Determine the constant that should be added to the following binomial so that it becomes a perfect square trinomial. Then \( w \) \( x^{2}-20 x \) The perfect square trinomial is \( x^{2}-20 x+\square \). (Type an integer or a simplified fraction.) The factored perfect square trinomial is \( \square \). (Use integers or fractions for any numbers in the expression.)

Prompt \#10: Let \( g(x)=-x^{3}+432 x+200 \). Note Question \#10(a): Determine \( g^{\prime}(x) \). that \( g(x) \) is a polynomial and therefore a continuous function.

What is the imaginary part of the conjugate of \( 6+3 i \). Your Answer:

4. [-/1 Points] DETAILS MY NOTES LARCALC9 5.4.105. 0/10 submissi Find the indefinite integral. \( \int \frac{e^{\sqrt{5 x}}}{\sqrt{5 x}} d x \) Des \( +C \)

Divide. \( \left.\qquad 8 x^{3}-18 x^{2}+7 x-2\right) \div(2 x-3) \) Your answer should give the quotient and the remainder. Quotient: Remainder: \( \square \)

You decide to begin selling ice cream cones at the local star wars convention. Your cost for each ice cream cone is \( \$ 2.39 \) plus you have to pay a fixed weekly fee of \( \$ 160 \) for the booth. Your plan is to sell each ice cream cone for \( \$ 3.69 \). a. Write a function, \( C(n) \), to represent your total costs for the week if you sell \( n \) ice cream cones. \( C(n)=\square \) b. Write a function, \( R(n) \), to represent the revenue from the sale of \( n \) ice cream cones during the week. \( R(n)=\square \) c. Write a function, \( P(n) \), that represents the profits for selling \( n \) ice cream cones in a given week. \( P(n)=\square \) d. How many items must you sell to break even? \( \square \)