1)How much more area does a 18-inch rim have compared to a 16-inch rim on a car? Round the answer to 2 decimal places.
2)The area of a sector is 110.60 sq yd and the radius of the sector is 10.82 yd. What is the measure of the central angle rounded to the nearest tenth?
3)The radius of a twelve-cut pizza is 7.5 inches and the radius of an eight-cut pizza is 5.25 inches. Compare the areas of the two pizzas. Round the answer to 2 decimal places.
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Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem. y' = y − 5x, y(3) = 1.
y1 = ______
y2 =______
y3 =_______
y4=________
Please show all work, neatly, line by line and justify steps so that I can learn.
Thank you!
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The radius of a sphere is measured to be 6 inches, with a possible error of 0.02 inch. Using differentiation, approximate the maximum possible error in calculating the volume of the sphere.
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If money is flowing continuously at a constant rate of $2, 000 per year over 5 years at 6% interest compounded continuously, find the following.
1. The total money flow over the 5-year period.
2. The accumulated amount of money flow, compounded continuously, at time T = 5.
3.The total interest earned.
4.The present value of the amount of money with interest.
In: Math
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A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude of 14 km and climbs at an angle of 20 degrees. At what rate is the distance from the plane to the radar station increasing 4 minutes later?
The distance is increasing at km/min.
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Use spherical coordinates.
Evaluate
| (x2 + y2) dV | |
| E |
,
where E lies between the spheres
x2 + y2 + z2 = 1 and x2 + y2 + z2 = 9.
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Exercise 2 2.1. Write each expression as a single logarithm and, if possible, simplify. ln (x - 4) - ln (x+ 2); ln (x) - 3 [ln (x - 5) + ln (x + 5)] ; log x − 3log(x – 1) 2.2. Solve for x. ln(x – 1)= 1 ; e2x = 4 ; log3x + log3(x2 – 8) = log38x ; 4x2(2x) − 9(2x) = 0
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f(x)= 2x^4 - 4x^2 + 1
a. Indicate where the function is increasing or decreasing.
b. List the coordinates of where extrema occur.
c. State where the graph is concave up or concave down.
d. List the coordinates of where points of inflection occur.
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Verify the Divergence Theorem for the vector eld
F(x; y; z) = hy; x; z2i on the region E bounded by the planes y + z = 2,
z = 0 and the cylinder x2 + y2 = 1.
Surface Integral:
Triple Integral:
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2.
(a) Find an equation of the tangent plane to the surface x4 +y4 +z4 = 18 at (2, 1, 1). Find a derivative in direction (2,2,1) at point (2,1,1). (b) Use Lagrange multipliers to find the minimum and maximum values of f(x,y,z) = 8x + y + z on the surface x4 + y4 + z4 = 18.
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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = x3 + y3 − 3x2 − 3y2 − 9x
| local maximum value(s) |
5 |
||
| local minimum value(s) |
−31 |
||
| saddle point(s) |
(x, y, f) = |
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Solve the following system of equations using Gaussian or Gauss-Jordan elimination.
w + x + y + z = -2
2w +2x - 2y - 2z = -12
3w - 2x + 2y + z = 4
w - x + 7y + 3z = 4
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A particle moves from point A = (0, 0, 0) to point B = (2π, 0, 2π), under the action of the force F = xi + yj − zk .
a. Calculate the work done by the force F on the particle if it moves along the conic-helical curve
r(t) = (t cost )i + (t sint )j + tk with 0 ≤ t ≤ 2π.
b. Find a parametric vector equation for the straight line connecting A to B, and calculate the work done by the force F on the particle as it moves along this straight line.
c. Is the force F conservative or not?
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Suppose a company's revenue function is given by
R(q)=−q3+320q2R(q)=-q3+320q2 and its cost function is given by
C(q)=290+20qC(q)=290+20q, where qq is hundreds of units
sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of
revenue and cost, respectively.
A) Find a simplified expression for the marginal profit function.
(Be sure to use the proper variable in your answer.)
MP(q)=MP(q)=
B) How many items (in hundreds) need to be sold to maximize
profits? (Round your answer to two decimal places.)
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