Math 110 Course Resources - Optimization Course Packet on applications: Maximizing profit Mt. Nittany Property Management Company and Happy Valley Rentals are two different businesses that manage numerous apartments around town. Both companies use the same monthly profit model given by \[ P(x)=-14 x^{2}+1848 x-22300 \] where \( x \) represents the number of apartments rented in a month and \( P(x) \) is in dollars. (a) Assuming Mt. Nittany Property Management Company manages 100 apartments, find the number of apartments they should rent out each month to maximize profits and calculate their maximum monthly profits. Number of apartments \( =66 \) Maximum monthly profit \( =38684 \) (b) Assuming Happy Valley Rentals manages 50 apartments, find the number of apartments they should rent out each month to maximize profits and calculate their maximum monthly profits. Number of apartments \( =\square \times \) dollars Maximum monthly profits \( =\square \)

A projectile is fired from ground level with an initial speed of \( 550 \mathrm{~m} / \mathrm{sec} \) and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is \( 9.8 \mathrm{~m} / \mathrm{sec}^{2} \). (a) The range of the projectile is (b) The maximum height of the projectile is (c) The speed with which the projectile hits the ground is submit answer Next item

ind the net change in the value of the function between the give nputs. \( f(x)=x^{2} \); from -1 tol \( \begin{array}{llll}\text { a) } 2 & \text { b) } 3 & \text { c) } 4 & \text { d) } 0\end{array} \)

Question 5 of 10 A spinner is divided into 10 equal sections numbered 1 through 10. Which 2 events are disjoint?

What pattern do you notice in problem 2 ? How could it help you solve a problem such as \( 297 \times 2 \) ? The pattern is n

15 Fungsi \( f \) ditakrifkan sebagai \( f(x)=\frac{2 x}{x+3} \). A function \( f \) is defined by \( f(x)=\frac{2 x}{x+3} \) (a) Cari \( f^{\prime}(1) \). Find \( f^{\prime}(1) \). (b) Seterusnya, anggarkan nilai bagi \( \frac{2(1.01)}{1.01+3} \). Hence, estimate the value of \( \frac{2(1.01)}{1.01+3} \).