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

Given: julianne  total startup cost = $52000

Operating cost per day =$680

Earn money from her lesson fee per day = $960

Find out the inequality of situation

Given d be the number of days

To proof: julianne spends on operating cost in d day = $680d

julianne earn from lesson fee in d day  = $960d

Total profit in d day = 960d-680d

Part A) Total profit should be greater than 52000. Because this is startup investment.

According to question inequality becomes

Part B) Now solve for d

After 186 days, Julianne will get profit from dance studio.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

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