Using the pair of compasses and ruler only, construct

1. Triangle GBC with angle CBG = 30*, /BC/ = 9.5cm and /BG/= 12cm
2. L1, the locus of points 6cm from C
3. L2, the perpendicular from C to BG
4. Locate A and D, the intersection of li and BG
5. Measure /AD/ and angle ACD

Find the area of the surface obtained by rotating the circle x^2+y^2=49 about the line y=7. (Keep two decimal places)

Find the absolute maximum and minimum values of the function f(x, y) = x^2 + ((4/3) y^3) − 1 on the disk x^2 + y^2 ≤ 1.

Find the volume of the solid that lies within the sphere x2+y2+z2=64, above the xy plane, and outside the cone z=7sqrt(x2+y2)

A company calculates the following for an item that they produce and sell. The revenue, R(x), from the sale of 90 items is 2300 dollars. The marginal revenue when 90 items are sold is 61 dollars per item. The cost, C(x), to produce 90 items is 1250 dollars. The marginal cost when 90 items are produced is 16 dollars per item. (a) Estimate the revenue from the sale of 89 items. (b) Estimate the cost from the sale of 94 items. (c) Estimate the profit from the sale of 91 items.

Determine whether the curve denoted by the vector function r(t) = <2 + sin(5t), -6, 3/2 (cos(5t))> lies on the surface 9x^2 - 36x - y^2 + 4z^2 = -36.

P1.

1. Write the Taylor series for f(x) = cos x about x = 0.

2. State the Taylor polynomials T2(x), T4(x), and T6(x) (note that T3(x)
   will be the same as T2(x), and T5(x) will be the same as T4(x)).

3. Plot f(x), T2(x), T4(x), and T6(x), together on one graph, using demos

or similar (cut-and-paste or reproduce below).

If the producer of a commodity spends x thousand dollars on advertising, then Q(x)=43-10e^(-1/2x) thousand units of the commodity will be sold.

(a) How many units will be sold if no money is spent on advertising? How many units will be sold if 5,000 dollars are spent on advertising?

(b) How much should be spent on advertising to sell 40,000 units?

(c) Compute the limit limx→∞ Q(x). What does this limit mean in the given context of the problem?

Please show step by step! Thank you

Use Newton’s method to find x1, x2 and x3 with the given x0

2/x− x^2 + 1 = 0 x0 = 2

Evaluate the iterated integral.

integral sqrt(pi) to 0 integral 3x to 0 integral xz to 0 of 15x^2 sin(y) dydzdx

An underground tank is a hemisphere with radius 4 feet (i.e. it is half a sphere, and so horizontal cross-sections are circles of varying radius). It is filled to the top with oil weighing 45 lb per cubic foot. The top of the tank is at ground level, and the oil in the tank is pumped to a height of 10 feet above ground level. How much work is done? Set up the integral, but then just use your calculator to evaluate it. The picture is a two-dimensional picture of a vertical cross-section (through the center) of the tank.

(a). Let S be the surface defined by x^4 − 3x^2y^2 + 4z^2 = 17. Find the equation of the tangent plane to the surface S at (1, 0, 2).

(b)

Let f(x,y) = e^2xy

. Let P = (2,0) and Q = (3,2). Find the directional derivative of f at P in the

direction of PQ.

lim_x-->0⁺(4x+1)^cotx=

could you please show work and explain which rules you used.

Thank you

A travel agency is planning a trip to England for 100 members of a college faculty. The plane fare will be $600 per faculty member if all members attend the trip. With each cancellation, however l, the fare will increase by$250 per faculty member.

the cost to the agency is $20,000 plus $40 for each passenger.

What is the price that will generate the maximum profit for the agency?