### Velocity and Temperature Fields : Flow Fields, Acceleration, Irrotational Flow and Stokes' Theorem

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Please see the attached file for the fully formatted problems.

The current I , in amperes, flowing through a particular AC circuit at time t seconds is I = 120sin(70(pi)t-pi/6) What is the period of the current? 1/35 seconds pi/120 seconds 1/420 seconds 70m seconds

1. A test vehicle on a track goes through photo gates spaced 25 m apart at the following times: 2.00 sec, 3.30 sec, 4.30 sec a. Plot the position versus time of the vehicle. b. Plot the average speed of the vehicle in the time intervals versus time. 2. A rally driver has to maintain a constant speed between c

Please see the attached file for complete description 1. Write the first five terms of the arithmetic sequence: a1 = 3; d = 3 2. A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If t

Please see attached file for full problem description. 1. Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement. a. If then b. If f and g are continuous functions on [a,b], then c. If f

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Give exact and approx to three decimal places x^2+12x+36=64 Thank you!

Please help, figured out first two primes but am having allot of problems figuring out the third prime. Also need help with additional problem. Thanks Find lim x ->∞ ( (3x-2) / (3x+2) )^x (3x - 2)^x / (3x+2)^x = lim x ->∞ f'(x)/g'(x) x(3x - 2)^(x-1)*(3)/ x(3x-2)^(x-1)*(3) =(3x - 2)^(x-1)/ (3x

Please choose the correct answer: ∫ 12x(x - 2)^10 dx = x^12 + (24/11)x^11 + C x^12 + (2/11)x^11 + C (12/11)(x - 2)^11 + C (12/11)x(x - 2)^11 + c (x - 20/11)(x - 2)^11 + C (x + 2/11)(x - 2)^11 + C none of these b

13. Find the area under the curve y = 3e^-x - e^x , from x = 0 to x = ln(3)/2. 3 - 2(2^1/2 ) 4 - 2(3^1/2 ) 1 6 - 2(5^1/2 ) 7 - 2(6^1/2 ) none of these 14. Calculate, correct to the nearest hundredth, 2.25 ∫(2.73x^2 - 8.41x + 7) dx = 0.5

Q#11. The graph of y=f(x)=x^2 + 2x is shown in the graph. i) Find the slope of the secant line joining (2, f(2)) and (4, f(4)). ii) Find the slope of the secant line joining (2, f(2) and (2+h, f(2+h)) _____ + _____ h Q#12. Suppose an object moves along the y axis so that its locations is y=f(x)=x^2+3x at time x(y

1. R is the region bounded by the curve y = x^2 -2x and the x axis. Sketch the given region R and then find its area. 2. Using the following integral and the facts that v(t) = x'(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Answer the questions a - c. x'

The population P of a city is given by P = 2000e^kt . Let t=0 correspond to the year 1960 and suppose the population in 1950 was 1500. Find the value of k ( to 3 decimal places) and then predict the population in 2000. Please show all steps & graph, solve using derivatives or ln on calc.

3.A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope is tied to the bucket and the other end dangles loosely to the ground. A construction worker holds the end of the rope at a constant height (1.5 m) and walks away from beneath the pulley at 1.6 m/s. How

Question (1) First find a general solution of the differential equation dy/dx=3y. Then find a particular solution that satisfies the initial condition that y(1) = 4 Question (2) Solve the initial value problem dy/dx=y^3 , y(0) = 1 Question (3) Find the centre and radius of the circle described in the equation 2x2 + 2

By completing the square, identify the surface: x^2 + 4y^2 - z^2 - 6x + 8y + 4z = 0

A force of 650 pounds compresses a spring 5 inches from its natural length. Find the work done in compressing the spring 2 additional inches. Answer in inch-pounds.

Suppose that f is continuous on [a,b], f(z) < 0, and f (b) > 0. Set z = sup{x: f (t) < 0 for all t contained in [a, x]}. Prove that f (z) = 0. This is key to the proof of the intermediate value theorem. Incorporate the definition of least upper bound into your argument.

Let E be a nonempty subset of R and f:E-->R. State the definition f is uniformly continuous on E. Prove f(x) =x^2 is uniformly continuous on the interval[0,1]. keywords: uniform continuity

The purpose of this project is to find the values of x and y that will yield the optimum (maximum or minimum) value of a system and the optimum value of a system using algebraic and graphical methods. Follow these ten steps (see mp1.jpg) to determine the optimum value of z and the values of x and y that yield the optimum valu

The following table shows the average number of hours worked per week at a place of... Calculus Functions. See attached file for full problem description.

See attached file for full problem description. Do only the 4th problem.

The flywheel of a gasoline engine rotates at an angular speed of 3240 rpm. Find its angular displacement (in revolution) in 10 sec.

For speeds between 40 and 65 mph, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 2.23 per gallon, and the driver is paid 15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck.

Find the value of cot 35.2 degree rounded to four significant digits.

Archimedes principal of buoancy states that an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid the object displaces. A rectangular box 1foot X 2 feet X 3 feet and weighing 384 lbs. is dropped into a 100 foot deep freshwater lake (density 62.4 lbs/cubic foot). The box immediately begins to

See attached file for full problem description. Can you show more steps in the problems how you got the answer?

A stone is dropped from a high cliff and falls with velocity v = 32t feet per second. How many feet does the stone travel during the first 3 seconds?

Use rectangles to approximate the area bounded by the graph of the function f(x) = x3, the x-axis, and the lines x = 0 and x = 2. Use n = 4 subintervals.

If we break the interval from x = -1 to x = 1 into n = 4 subintervals, what is the width of each subinterval?