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Math 104: Homework 7-
1. (a) Let S be a subset of R, and let f: S → R and g: R → R be uniformly continuous functions. Prove that the composition g ? f: S → R is uniformly continuous.
(b) Let f and g be two uniformly continuous functions from S to R. Prove that f + g is uniformly continuous.
(c) Show that there exist uniformly continuous functions f and g from S to R such that the multiplication f · g is not uniformly continuous.
2. Let f be a real-valued continuous function. Recall that for any subset S ⊆ R, then f(S) is defined as { f(x) : x ∈ S}. Suppose that f(I) is open for any open interval I. Prove that f is monotonic.
How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards? A bagel show has onion, poppy seed, egg, salty, pumpernickel, sesame seed, raisin, and plain bagels. How many ways are there to choose:
The owner of a restaurant serving continental style entrees was interested in studying ordering patterns of patrons from the friday to sunday weekend time period.records are maintained that indicated the demand for desert during the same time..
A worker on scaffolding 70 ft above the ground needs to lift a 450 lb bucket of cement from the ground to a point 25 feet above the ground by pulling on a rope weighing 5 lb/ft. How much work is required?
Represent the impedance by a complex number, in rectangular form and in polar form. Find the magnitude of the impedance and its phase angle. Does the voltage lead or lag the current? Explain.
Assume that d=sa+tb is a linear combination of integers a and b. Find infinitely many pairs of integers ( s sub k, t sub k ) with d=s sub k a + t sub k b
Name at least five important factors to be considered in selecting a software vendor. For each factor, explain why it should be considered and potential consequences of not considering the factor in selection of a software vendor.
(Round the number that you compute and use to the nearest whole number.) According to the model, what will the enrollment be in the year 2025?
The second number is 6 more than the first. What are the possible values for the first of the two numbers?
For the points and Q, find (a) the distance d (P, Q) and (b) the coordinates of the midpoint of the segment PQ. d= (P,Q)
With one method called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is acepted if everyitem in the sample is okay
Kayla left school and traveled toward the ocean at an average speed of 24 km/h. Danielle left three hours later and traveled in the same direction but with an average speed of 60 km/h. How long did Kayla travel before Danielle caught up
one side of a triangular lot is 150 ft and the angel oppiste this side is 55 degrees. another angel is 63 degrees.
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