Question

F varies jointly as Q and R and inversely with the square of D. If

F=80

when

Q=4,

R=16

and

D=0.4,

determine F when

Q=12,

R=20

and

D=0.2.

Answer #1

The intensity I of light (measured in foot-candles) varies
inversely with the square of the distance from the bulb. Suppose
the intensity of a 100-watt light bulb at a distance of 2 meters is
0.075 foot-candle. Determine the intensity of the bulb at a
distance of 3 meters.

Prove: If D = Q\{3}. R = Q\{-3}, and f:D-> R is defined by
f(x) = 1+3x/3-x for all x in D, then f is one-to-one and onto.

12. y varies directly as x. y = 12 when x = 5.
Find y when x =2
Y = _?__ (Simplify your answer).
13.
y varies directly as x and inversely as the square of z. y =48
when x =64 and z= 4. Find y when x= 2 and z =4.
Y = _?__ (Simplify your answer. Type an integer or a simplified
fraction).

Triangle S R Q is shown. Angle S R Q is a right angle. An
altitude is drawn from point R to point T on side S Q to form a
right angle. The length of T Q is 16 and the length of R Q is 20.
What is the length of Line segment S R? 9 units 12 units 15 units
18 units

Given the cost function:
Cost equals 0.2 q cubed minus 6 q squared plus 80 q plus Upper
F
,
and marginal cost:
0.6q2
minus
12q + 80
where q = output, and F = fixed costs = $100
.
The demand equation is:
p = 100
minus
2
q.
Determine the profit-maximizing price and output for a
monopolist.
The profit-maximizing output level occurs at nothing
units of output (round
your answer to the nearest tenth).
The profit-maximizing price occurs...

Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4},
Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by
f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4,
b)}.
(a) Is Function f and g invertible? If yes find f −1
and g −1 or if not why?
(b) Find f o g and g o...

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.92585919
R Square
0.85721525
Adjusted R Square
0.84928276
Standard Error
14.7134321
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
23394.2185
23394.2185
108.063881
4.9013E-09
Residual
18
3896.73153
216.485085
Total
19
27290.95
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-260.93886
39.3752125
-6.626983
3.2026E-06
-343.66312
-178.21461
-343.66312
-178.21461
Height
5.92431175
0.56989864
10.3953779
4.9013E-09
4.72699913
7.12162438
4.72699913
7.12162438
RESIDUAL OUTPUT
Observation
Predicted Weight
Residuals
1
106.368464
8.63153552...

Let V = R and F = Q (V is a F-vector space). Is the subset S1 =
{1, √ 2, √ 3} (of V ) linearly independent? Answer the same
question for S2 = {1, √3 2, √3 4}.

The system Px +Qy =R; Fx + Gy = H has solution(3,-1), where
F,G,H,P,Q, and R are nonzero real numbers.
Select all the systems that are also guaranteed to have the
solution (3,-1). (Select all that applies)
A. (P+F)x+(Q+G)y= R+H and Fx+Gy=H
B. (P+F)x+Qy= R+H and Fx+(G+Q)y=H
C.Px+Qy=R and (3P+F)x+(3Q+G)y=3H+R
D. Px+Qy=R and (F-2P)x+(G-2Q)y=H-2R
E. Px+Qy+R and 5Fx+ 5Gy

A chain of hardware stores finds that the demand D for a special
power tool varies inversely with the advertised price P of the
tool. Suppose that when the price is advertised at $85, there is a
monthly demand for 10000 units at all participating stores.
Important Note: MapleTA doesn't recognize commas in big numbers, so
don't include them in your answers. (a) Find the proportionality
constant k. k =
(b) Determine the variation equation (include the value of k...

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