Given parameters:
Number of boxes Athena bought for the party = x
Number of cookies per box = 10
Number of cookies she brought to the party = 70
Number removed = 2 boxes
Unknown:
Equation of the number of boxes = ?
Solution:
1 box of cookies contains 10 cookies
If Athena, removed 2 boxes, in those two boxes, we have 20 cookies
Total number of cookies = 70 + 20 = 90 cookies;
So;
x =
Therefore;
x = boxes
V = Length x Width x Height = 288
If we call the width w
then length = 3w
And height = 288/(3w x w)
Assuming none of the material used overlaps the box will need 6 faces ( top, bottom, 2 ends and 2 sides)
Area of material = 2 x LW + 2 x HW + 2 x HL
= 2(3w x w + 288/(3w x w) x w + 288/(3w x w) x 3w)
= 2(3w^2 + 288/3w + 288/w)
= 2(3w^2 + 96/w + 288/w)
= 2(3w^2 + 384/w)
= 6w^2 + 768/w
Taking the derivative in terms of w
A’ = 12w - 768/w^2
A’ is zero when 12w = 768/w^2
w^3 = 768/12 = 64
w = cube root of 64 = 4
This makes the box with the minimum materials 12 x 4 x 6
So the length that uses the minimum material is 12 inches
Answer:
x × 1/2 - 3
Step-by-step explanation:
in slope intercept form an equation is written in y=mx+b where m is the slope and b is the y intercept
from the graph you can see the line goes up 1 and right 2, up 1 right 2, etc. that means the slope is positive 1/2
the line cross the y access at -3, therefore the y intercept is -3
so
X is -2 and Y is -3 good luck
The rate at which the gas powered pump deliver water is 160.9 litres per seconds
<h3>How to convert rate?</h3>
The gas powered water pump delivers 42.50 gallons of water per minute.
Therefore,
1 gallon = 3.78541 litres
42.50 gallons = ?
cross multiply
volume = 42.50 × 3.78541 = 160.879925 litres
Hence,
60 seconds = 1 minutes
1 second = ?
time = 1 / 60 = 0.01666666666 seconds
Hence,
rate = 160.9 litres per second
learn more on rate here: brainly.com/question/20561529
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