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Evaluate ∫C (x + 2y) ds, where C is the curve defined by y = √(4 − x2), for x ∈ [0, 1].
The lengths (in minutes) of a random selection of popular children’s animated films are
listed below. Estimate the true mean length of all children’s animated films with 95%
confidence.
90 84 83 91 75 88 78 96 78 79 77
Given r1 = 3i − 4j + 3k, r2 = 5i + 3j − 6k, r3 = 2i + 7j + 3k and r4 = 4i + 3j + 5k.
Find the scalars a, b and c such that r4 = ar1 + br2 + cr3
2. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 5 per hour. Thus, the Poisson parameter for arrivals over a period of hours is μ = 5t.
(a) What is the probability that exactly 4 small aircraft arrive during a 1-hour period?
(b) What is the probability that at least 4 arrive during a 1-hour period?
(c) If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?
Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.
a. Show that f is one-to-one and onto.
b. Show that g is one-to-one and onto.
c. Determine the composition function g o f
d. Determine the inverse functions f -1 and g -1 .
e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1
Every continuous function is differentiable.
True or false with full explanation.
1. Two charges are 60cm apart, in air. One charge Q1 is +1.67 x 10-7C; The other Q2 is
-1.67 x 10-7 C. What is the electric field intensity at P midway between the charges?
2. The average distance between the electron and the proton in a certain atom is 5 x 10-10m. How strong is the electric field that the proton experiences?
3. Two charges Q1 = 2.3 x 10-9C and Q2 = 3.5 x 10-9C, are 55mm apart. What is the electric field halfway between them?
4. Two charges of 6uC are 2.5m apart. Where is the electric field along the line joining them equal to zero?
5. What is the electric field at one vertex of an equilateral triangle whose sides are 10cm long if there are charges of -30uC at the other vertexes?
Explain: Can the force caused by an electric field be greater than the force due to a gravitational field? Give an example to prove this.
Solve the inequalities. Give your answer in interval notation, and indicate the answer geometrically on the real-number line.
a) t + 6 ≤ 2 + 3t
b) 3(2 – 3x) > 4(1 – 4x)
Determine the digit 100 places to the right of the decimal point in the decimal representation 7/27. (Apply Polya’s Strategy)
A magnetic field B= 0.6T is directed upward through a circular loop of diameter 7 cm and 500 turns. The loop is initially horizontal, so it is perpendicular to the magnetic field. It rotates through a horizontal axis so that the plane of the loop is at 74° with the horizontal axis within 1 second. What is the magnitude of the induced emf?
#339914 on Dec 2023