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Mathematics

1 answer:

anzhelika [568]3 years ago

5 0

Answer:

true

Step-by-step explanation:

$\frac{x}{2}$

* substitute 30 for x *

$\frac{30}{2}$

we're left with 15 < 20 which is true

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Break Even Analysis for Small Business 1) Jesse wants to start a business making and selling skateboards. She will charge $75 fo

Bas_tet [7]

Answer:

a) r(b) = 75b

b) c(b) = 30b +500

Step-by-step explanation:

Revenue is the product of the selling price per unit and the number of units. The cost will be the sum of fixed (overhead) cost and production cost per unit multiplied by the number of units produced.

Let b represent the number of skateboards Jesse produces in a month.

Jesse receives $75 for each skateboard sold. Her revenue from selling 'b' skateboards is ...

r(b) = 75b

It costs Jesse $30 for each skateboard produced, and $500 for overhead. Her total cost is ...

c(b) = 30b +500

_____

<em>Additional comment</em>

In order to break even, Jesse's revenue must equal her cost:

75b = 30b +500

45b = 500

b = 11 1/9

Jesse must produce and sell 12 skateboards each month to cover her costs. (In a real business, there are additional considerations related to inventory, shrinkage, returns, discounts, and other things that may increase cost or reduce revenue.) After covering costs, each additional skateboard sold will give Jesse a profit of $45.

5 0

3 years ago

The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec.

Andrej [43]

The ladder, the ground and the wall form a right triangle; the ladder length (L) is the longest side of this triangle. L^2 = h^2 + x^2, where h represents the height of the point on the wall where the ladder touches the wall, and x represents the distance of the base of the ladder from the wall.

We need dh/dt, which will be negative because the top of the ladder is sliding down the wall.

Starting with h^2 + x^2 = L^2, we differentiate (and subst. known values such as x = 5 feet and 4 ft/sec to find dh/dt. Note that since the ladder length does not change, dL/dt = 0. This leaves us with

dh dx
2h ---- + 2x ----- = 0.
dt dt

Since x^2 + h^2 = 15^2 = 225, h^2 = 225 - (5 ft)^2 = 200, or
200 ft^2 = h^2. Then h = + sqrt(200 ft^2)

Substituting this into the differential equation, above:

2[sqrt(200)] (dh/dt) + 2 (5) (4 ft/sec) = 0. Solve this for the desired quantity, dh/dt:

[sqrt(200)] (dh/dt) + (5)(4) = 0, or

dh/dt = -20 / sqrt(200) = (-1.41 ft / sec) (answer)

This result is negative because the top of the ladder is moving downward.

4 0

4 years ago

F(x)= x+28/x-7 for inverse functions

ioda

The inverse function of the given function is $\mathbf{= \dfrac{28+7x}{x-1}}$