Question Solved1 Answer What is the solution for this problem? As you look out of your dorm window, a flower pot suddenly falls past. The pot is visible for a time t, and the vertical length of your window is Lw. Take down to be the positive direction, so that downward velocities are positive and the acceleration due to gravity is the positive quantity g. Assume that the flower pot was dropped by someone on the floor above you (rather than thrown downward). From what height h above the bottom of your window was the flower pot dropped? Express your answer in terms of Lw, t, and g.

The region R enclosed between the graph of the function y =x^2−4x+5 and the x-axis for 0 ≤ x ≤ 4 is partitioned into foursubintervals. Determine the areas of the four rectangles using MRAMand then approximate the area of R. Round areas to the nearesthundredth. Show and explain your work.

A planet of mass 4 ⨯ 1024 kg is at location 5 ⨯ 1011, −4 ⨯ 1011, 0 m. A star of mass 4 ⨯ 1030 kg is at location −6 ⨯ 1011, 5 ⨯ 1011, 0 m. It will be useful to draw a diagram of the situation, including the relevant vectors. (a) What is the relative position vector r pointing from the planet to the star? r = 〈−11·1011, 9·1011, 0〉 m (b) What is the distance between the planet and the star? |r| = m (c) What is the unit vector in the direction of r? = 〈−.774, .633, 0 〉 (d) What is the magnitude of the force exerted on the planet by the star? |Fon planet| = N (e) What is the magnitude of the force exerted on the star by the planet? |Fon star| = N (f) What is the force (vector) exerted on the planet by the star? (Note the change in units.) Fon planet = 〈−3.35, 4.09, 0〉 ⨯ 1020 N (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.) Fon star = ⨯ 1020 N

Plot a, (Stewart 9.3 30 and 34, modified) Let a = (1, 2) and b = (-4,1). (a) Find the vector projection of b onto a, denoted projab and find its length (called the scalar projection). b and projab in the plane. (b) The orthogonal projection of b onto a, denoted orthab is the vector b - projab. Find orthab and plot it in the plane. Why do you think we call orthab the orthogonal projection of b onto a? What vector(s) is it perpendicular to in the example you sketched? (c) Show for any non-zero vectors a and b that orthab is perpendicular to a.

(a) Use the definition given below with right endpoints to express the area under the curve y = x3 from 0 to 1 as a limit. = The area A of the region S that is bounded above by the graph of a continuous function y = f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum of the areas of approximating rectangles. n lim Rn A = n00 lim [f(x4)Ax + f(x2)4x + = + f(x,)Ax] = lim. į f(x;)Ax n00 i=1 n lim n00 i = 1 (b) Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part (a). 12 13 + 23 + 33 + ..-( ) 3 = n(n + 1) 2

A planet of mass 3 x 1024 kg is at location (5 x 1011, -5 x 1011, 0) m. A star of mass 3 x 1030 kg is at location (-5 x 1011, 4 x 1011, 0) m. It will be useful to draw a diagram of the situation, including the relevant vectors. (a) What is the relative position vector r pointing from the planet to the star? r= m (b) What is the distance between the planet and the star? Irl m (c) What is the unit vector in the direction of r? (d) What is the magnitude of the force exerted on the planet by the star? |Fon planet| = N (e) What is the magnitude of the force exerted on the star by the planet? |Fon star] = N (f) What is the force (vector) exerted on the planet by the star? (Note the change in units.) Fon planet = x 1020 N (g) What is the force (vector) exerted on the star by the planet? (Note the change in units.) Fon star = x 1020 N

Consider the following reaction: A + 2B → E Using steady-state approximation determine which of the following can determine the overall rate law (assume that the rate determining step is unknown), if the reaction mechanism consists of the following elementary steps: 1. A + B → 2C (rate constants: k1 for forward reaction; k2 for reverse reaction) 2. 2C + B → E (rate constant: k3) Question 4 options: a) k3[B][C]2 b) (k3k1[A]2[B])/(k2+k3[A]) c) (k3k1[A][B]2)/(k3-k2[B]) d) (k3k1[A][B]2)/(k2+k3[B]) e) (k3k1[A][B]2)/(k3+k2[B])