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(a)
To calculate: The probability that a call will come within 12 minute when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:
P(t)=1−e−t3
(b)
To calculate: The probability that a call will come within 2 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:
P(t)=1−e−t3
(c)
To calculate: The probability that a call will come within 5 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:
P(t)=1−e−t3
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Chapter 4 Solutions
Calculus: An Applied Approach (MindTap Course List)
- (1) (16 points) Let f(x, y) = 2x + 3y + In(xy) (a) (6 points) Calculate the gradient field Vf(x, y) and determine all points (x, y) where ▼f(x, y) = (0, 0). (b) (4 points) Calculate the second derivative matrix D²f(x,y).arrow_forwardLet f(x, y) = 2x + 3y+ In(xy)arrow_forward(3) (16 points) Let D = [0, π/2] × [0, 7/6]. Define T: DCR2 R3 by → T(0, 4) = (2 sin cos 0, 2 sin sin 0, 2 cos x). Let S be the surface parametrized by T. (a) (8 points) Determine the normal, call it n(p), for the tangent plane TS at an arbitrary point p = T(0, 4). (b) (4 points) Show that n(p) parallel to the position vector T(0, 4) determined by p? Do the two vectors have the same direction or opposite direction? Explain. (c) (4 points) At which points p, if any, is TS parallel to the xy-plane?arrow_forward
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