An electronic store chain sells headphones. The company is about to introduce new headphone model that is expected to sell very well across its various stores. these are the projected and cost functions for the headphones: R(x)=-210x²+6,970x
C(x)=-170x+39,690
which two statements are true?
• The maximum profit is $57,834
• The maximum profit is $21,000
• a selling price of $27 results in the maximum profit
• a selling price of $17 results in the maximum profit
• a selling price of $16.60 results in the maximum profit

Step-by-step explanation:

Given sin 30° = 1/2, to check which of the statements is correct we will apply the Pythagoras theorem to a right angled triangle shown in the attachment.

using the SOH CAH TOA trig identity on the right angled triangle, ACD gotten from the equilateral triangle ABC;

From ΔACD, AD is the hypotenuse, DC is the opposite side to the angle 30° and AC is the adjacent.

From the diagram, sin30° = opp/hyp = DC/AD

sin30° = 1/2

Taking consideration of the acute angle 60°, the opposite side to the angle will be AC and the adjacent side will be CD.

According to CAH, cos 60° = adj/hyp = CD/AD

Given CD = 1 and AD = 2

cos60° = 1/2

This shows that sin30° = cos60° = 1/2

Note that ∠CDA and ∠DAC are angles complementary. Complementary angles are angles which have its sum to be 90°