Questions asked
1. Use the distance formula to determine whether points P, Q, and R are collinear. a. P(-2, -3), Q(2, -1), and R(10, 3) b. P(2, 7), Q(-2, -7), and R(3, 10.5)
Consider the function in the graph to the right. The function has a relative maximum of at x = The function has a relative minimum of at x = The function is increasing on the interval(s): The function is decreasing on the interval(s): The domain of the function is: The range of the function is:
1. (7 points) In the lectures, we derived an expression for the velocity field for viscous flow between two parallel plates for two scenarios: With stationary plates and a pressure gradient ($\frac{\partial p}{\partial x}$) in the direction of flow, and with moving plates but no pressure gradient. Here we combine these two scenarios: Suppose now that we again have two plates that are a distance of 2h apart, with the top plate is moving with a velocity of $U_U$, and the bottom plate is moving with a velocity $U_L$, and with a nonzero pressure gradient ($\frac{\partial p}{\partial x}$) (which we can assume to be constant). (a) Determine the velocity profile of this flow. (b) Determine the volumetric flow rate between the plates, per unit width.
H3C OH H2SO4, ? OH HNO3, H2SO4 OH OH ONa + K2Cr2O7 H2SO4 [meta-product] Cl2, FeCl3 [1,3,5-substituted]
C$_7$H$_{14}$O C$_9$H$_{10}$O$_3$ C$_{10}$H$_{10}$O$_2$ C$_9$H$_{11}$Cl C$_{10}$H$_{20}$O
4. [3pt] A charge +4q is placed at the origin and another charge -2q is placed on the x-axis at x = 16.0 cm. At which point on the x-axis should a third charge be placed such that the electric force acting on it is zero?
Class B
In Exercises 39-44, determine the values of x, if any, at which each function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. 39. \(f(x) = \begin{cases} 2x - 4 & \text{if } x \le 0 \\ 1 & \text{if } x > 0 \end{cases}\) 40. \(f(x) = \begin{cases} x^2 + 1 & \text{if } x \ne 0 \\ 0 & \text{if } x = 0 \end{cases}\) 41. \(f(x) = \begin{cases} x + 5 & \text{if } x \le 0 \\ -x^2 + 5 & \text{if } x > 0 \end{cases}\)
Texts: An electric motor running at 1,200 rpm drives a punch press shaft by means of a 130 mm wide and 8 mm thick belt. When the clutch is engaged, the belt slips. The original contact angle on the 200 mm motor pulley is 160°. The original tension ratio is 2.4, and the net rated tension per belt width is 12 N/mm. If an increase in transmission capacity of 20% will prevent slippage, determine the new angle of contact. A. 220° B. 210° C. 190° D. 225°
(Scenario: Cold Medicine for Pfizer) Use Scenario: Cold Medicine for Pfizer. Pfizer has developed a new cold medicine. For efficient delivery, the new medicine requires an inhaler, which can be produced at a constant marginal cost of $2 per inhaler. Pfizer has a patent that gives it a monopoly on its inhaler. If Pfizer behaves as a profit maximizing monopolist, then monopoly profits will be: Scenario: Cold Medicine for Pfizer Demand Curve: $P = 10 - 0.5Q$ Marginal Revenue Curve: $MR = 10 - Q$ Marginal Cost = Average Total Cost = 2 a) $16 b) $8 c) $32 d) $0
