The two parabolas intersect for
and so the base of each solid is the set
The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, 
. But since -2 ≤ x ≤ 2, this reduces to 
.
a. Square cross sections will contribute a volume of
where ∆x is the thickness of the section. Then the volume would be
where we take advantage of symmetry in the first line.
b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of
We end up with the same integral as before except for the leading constant:
Using the result of part (a), the volume is
c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is
and using the result of part (a) again, the volume is
Well first you have to divide 3 by 4, which is 0.75 or 3/4
One company wants $10 per 3.5 hours, so they want 10 / 3.5 ≈ 2,86 dollars per hour (after rounding to the closest hundreths).
Second company wants $1.25 per half an hour, so they want 2 * 1,25 = 2,50 dollars per hour.
The unit rate is 2,86:2,50
Answer:
y= 48 + 0.1x
x= miles driven
Step-by-step explanation:
<u>We need to calculate the fixed and variable cost (per mile) of renting a car. To do that, we will use the high-low method:</u>
Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)
Variable cost per unit= (65 - 58) / (170 - 100)
Variable cost per unit= $0.1 per mile
Fixed costs= Highest activity cost - (Variable cost per unit * HAU)
Fixed costs= 65 - (0.1*170)
Fixed costs= $48
Fixed costs= LAC - (Variable cost per unit* LAU)
Fixed costs= 58 - (0.1*100)
Fixed costs= $48
y= 48 + 0.1x
x= miles driven
Answer:
c=10mm
Step-by-step explanation:
Using pythagoras theorem,
hypotenuse²=base²+altitude²
=√19²+9²
=19+81
=100
Hypotenuse²=100
Hypotenuse=√100
=10
