2. Find two numbers whose difference is 100 and whose product is a minimum. 3. Find two positive numbers whose product is 100 and whose sum is a minimum. 4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares? S.What is the maximum vertical distance between the line y x +2 and the parabolay = x2 for -1 < x < 2? 6. What is the minimum vertical distance between the parabolas yx 2 1and y = x- x? 7. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible. 8. Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible. 9. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is kN Y = X 1#\ y 2 Y= 10 0-> s whoe x# 00 & xty= Minimize min. xt 10 0 (3 MIJExt MixEAt mixt mtx)1100x-2 l@0

Q: 2. CAUCHY SEQUENCES Fix a constant ≤K≤7. Let (n)-1 be a sequence such that x₁ = K and for all n 9…

A:

Q: 4. Determine the 75th derivative of each of the following functions. f(x) = 3 cos 2x b)

A: given function is f(x)=3cos(2x) we know d dx(cos(ax))=-asin(ax)  and d dx(sin(ax))=acos(ax)

Q: Evaluate the integrals. 3 6 k dt 4+ t2 3pi/2i+3pi/4k (4 – t² In 3 6te'i + 7e'j+2 In tk dt 3.756

A:

Q: (b) How will an increase of $1 in the hourly labor rate affect the total cost? The total cost will…

A: The current total cost is  80+0.3*27*27 +50*2- 27*2= 344.7

Q: 18. Find the distance AB between the centers of the two rollers in Fig. 6-43.

A:

Q: b. Use part (a) to perform the F test [show the formula used to calculate F-statistic value] for…

A:

Q: Prove that every graph G on {1, ... n} which is acyclic and has n – 2 edges has exactly 2 connected…

A: A graph with v vertices and e edges has at least v-e connected components. By induction on e, If e=0…

Q: 1. Solve the problem max 1- (x- 1)2- e

A: Here, consider the function f(x, y)=1-(x-1)2-ey2 subject to x2+y2≤1. The required partial…

Q: Preview Activity 5.1.1. Suppose that the following information is known about a function f: the…

A:

Q: b Show that the real valued series, 1 sin(r? + 5x +6) 4t 3t is uniformly convergent for r eR

A:

Q: I need help with question 2, parts a -e

A:

Q: Let set A = {1,2,3,4} and let R1 and R2 be binary relations on A. Specifically, let: R1 = {(1,1),…

A: R1 = { (1, 1) , (1, 2), (2, 1), (2, 2), (2, 4), (3, 4), (4, 2), (4,3) (4, 4)} R2 = { (1, 2), (1, 3),…

Q: 6. The equation for the regression line relating the salary and the year first employed is given…

A: Given: The regression equation is: Predicted Salary=4255424-2099 Start Year

Q: x 3+1 a): lim x -1 x+1

A:

Q: Ginen the point P=(x)y) vn 2)- la) find the distance ralx?ty2 the origin O = (0,0) to P= (x,y) amor…

A: Given 2) P=6,2

Q: 5. Ascience experiment involves periodically measuring the nuinber of old bells present on a piece…

A:

Q: Assume that the distribution of heights of young women aged 16 to 22 is approximately Nomal with…

A: c) The population mean is μ=62.05 The mean and standard deviations are  x=62.65753425sd=2.95906882…

Q: a) Given that the angle between the ray in the water and the perpendicular to the water is 29.7°,…

A:

Q: 22. A hex head bolt, Fig. 6-47, measures 0.500 in. across the flats. Find the distance x across the…

A: (22) Given that , Distance across the flats = 0.500 inch find the distance x across the corners.

Q: FIGURE 6-36 315 186 121 65.1 306 156 106 FIGURE 6-37 586 216 FIGURE 6-38 Slant height 21.8i FIGURE…

A:

Q: Solve the problem max xy+x+ y subject to x2+ y² < 2, x +y 1.

A: We have to find the maximum value of xy + x + y by using the given conditions

Q: 20. A surveyor starts at A in Fig. 6-45 and lays out lines AB, BC, and CA. Find the three interior…

A:

Q: 3. A lucky customer at a used car dealership will get to randomly select one key from a barrel of…

A: The probability of event that either A or B will happen can be given as, P(A∪B)=P(A)+P(B)-P(A∩B),…

Q: Cond Consider Thomee's function. hi [o hox) a fer x e [e] ae irationals and 0 for x. Tonlar Show.…

A:

Q: 1. An urn contains 4 red balls, 3 blue balls, 2 green balls and one black ball. One ball is selected…

A: Given information: 1. It was stated that an urn contains 4 red balls, 3 blue balls, 2 green balls…

Q: 27. A beam AB is supported by two crossed beams (Fig. 6-52). Find distance x. 28. Common Rafters:…

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.