Alrighty
squaer base so length=width, nice
v=lwh
but in this case, l=w, so replace l with w
V=w²h
and volume is 32000
32000=w²h
the amount of materials is the surface area
note that there is no top
so
SA=LW+2H(L+W)
L=W so
SA=W²+2H(2W)
SA=W²+4HW
alrighty
we gots
SA=W²+4HW and
32000=W²H
we want to minimize the square foottage
get rid of one of the variables
32000=W²H
solve for H
32000/W²=H
subsitute
SA=W²+4WH
SA=W²+4W(32000/W²)
SA=W²+128000/W
take derivitive to find the minimum
dSA/dW=2W-128000/W²
where does it equal 0?
0=2W-1280000/W²
128000/W²=2W
128000=2W³
64000=W³
40=W
so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
20=H
the box is 20cm height and the width and length are 40cm
equation in slope-intercept form is:

Step-by-step explanation:
The general form of slope-intercept form is:

where m is the slope and b is the y-intercept
In the question we are given slope m=9 and a point(0,7)
We will find b i.e y-intercept

So, value of b=7 and value of slope m=9
So, equation in slope-intercept form is:

Keywords: slope-intercept form
Learn more about slope-intercept form at:
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Answer:
False
Step-by-step explanation:
In this case, i woudnt reccomend to use integration by parts, becuase you are not simplifying the expression by doing an integration and a derivation. It is not easy to integrate 1/x³+1, and if you derivate it, then a natural logarithm would appear, and the integral wont be easier after this parts step.
It is a better idea to use integration by substitution. Note that if you replace x³+1 by a variable y, we have that dy = 3x² dx. We can easily make a 3xdx appear in the integral by multiplying and dividing by 3, solving the integral easily:

(Note that, if x ranges from 0 to 1, then u = x³+1 ranges from 0³+1 = 1 to 1³+1 = 2)
The correct answer is B: 2,4,5, 10
We know that 100 is not divisible by 3 because 100/3 is 33.33 repeating, which is an irrational number.
We also know that 100 is not divisible by 6 because 100/6 is 16.66 repeating which is also an irrational number.
100/2=50 (rational)
100/4=25 (rational)
100/5=20 (rational)
100/10=20 (rational)
Hope this helps!