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

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Q: Question 21 > 10 -8 -6 8 -5 4 -3 7 -8 7 [E] [D] = 8 2 -1 1 -2 9. 5 6 1 2 4 10 3[E] – 4[D] = -

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Q: 2 excos2rdr / 2) 0

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Q: Question 5, Show that a + b = |a|+ [b] ⇒ ab > 0.

A: To Show : a+b=a+b ⇔ab&gt;0

Q: Show how James Garfield (1831-1881) proved Pythagorean Theorem

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Q: d) At what time are the ships closest? Remember to justify with analysis of your number line and…

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Q: l'Hôpital's Rule

A: Given equation

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Q: Quèstion 8 If det A = - 4, det B = 2, then det B2A1 = %3D -16 O -8

A: We know that  Det(A^-1)=1/det(A) Det(A^n)=(det(A))^n Det(AB)=det(A)det(B)

Q: As an advanced math learner, what would be the top 10 most used theorums in Real Analysis?

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Q: Question 5 of 5 Simplify 28

A: Given,

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Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

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Q: 1. Expand the following expressions: a) (x+1)(x-4)

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Q: (1+n)"+1 Find a3

A: Given an  = (1+n)n+1

Q: 1.) What do you think the world will be like if Calculus wasn't discovered?

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Q: SUIOב What is the value of k so that dx eklkx-1)=4ek*x-k, %3D

A: Topic - derivatives

Q: 1. Show that dr

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Q: Question 3 Show that 118 a 183 b 132 12 b2 c2 = = (b-a)(c-a)(c-b)

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Q: Compute ()

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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.