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The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 30 + 0.006p3 and that its demand function is D(p) = 150 – 0.12p2, where p is the price. Determine the price for which the supply equals the demand. (5 points)

Verify the identity. cos 4u = cos22u – sin22u (7 points)  

Describe how the graph of y = x2 can be transformed to the graph of the given equation. y = (x – 2)2 – 15 (5 points)  

State how many imaginary and real zeros the function has. (5 points)f(x) = x4 – 8×3 + 17×2 – 8x +16 

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (5 points)4, -8, and 2 + 3i 

Find the zeros of the polynomial function and state the multiplicity of each. (5 points)f(x) = 5(x + 6)2(x – 6)3  

Divide using synthetic division, and write a summary statement in fraction form. (5 points)    

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 3 (5 points)

Find the exact value of the composition. sin (arctan (2)) (5 points)

Find the zeros of the function. (5 points) f(x) = x2 + 3x + 2