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UkoKoshka [18]
3 years ago
7

Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: S(p) = 400 - 4

p + 0.00002p4 and D(p) = 2800 - 0.0012p3, where p is the price. Determine the price for which the supply equals the demand.
A) $93.24
B) $100.24
C) $96.24
D) $99.24
Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
6 0
S(p) = 400 - 4p + 0.00002p^4
D(p) = 2800 - 0.0012p^3

S(p) = D(p)
400 - 4p + 0.00002p^4 = 2800 - 0.0012p^3
0.00002p^4 + 0.0012p^3 - 4p - 2400 = 0
p = $96.24
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liubo4ka [24]
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\bf \cfrac{76~\underline{feet}}{\underline{sec}}\cdot \cfrac{mile}{5280~\underline{feet}}\cdot \cfrac{3600~\underline{sec}}{hr}\implies \cfrac{76\cdot 3600~mile}{5280~hr}
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\textit{how many miles does it do in 3.1hrs?}\quad \cfrac{570}{11}\cdot 3.1
6 0
3 years ago
The difference between the roots of the quadratic equation x2+x+c=0 is 6. Find c.
NemiM [27]
We have that
x_{1} - x_{2} = 6
Let y be the first root, then y - 6 will be the second one. Since both roots make the quadratic equation equal to 0, we have that:
y^{2}  + y + c =  (y - 6)^{2}  + (y - 6) +c
Solve for y:
y^{2} +y +c = y^{2} - 12y + 36 + y - 6 +c \\ y + 12y - y = 30 \\ y =  \frac{5}{2}
Plug in y = 5/2 into original quadratic equation and solve for c:
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6 0
4 years ago
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dolphi86 [110]
The answer is:
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3 0
3 years ago
Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours. At this rate of decay,
salantis [7]

Answer:

9,942 bacteria were there at 10 hours.

Step-by-step explanation:

Equation for population decay:

The equation for population decay, after t hours, is given by:

P(t) = P(0)(1-r)^t

In which P(0) is the initial population and r is the decay rate, as a decimal.

Researchers recorded that a certain bacteria population declined from 200,000 to 900 in 18 hours.

This means that P(0) = 200000 and that when t = 18, P(t) = 900. So we use this to find r.

P(t) = P(0)(1-r)^t

900 = 200000(1-r)^{18}

(1-r)^{18} = \frac{900}{200000}

\sqrt[18]{(1-r)^{18}} = \sqrt[18]{\frac{900}{200000}}

1 - r = (\frac{900}{200000})^{\frac{1}{18}}

1 - r = 0.7407

So

P(t) = P(0)(1-r)^t

P(t) = 200000(0.7407)^t

At this rate of decay, how many bacteria was there at 10 hours?

This is P(10). So

P(10) = 200000(0.7407)^{10} = 9941.5

Rounding to the nearest whole number:

9,942 bacteria were there at 10 hours.

5 0
3 years ago
-2r+11=13 2r=2 r= I need help
Artemon [7]

Answer:

-2r = 2 - Subtract 11 from both sides

r = -1

5 0
2 years ago
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