1) We have 1300 packing peanuts, and 20 ft^2. Therefore, to find out how many packing peanuts there are per square foot, we divide the number of peanuts (1300) by the number of square feet (20 ft^2). This gives us 1300 / 20 = 65 packing peanuts per square foot.
2) We do not know the current volume of the box which fits the 1300 packing peanuts (all we know is its area). But it is reasonable to expect that if we increase the volume by 25%, the number of packing peanuts will also increase by 25%. This means we can fit 1300*(1.25) = 1625 peanuts in the larger box.
3) This will depend on how the box is larger. If its height remains the same, and its floor area increases to accommodate the greater volume, then the number of packing peanuts per square foot remains the same.
However, if the height of the box is different, then the number of packing peanuts per square foot will change, since the floor area will not increase by the same 25% any more.

3 0

2 years ago

Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the following. (Enter your ans

zubka84 [21]

a) Intervals of increase is where the derivative is positive
b) Intervals of decrease is where the derivative is negative. 

c) Inflection points of the function are where the graph changes concavity that is the point where the second derivative is zero 

d)
Concave up- Second derivative positive 
Concave down- second derivative negative 

f(x) = 4x^4 − 32x^3 + 89x^2 − 95x + 31
f '(x) = 16x^3 - 96x^2 + 178x - 95 
f "(x) = 48x^2 - 192x + 178 

By rational root theorem the f '(x) has one rational root and factors to: 
f '(x) = (2x - 5)*(8x^2 - 28x + 19) 

Using the quadratic formula to find it's two irrational real roots. 
The f "(x) = 48x^2 - 192x + 178 only has irrational real roots, use quadratic formula which will be the inflection points as well.

4 0

3 years ago

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