Julianne opens a dance studio. her start-up costs for the building, advertising, and supplies total $52,000. each day, she spends $680 on operating costs (like utilities and wages). she earns $960 per day from her students' lesson fees. part a: write an equation or inequality to represent this situation. let d be the number of days. part b: when will lulianne begin making a profit? show all the work you did to arrive at your answer

To answer this question, we have the start-up costs of $ 52,000

Operating costs in dollars are 680

The daily gain in dollars in 960

Part A.

The inequality that this situation represents

So:

Where "d" represents the number of days.

Part B.

To start earning, you must replace all the initial investment and cover the expenses per day. The time that must pass for this to happen is obtained by clearing "d" from the inequality.

d> 185.71 days

Then, the sum of the net profits will be greater than the initial investment after 186 days of starting the business.

note: A monthly inflation of $ 0 is assumed

Part A :

Part B : After 185.71 days Lulianne will begin making a profit.

Step-by-step explanation:

Given :

Julianne start-up costs for the building, advertising, and supplies total $52,000.

She spends $680 on operating costs on each day.

She earns $960 per day from her students lesson fees.

To Find :

Part A: Write an equation or inequality to represent this situation. Let d be the number of days.

Part B: When will Lulianne begin making a profit?

Solution :

She spends on operating costs on each day=  $680

She spends on operating costs on d days=  $680 d

She earns  per day from her students lesson fees= $960

She earns  in d days from her students lesson fees= $960 d

So,

remaining money =She earns  in d days from her students lesson fees -She spends on operating costs on d days

= $960 d- $680 d = $280 d

So, she left with $280 d in days .

Her start up cost was $52,000

So, the inequality to represent the situation :

⇒

⇒

⇒

Thus, after 185.71 days lulianne will begin making a profit.

Hence , the inequality to represent the situation :

and after 185.71 days lulianne will begin making a profit.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)