y=3
Answer: Alvin = 42 yrs , Elga = 21 yrs
Step-by-step explanation:
Let Elga's age be x , and Alvin's age be y ,since Alvin is two times Elga's age , then
Alvin's age = 2x , that is
y = 2x ............... equation 1
The sum of their ages is 63 implies
x + y = 63 .............. equation 2
Solving the resulting linear equations by substitution method.
Substitute equation 1 into equation 2 , we have
x + 2x = 63
3x = 63
x = 63/3
x = 21
Therefore : Elga is 21 years old , then Alvin will be 21 x 2, which will be 42
Answer:
Option B is correct
It must be a positive number since it represents a number of hours.
Step-by-step explanation:
As per the statement:
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.
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Given the equation as:
Using distributive property,
Combine like terms;
Subtract 40 from both sides we have;
Divide both sides by -8 we have;
h = 14 hours
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Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.
