t) A car rental agency rents 210 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income?

$34.5

$5,951.5

Step-by-step explanation:

P(x)=27+x

Quantity (x)=210-5x

Income(y)=price×quantity

=(27+x)(210-5x)

=5670-135x+210-5x^2

y= -5x^2+75x+5670

dy/dx= -10x+75=0

-10x=-75

x=-75/-10

=7.5

x=7.5

Maximum income=27+x

=27+7.5

=$34.5

Total income=(27+x)(210-5x)

=(27+7.5){210-5(7.5)}

=(34.5)(210-37.5)

=(34.5)(172.5)

=$5,951.25

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.