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2 answers:
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Z
Z=kX
When x=6, z=18,
Finding value of z,
18=k*6
k=3
Z=3X
when x=10,
Z=3*10
Z=30
Part B;
Z
z=
Where x is a constant of proportionality,
when x=3, z=2
2=
a=3*2
a=6
When x is 13,
Z=
Z=kX
When x=6, z=18,
Finding value of z,
18=k*6
k=3
Z=3X
when x=10,
Z=3*10
Z=30
Part B;
Z
z=
Where x is a constant of proportionality,
when x=3, z=2
2=
a=3*2
a=6
When x is 13,
Z=
Answer:
Maximum volume of the box will be 7.41 cubic feet.
Step-by-step explanation:
Open box has been made from a metal sheet measuring 3 ft and 8 ft.
Let four square pieces were removed from the four corners with one side measurement x ft.
Volume of the open box = Length × width × height
Length of the box = (3 - 2x) ft
Width of the box = (8 - 2x) ft
Height of the box = x ft
Volume of the box = (3 - 2x)(8 - 2x)x
V = (24 - 6x - 16x + 4x²)x
V = 24x - 22x² + 4x³
Now we take the derivative of V with respect to x and equate the derivative to zero,
V' = 24 - 44x + 12x²
V' = 0
12x² - 44x + 24 = 0
3x² - 11x + 6 = 0
3x² - 9x - 2x + 6 = 0
3x(x - 3) - 2(x - 3) = 0
(3x - 2)(x - 3) = 0
(3x - 2) = 0
and (x - 3) = 0
Therefore, x = 3,
For x = 0.67
Length of the box = (3 - 2x) = 3 - 1.34
= 1.66 ft
Width of the box = (8 - 2x) = 8 - 1.34
= 6.66 ft
Volume of the box = 0.67 × 1.66 × 6.66
V = 7.41 cubic feet.
Similarly, for x = 3,
Length of the box = (3 - 2\times 3) = -3
which is negative but the length of the box can not be negative.
Therefore, maximum volume of the box will be 7.41 cubic feet.
Check the picture below.
now, you can pretty much count the units off the grid for the segments ST and RU, so each is 7 units long, and are parallel, meaning that the other two segments are also parallel, and therefore the same length each.
so we can just find the length for hmmmm say SR, since SR = TU, TU is the same length,
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{-5}~,~\stackrel{y_2}{5})\qquad \qquad % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ SR=\sqrt{[-5-(-2)]^2+[5-1]^2}\implies SR=\sqrt{(-5+2)^2+(5-1)^2} \\\\\\ SR=\sqrt{(-3)^2+4^2}\implies SR=\sqrt{25}\implies SR=5](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0AS%28%5Cstackrel%7Bx_1%7D%7B-2%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%0AR%28%5Cstackrel%7Bx_2%7D%7B-5%7D~%2C~%5Cstackrel%7By_2%7D%7B5%7D%29%5Cqquad%20%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%5B-5-%28-2%29%5D%5E2%2B%5B5-1%5D%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B%28-5%2B2%29%5E2%2B%285-1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ASR%3D%5Csqrt%7B%28-3%29%5E2%2B4%5E2%7D%5Cimplies%20SR%3D%5Csqrt%7B25%7D%5Cimplies%20SR%3D5)
sum all segments up, and that's perimeter.
now, you can pretty much count the units off the grid for the segments ST and RU, so each is 7 units long, and are parallel, meaning that the other two segments are also parallel, and therefore the same length each.
so we can just find the length for hmmmm say SR, since SR = TU, TU is the same length,
sum all segments up, and that's perimeter.