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mafiozo [28]
3 years ago
14

Bikes'R'Us manufactures bikes, which sell for $250. It costs the $180 per bike, plus a startup fee of $3,500. After how many bik

es sold will the manufacturer break even?
Mathematics
1 answer:
lions [1.4K]3 years ago
3 0

<u>Answer:</u>

The bikes sold at break even by the manufacturer is 50 units

<u>Explanation:</u>

We know that break even point is given by  the following formula,

$\frac{\text { Fixed costs }}{\text { (Price per unit - Variable costs) }}$

We are given startup fee = $3500 which is the fixed cost,

the bikes sell for $250 which is the price per unit and

cost per bike is equal to $180

So substituting these values in the formula we get

= \frac{3500}{(250-180)}

= \frac{3500}{(70)}  = 50

= 50 units which is the number of bikes sold at break even by the manufacturer.

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<h3><u>Question:</u></h3>

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units.

The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

<h3><u>Answer:</u></h3>

Dimensions of cylinder A are multiplied by \frac{3}{2}  to produce the corresponding dimensions of cylinder B

<h3><u>Solution:</u></h3>

Cylinders A and B are similar solids.

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The base of cylinder B has an area of 9 \pi units

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From given question,

Dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B

Therefore, we can say,

\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }

<h3><u>Cylinder A:</u></h3>

The circumference of base of cylinder (circle ) is given as:

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Given that  base of cylinder A has a circumference of 4 \pi units

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4 \pi = 2 \pi r\\\\r = 2

Thus the dimension of cylinder A is radius = 2 units

<h3><u>Cylinder B:</u></h3>

The area of base of cylinder (circle) is given as:

A = \pi r^2

Given that,  the base of cylinder B has an area of 9 \pi units

Therefore,

\pi r^2 = 9 \pi\\\\r^2 = 9\\\\r = 3

Thus the dimension of cylinder B is radius = 3 units

\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }\\\\2 \times x = 3\\\\x = \frac{3}{2}

Thus dimensions of cylinder A are multiplied by \frac{3}{2}  to produce the corresponding dimensions of cylinder B

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Input the given values of the slope and the point into the equation for point-slope form:

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The equation written in point-slope form is: y + 2 = 3(x - 6)

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