1. Solve linear system using Gaussian elimination

a)

x₁ + 2x₂ + x₃ = 2

-x₁ − 3x₂ + 2x₃ = -3

  x₁ − 6x₂ + 3x₃ = -6

b)

-2b + 2c = 10

3a + 12b -3c = -6

6a + 18b + 0c = 19

c)

4x - 1y + 4z + 3t = 5

1x - 4z + 6t = 7

5x - 5y + 1z + 2t = -5

4x + 1y + 3z + 3t = 6

1). A group of students plans a tour. The charge per student is $66 if 25 students go on a trip. If more that 25 students participated, the charge per student is reduced by $2 times the number of students over 25. Find the number of students that will furnish the maximum revenue. The number of students that will furnish the maximum revenue is ______? The maximum revenue is $_______?

2) A motorboat is capable of traveling at a speed of 15 miles per hour in still water. On a particular​ day, it took 30 minutes longer to travel a distance of 18 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that​ day?

Consider the region illustrated below, bounded above by ? = ?(?) = 10 cos ( ?? 9 ) and below by ? = ?(?) = ? −?+3 . The curves intersect at the points (?, ?(?)) and (?, ?(?)), where 0 < ? < ? < 5. Do not try to find or estimate the values of ? or ?.

a. The total area of the region.

b. The volume of the solid that has this region as its base, where cross-sections perpendicular to the ?-axis are semicircles with their diameters on the xy-plane.

c. The volume of the solid that results by revolving this region about the x-axis.

d. The volume of the solid that results by revolving this region about the line ? = 5.

For the following find: (Show detailed working)

1) general solution of the associated homogns DE

2)  form of the particular solution associated with the undetermined coefficients method. Do not evaluate coefficients

a) (d² y / dx²) - dy/dx = x - 3

b) (d² y / dx²) + 2 dy/dx + y = (1+x)e^-x + x²

^c) (d² y / dx²) + y = sin(2x)

1. Explain how the first derivative test of a function determines where the function is increasing and decreasing.
2. Explain how to apply the second derivative test.
3. What is an inflection point?
4. Why are special methods such as L'Hopital's Rules, needed to evaluate indeterminate forms?

At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

Show a composite shape that you could divide up multiple ways to find its area. (illustrate at 3 different ways to divide it up and label dimensions of each division)

for u=<2,1,-3> and v=<1,0,2>,

a) find the angle between u and v

b) use the formula proj_a b=((a•b)/|b|^2)b to find vector projection of v onto u

c) sketch vectors u, v, and the projection found with only using arrows

d) find the area of the parallelogram determined by u and v

The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function.

C(x) = 2000 + 2x − 0.0001x²    (0 ≤ x ≤ 6000)

a. What is the actual cost incurred in producing the 991st and the 1971st disc?

b. What is the marginal cost when x = 990 and 1970?

Williams Commuter Air Service realizes a monthly revenue represented by the following function, where R(x) is measured in dollars and the price charged per passenger is x dollars.

R(x) = 9,600x − 120x²

a. Find the marginal revenue R'(x).

b. Compute the following values.

-R'(39)

-R'(40)

-R'(41)

c. Based on the results of part (b), what price (in dollars) should the airline charge in order to maximize their revenue?

Can somebody explain to me Derivative of Parametric Equations? May I know its importance and applications in real life? i need it for my essay. Thank you

PS. I can't find it on the internet

The scores on a standardized test are normally distributed with a mean of 95 and standard deviation of 20. What test score is 0.5 standard deviations above the mean?

Use Pascal’s triangle to find the possible value(s) of nn if nC3=(n3)=20.

Find the horizontal and vertical tangents to the graph of the cardioid ? = 1 − cos?, 0 ≤ ? ≤ 2?