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3 years ago

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The cost function for q units of a certain item is C(q)equals109 q plus 90. The revenue function for the same item is R(q)equa

ls109 q plus StartFraction 45 q Over ln q EndFraction . a. Find the marginal cost. b. Find the profit function. c. Find the profit from one more unit sold when 8 units are sold.

1 answer:

Tcecarenko [31]3 years ago

6 0

Answer:

a) $109

b) $P(q) = \frac{45q}{ln(q)} +90$

c) $$11.20$

Step-by-step explanation:

a) The marginal cost, or the cost per additional unit, is given by the derivate of the cost function:

$C(q) = 109q+90\\C(q) = \$109$

b) Profit is given by Revenue minus Cost:

$P(q) = R(q) - C(q)\\P(q) = \frac{45q}{ln(q)} +90$

c) The marginal profit for 8 units, is given by the difference in profit for 9 units and 8 units:

$M = P(9)-P(8)\\M= \frac{45*9}{ln(q)} +90 - (\frac{45*8}{ln(8)}+90 )\\M=\$11.20$

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Stella [2.4K]

Answer:

(4,5)

Step-by-step explanation:

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3 years ago

Identify the functions that are continuous on the set of real numbers and arrange them in ascending order of their limits as x t

Studentka2010 [4]

Answer:

g(x)<j(x)<k(x)<f(x)<m(x)<h(x)

Step-by-step explanation:

1. $f(x)=\frac{x^2+x-20}{x^2+4}$

The denominator of f is defined for all real values of x

Therefore, the function is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x^2+x-20}{x^2+4}=\frac{25+5-20}{25+4}=\frac{10}{29}=0.345$

3. $h(x)=\frac{3x-5}{x^2-5x+7}$

$x^2-5x+7=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function h is defined for all real values.

$\lim_{x\rightarrow 5}\frac{3x-5}{x^2-5x+7}=\frac{15-5}{25-25+7}=\frac{10}{7}=1.43$

2. $g(x)=\frac{x-17}{x^2+75}$

The denominator of g is defined for all real values of x.

Therefore, the function g is continuous on the set of real numbers

$\lim_{x\rightarrow 5}\frac{x-17}{x^2+75}=\frac{5-17}{25+75}=\frac{-12}{100}=-0.12$

4. $i(x)=\frac{x^2-9}{x-9}$

x-9=0

x=9

The function i is not defined for x=9

Therefore, the function i is not continuous on the set of real numbers.

5. $j(x)=\frac{4x^2-7x-65}{x^2+10}$

The denominator of j is defined for all real values of x.

Therefore, the function j is continuous on the set of real numbers.

$\lim_{x\rightarrow 5}\frac{4x^2-7x-65}{x^2+10}=\frac{100-35-65}{25+10}=0$

6. $k(x)=\frac{x+1}{x^2+x+29}$

$x^2+x+29=0$

It cannot be factorize .

Therefore, it has no real values for which it is not defined .

Hence, function k is defined for all real values.

$\lim_{x\rightarrow 5}\frac{x+1}{x^2+x+29}=\frac{5+1}{25+5+29}=\frac{6}{59}=0.102$

7. $l(x)=\frac{5x-1}{x^2-9x+8}$

$x^2-9x+8=0$

$x^2-8x-x+8=0$

$x(x-8)-1(x-8)=0$

$(x-8)(x-1)=0$

$x=8,1$

The function is not defined for x=8 and x=1

Hence, function l is not defined for all real values.

8. $m(x)=\frac{x^2+5x-24}{x^2+11}$

The denominator of m is defined for all real values of x.

Therefore, the function m is continuous on the set of real numbers.

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3 years ago

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a_sh-v [17]

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-13
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4 years ago

Albertson's found that the demand for Coke products varies inversely as the price of the product. When the price of a Coke produ

romanna [79]

Answer:

859

Step-by-step explanation:

The demand for Coke products varies inversely as the price of Cole products.

Mathematically:

D α 1/p

Where D = demand, p = price of coke product

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Where k = constant of proportionality.

Let us find k.

k = D * p

When Demand, D, is 1250, price, p, is $2.75:

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Now, when price, p, is $4, the demand will be:

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The demand for the product is 859 when the price is $4.

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3 years ago

Sam the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. How fa

Liula [17]

Answer:

24.59 feet

Step-by-step explanation:

Let x represent the distance between Sam and the bird.

We have been given that am the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. We are asked to find the distance between Sam and the bird.

We can see from our attachment that Sam, the bird and angle of depression forms a right triangle with respect to ground. We can see that side 10 ft is opposite side and and side x is hypotenuse for the 24 degree angle.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(24^{\circ})=\frac{10}{x}$

$x=\frac{10}{\text{sin}(24^{\circ})}$

$x=\frac{10}{0.406736643076}$

$x=24.5859333557$

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Therefore, the bird is approximately 24.59 feet away from Sam.

8 0

3 years ago