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2 years ago

If kevin makes c toys in m minutes, how many toys can he make per hour

Mathematics

1 answer:

mina [271]2 years ago

7 0

Answer:

$\frac{60c}{m}$

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = $\frac{c}{m}$

Number of toys made in 60 minutes = $\frac{c}{m} \times 60 = \frac{60c}{m}$

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = $\frac{60c}{m}$

Therefore, we can say that Kevin makes $\frac{60c}{m}$ toys per an hour.

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Can someone help please

myrzilka [38]

<h3>Answer: 15x^(7/3) - 8x^(7/4) + x + 9000</h3>

=========================================================

Explanation:

If you know the cost function C(x), to find the marginal cost, we apply the derivative.

Marginal cost = derivative of cost function

Marginal cost = C ' (x)

Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.

$\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\$

$C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$

D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).

To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.

Therefore, we go from this

$C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$

to this

$C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\$

which is the final answer.

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We have been given a parent function $f(x)=x^{3}$ and we need to transform this function into $g(x)=\frac{1}{2}(x-4)^{3}+5$ .

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