Question

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 1 to 6 Upper P prime left parenthesis x Subscript i Baseline right parenthesis Upper Delta x∑i=16P′xiΔx

with

Upper Delta x equals 40Δx=40.

Answer #1

Suppose that E and F are two events and that
Upper P left parenthesis Upper E right
parenthesisP(E)equals=0.8
and
Upper P left parenthesis F|E right
parenthesisP(F|E)equals=0.2
What is
Upper P left parenthesis Upper E and Upper F right
parenthesisP(E and F)?

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...

The vector field F with rightwards arrow on top left parenthesis
x comma y right parenthesis equals open angle brackets s e c
squared x comma space 3 y squared close angle brackets is
conservative.
Find f left parenthesis x comma y right parenthesis such that F
with rightwards arrow on top equals nabla f .
a.
f equals 2 space s e c x plus 6 y
b.
f equals y tan x plus x y cubed...

Let P(Z)equals=0.390.39, P(Y)equals=0.410.41, and
P(Zintersect∩Y)equals=0.170.17. Use a Venn diagram to find (a)
Upper P left parenthesis Upper Z prime intersect Upper Y prime
right parenthesisPZ′∩Y′, (b) Upper P left parenthesis Upper Z
prime union Upper Y prime right parenthesisPZ′∪Y′, (c) Upper P
left parenthesis Upper Z prime union Upper Y right
parenthesisPZ′∪Y, and (d) Upper P left parenthesis Upper Z
intersect Upper Y prime right parenthesisPZ∩Y′.

1. (a) Construct the matrix Upper A equals left bracket Upper A
Subscript ij right bracketA=Aij if A is 2*3 and
Upper A Subscript ij Baseline equals negative i plus 4
jAij=−i+4j.
(b) Construct the 2*4 matrix Upper C equals left bracket left
parenthesis 3 i plus j right parenthesis squared right
bracketC=(3i+j)2.
2.
Solve the following matrix equation.
left bracket Start 2 By 2 Matrix 1st Row 1st Column 3 x 2nd
Column 4 y minus 5 2nd Row...

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?

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...

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.

Estimate the area under the graph of f left parenthesis x right
parenthesis equals 5 x cubed f(x)=5x3 between x equals 0 x=0 and x
equals 1 x=1 using each finite approximation below. a. A lower sum
with two rectangles of equal width b. A lower sum with four
rectangles of equal width c. An upper sum with two rectangles of
equal width d. An upper sum with four rectangles of equal width

For the demand function
q equals Upper D left parenthesis p right parenthesis equals 352
minus pq=D(p)=352−p,
find the following.
a) The elasticity
b) The elasticity at
pequals=118118,
stating whether the demand is elastic, inelastic or has unit
elasticity
c) The value(s) of p for which total revenue is a maximum
(assume that p is in dollars)

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