Question

The cost, in dollars, of producing x belts is given by Upper C left parenthesis x right parenthesis equals 805 plus 18 x minus 0.075 x squared. The revenue, in dollars, of producing and selling x belts is given by Upper R left parenthesis x right parenthesis equals 31 x Superscript six sevenths . Find the rate at which average profit is changing when 676 belts have been produced and sold. When 676 belts have been produced, the average profit is changing at nothing ▼ belts per dollar dollars per belt for each additional belt.

Answer #1

A record club has found that the marginal profit,
Upper P prime left parenthesis x right parenthesisP′(x) ,
in cents, is given by
Upper P prime left parenthesis x right parenthesis equals
negative 0.0008 x cubed plus 0.35 x squared plus 52.9
xP′(x)=−0.0008x^3+0.35x^2+52.9x
for
x less than or equals x≤400 ,
where x is the number of members currently enrolled in the club.
Approximate the total profit when
240 members are enrolled by computing the sum
Summation from i equals...

Given Cost and Price (demand) functions Upper C left
parenthesis q right parenthesis equals 120 q plus 45000 and p left
parenthesis q right parenthesis equals negative 2.1 q plus 900,
what is the marginal revenue when profits are $14000?

A vitamin water maker finds that the revenue, in dollars, from
the sale of x bottles of vitamin water is given by
Upper R left parenthesis x right parenthesis equals 8.6 x
Superscript 0.3 Baseline .R(x)=8.6x0.3.
Find the rate at which average revenue is changing when 70
bottles of vitamin water have been produced. Round the answer to
four decimal places.
A.negative $ 0.1318 divided by bottle−$0.1318/bottle
B. minus−$ 0.0044 divided by bottle$0.0044/bottle
C.$ 0.1318 divided by bottle$0.1318/bottle
D.$ 0.0044...

Market supply and demand for ovens are given by p equals Upper S
left parenthesis q right parenthesis equals 1750 plus 5 q and p
equals Upper D left parenthesis q right parenthesis equals 2500
minus 10 q. The equilibrium price is $2000 per oven.
(a) Find the market surplus up to equilibrium using the
integral definition.
(b) Verify the market surplus by calculating
MSequalsCSplusPS.

Match the following equation with its graph.
left parenthesis x minus 4 right parenthesis squared plus left
parenthesis y minus 3 right parenthesis squared equals
36(x−4)2+(y−3)2=36
Choose the correct graph below.
A.
-157-715xy
A coordinate system has a horizontal x-axis labeled from
negative 15 to 7 in increments of 1 and a vertical y-axis labeled
from negative 7 to 15 in increments of 1. A circle has center
(negative 4, 3) and radius 6.
B.
-157-157xy
A coordinate system has...

For the demand function
q equals Upper D left parenthesis x right parenthesis equals
StartFraction 400 Over x EndFractionq=D(x)=400x,
find the following.
a) The elasticity
b) The elasticity at
xequals=77,
stating whether the demand is elastic, inelastic, or has unit
elasticity
c) The value(s) of x for which total revenue is a maximum
(assume that x is in dollars)

The marginal cost of a product can be thought of as the cost of
producing one additional unit of output. For example, if the
marginal cost of producing the 50th product is $6.20, it cost
$6.20 to increase production from 49 to 50 units of output. Suppose
the marginal cost C (in dollars) to produce x thousand mp3 players
is given by the function Upper C left parenthesis x right
parenthesis equals x squared minus 120 x plus 7500.C(x) =...

Suppose that Upper X has a discrete uniform distribution f
left-parenthesis x right-parenthesis equals StartLayout
left-brace1st Row 1st Column 1 divided by 3, 2nd Column x equals
1,2,3 2nd Row 1st Column 0, 2nd Column otherwise EndLayout A random
sample of n equals 35 is selected from this population. Find the
probability that the sample mean is greater than 2.1 but less than
2.6. Express the final answer to four decimal places (e.g. 0.9876).
The probability is

A proton moves through a uniform magnetic field given by
ModifyingAbove Upper B With right-arrow equals left-parenthesis
10.5ModifyingAbove i With caret minus 21.6ModifyingAbove j With
caret plus 22.1ModifyingAbove k With caret right-parenthesis mT. At
time t1, the proton has a velocity given by v Overscript
right-arrow EndScripts equals v Subscript x Baseline i Overscript
caret EndScripts plus v Subscript y Baseline j Overscript caret
EndScripts plus left-parenthesis 1.52? km/s right-parenthesis k
Overscript caret EndScripts and the magnetic force on the...

A keyboarder's speed over a 55-min interval is given by the
following function, where Upper W left parenthesis t right
parenthesis W (t) is the speed, in words per minute, at time
t.
Upper W left parenthesis t right parenthesis W(t)equals=negative
3 t squared plus 6 t plus 45
a) Find the speed at the beginning of the interval.
b) Find the maximum speed and when it occurs.
c) Find the average speed over the 55-min interval.

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