I have been teaching AP Calculus AB and AP Calculus BC for over 13 years. In addition I have been teaching AP Physics 1 and 2 for the last 5 years. My degree was originally in Engineering from the University of Illinois. Both my parents were teachers and even when in industry I took on the role of advising and training. I have received several teaching awards. The one that I am most proud of it an award that I received my 4th year of teaching. The National Honor Society Seniors awarded me the No Bell Teachers award. During remote learning, I made video each day for all my classes. I did this so class time could be spent on problem solving. Many of my student said they watched my video multiple times and enjoyed my efficiency to make shorter videos with optional problem solving attachments. They have also suggested I make TikTok videos explaining math but can’t imagine doing that.
$37-44$ Use a computer algebra system to evaluate the integral.Compare the answer with the result of using tables. If theanswers are not the same, show that they are equivalent.$$\int \csc ^{5} x d x$$
Suppose that a plate is immersed vertically in a fluid withdensity $\rho$ and the width of the plate is $w(x)$ at a depth of$x$ meters beneath the surface of the fluid. If the top of theplate is at depth $a$ and the bottom is at depth $b$ , show that thehydrostatic force on one side of the plate is$$F=\int_{a}^{b} \rho g x w(x) d x$$
$23-24$ The masses $m_{i}$ are located at the points $P_{i} .$ Find themoments $M_{x}$ and $M_{y}$ and the center of mass of the system.$$m_{1}=4, m_{2}=2, m_{3}=4 ; \quad P_{1}(2,-3), P_{2}(-3,1), P_{3}(3,5)$$
$23-24$ The masses $m_{i}$ are located at the points $P_{i} .$ Find themoments $M_{x}$ and $M_{y}$ and the center of mass of the system.$$m_{1}=5, m_{2}=4, m_{3}=3, m_{4}=6; \quad P_{1}(-4,2), P_{2}(0,5), P_{3}(3,2), P_{4}(1,-2)$$
$34-35$ Calculate the moments $M_{x}$ and $M_{y}$ and the center of massof a lamina with the given density and shape.$$\rho=4$$
$34-35$ Calculate the moments $M_{x}$ and $M_{y}$ and the center of massof a lamina with the given density and shape.$$\rho=6$$
At time t=0, a particle is located at the point (1,2,3). It travels in a straight line to the point (4,1,4), has a speed of 2 at (1,2,3), and has a constant acceleration of 3I-j+k. Find an equation for the position vector r(t) of the particle at time t.
A spring has natural length 23 cm. Compare thework W1 done in stretchingthe spring from 23 cm to 33 cm with thework W2 done in stretchingit from 33 to 43 cm.(Use k for the spring constant)Howare W2 and W1 related?
Find the exact volume generated by rotating the region boundedby the given curves about the specified axis.y=3x^2 , y=x^2+8; about x=3
Find parametric equations of the line that passes through the point (1, -4) and is perpendicular to the line with vector equation r(t) = <-6 + 4t, 1 + 3t>. (Enter your answer as a comma-separated list of equations where x and y are in terms of the parameter t.)
The x- and y-coordinates of a moving particle aregiven by the parametric equations below. Find the magnitude anddirection of the acceleration for the specific value of t.x=4t, y=4-t, t=3Find the magnitude of the acceleration of the particle for thespecific value of t.The magnitude is approximately _____.
Find the area of the polar region that lies inside the cardioid r = 2(1 - sin(theta)) with the circle r = 2.