Suppose:
C=cost
c=cost per kilo-watt hour
w=number of watts
h=number of hours
thus
C=kwhc
where:
k=constant of proportionality:
k=C/(whc)
but
C=15 when w=6000, h=10/60=1/6 hours, c=7.5 cents per kw/h
thus
k=15/(6000*1/6*7.5)
k=0.002
thus:
C=0.002(whc)
hence:
when
h=70*2=140=140/6=70/3 hours the cost will be:
C=0.002(6000*70/3*7.5)
C=2100 cents
C=$21
Answer:
No because the line does not pass through the origin
Step-by-step explanation:
to be proportional it has to go through the origin
Answer:
I’m pretty sure it’s Jeremiah
Step-by-step explanation:
Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x = ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
Given parameters:
Cost per pound of Arabica coffee = $28 per pound
Cost of Robusta coffee = $8.75
Given number of pounds of Robusta Coffee = 3 pounds
Total cost of blend per pound = $15.50
Unknown:
Number of pounds of Arabica coffee = ?
Solution:
Let the number of pounds of Arabica coffee = A;
We have to interpret this problem algebraically and solve;
28A + 8.75(3) = 15.5(A + 3)
Now solve the expression above for A;
28A + 26.25 = 15.5A + 46.5
28A - 15.5A = 46.5 - 26.25
12.5A = 20.25
A = 1.62
Number of pounds of Arabica Coffee is 1.62 pound