1. Tickets for the school play cost $5 for students and $8 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2610. How many student and how many adult tickets were sold?

2. A $76,000 trust is to be invested in bonds paying 8%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment must equal the mortgage investment. To earn a $6670 annual income from the investments, how much should the bank invest in bonds?

3. Suppose that Janine desires 46 grams of protein and 38 grams of dietary fiber daily. One serving of kidney beans has 8 grams of protein and 6 grams of dietary fiber. One serving of refried pinto beans has 6 grams of protein and 6 grams of dietary fiber. If a serving of kidney beans costs $0.45 and a serving of refried pinto beans costs $0.35, then how many servings of each should Janine eat to minimize cost and still meet her requirements?

Suppose you want to buy a new car and trying to choose between two models:

Model A: costs $17,000 and its gas mileage is 20 miles per gallon and its insurance is $200 per year.

Model B: costs $25,000 and its gas mileage is 35 miles per gallon and its insurance is $400 per year.

If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:

Find a formula for the total cost of owning Model A where the number of years is the independent variable.

Find a formula for the total cost of owning Model B where the number of years is the independent variable.

Find the total cost for each model for the first five years.

If you plan to keep the car for four years, which model is more economical? How about if you plan to keep it for six years?

Find the number of years in which the total cost to keep the two cars will be the same.

Identify the number of months where neither car holds a cost of ownership advantage.

What effect would the cost of gas doubling have on cost of ownership? Graph or show hand calculations.

If you can sell neither car for 40% of its value at any time, how does the analysis change? Graph or show hand calculations.

Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.

1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is

Select one:

a. (−∞,−1]
b. (π,2π)

c. (−∞,−2]
d. (−π,2π)
e. ℝ

f. (−1,∞)

2. The limt→πr(t) where r(t)=〈t2,et,cos(t)〉 is

Select one:

a. 〈π2,eπ,−1〉

b. undefined

c. 〈π2,eπ,1〉
d. π2+eπ
e. 〈π2,eπ,0〉

3.Let v(t)=〈2t,4t,t2〉. Then the length of v′(t) is

Select one:

a. 20‾‾‾√+2t

b. 20+4t2

c. 20+2t‾‾‾‾‾‾‾√

d. 20+4t2‾‾‾‾‾‾‾‾√

e. 6+2t‾‾‾‾‾‾√
f. 1

4. The curvature of a circle centred at the origin with radius 1/3 is

Select one:

a. 1

b. 1/3

c. undefined

d. 3

e. 10

Evaluate the following integral using the Midpoint Rule​ M(n), the Trapezoidal Rule​ T(n), and​ Simpson's Rule​ S(n) using nequals4. Integral from 2 to 6 StartFraction dx Over x cubed plus x plus 1 EndFraction Using the Midpoint​ Rule, ​M(4)equals

plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area. A= (-5, 10) B (2,7) C (-1,0)

"If A and B are similar then A and B are orthogonally similar. " Prove or disprove this statement.

Find the vertex, focus, directrix, and focal width of the parabola.

(y + 2)^{2 = -8(x - 1)}

A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.18 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.)

1.) Find the sum V in cartesian and polar coordinates of V1=1000 m/s, V2=1800 m/s 2.) Find the difference of V in polar and cartesian coordinates for V3= 800 m/s and V4= 1400 m/s. The angles are angle1= 35 deg, angle2= 60 deg, angle3= 130 deg, angle4= 340 deg.

Find the area of the region enclosed by the graphs of
x=(1/2)(y^2)-3 and y=x-1

5. The rate of excretion of a biochemical compound is given by ? ′ (?) = 0.01? −0.01? , where t is the time in minutes. Find an expression for f(t), the total amount of chemical excreted, if 0 units are excreted at t = 0. a. Find a function for the position of an object if its velocity is given by ?(?) = ? 2 + ? + 16 and whose initial position is 10 meters. b. Find the position of the object at t = 3 seconds.

How have you contributed to classroom participation, either in class pre-pandemic or electronically post-pandemic?