5.3. By setting k = , or otherwise, show that 1 (18) (2m +1)2 m=0 where n 2m + 1, i.e. expression (18) corresponds to a sum of n2 only over odd n.

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A: We will use Newton's law of cooling to solve this question.

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A:

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

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A:

Q: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: п-1 k n-2 n-1 n-2 () x6n-10 = p %3D k - 4 X6n-9 = 4 n-1 n-1 n-1 k n-1 X6n-8 = h X'6n-7 = P k n-1 n-1…

A:

Q: n is increasing, and those on w 3x + 5.

A: Introduction: The input values of a function f(x) where f(x) has minimum or maximum values are…

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A:

Q: (d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal…

A:

Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

A: To find the population assume that the rate of change of mosquitoes remains constant at 180 per day.

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A: The given matrices are M=8541  and  N=5-1-52. Evaluate MN as follows.…

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A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

A:

Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

A:

Q: 2.5. Let 1, 0sns9 0, elsewhere and h[n] = { 1, 0sns N 0, elsewhere x[n] %3D where N s 9 is an…

A: Since you have asked multiple question, we will solve any one question for you. If you want any…

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A:

Q: #4 (Greenwell, #52, p. 271) The number of people P(t) (in hundreds) infected t days after an…

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Q: 3 If ƒ (x) = 2 + x, evaluate Σƒ (k+1). k=1

A: We can answer the question as below.

Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: If n=10 and p=0.5, find P(x=8) Give at least 4 decimal places.

A:

Q: Q1 (a) Calculate the coefficient of a'y z in (r+y+2)13. (b) In her discrete math class, Karen was…

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Q: Ex : Express the Sum o+ 2 +4+6+8 in Sigma nata tion. K = -2 %3D -2

A: First we find nth term of AP then replace k by k+3

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: Q3) IF N=[9; 8; 6; 5; 4] find 1- G=length(N) 2- C=N; 3- max (C) 4- min (N) 5- T=C+N

A:

Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

A: The population is increasing per day by a fixed number. So the population follows a linear model of…

Q: (5) Show that T(n)o(n) > n for all n E N. 11

A:

Q: If m*n Denofes -3伝 + Find the 2mn?

A: Given that m*n=2m-n2 therefore -3*5=2-3-52

Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with…

Q: Then k is equal to

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A:

Q: 1. Find two non-negative numbers such that the product of the first squared and the second is 108…

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Q: Suppose that q +1 is a constant. Calculate the sum n Sn > kq* = q+ 2q² + 3q° + · · · + ng" k=1

A:

Q: The average pollen count in a certain city on day x of the pollen season is P(x) = 6x − 0.2x2  (for…

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Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

A: Given data, total mosquitos = 554 everyday mosquitos increaments p(0) = 65

Q: Suppose m=nd where n is odd and 1<n<m. Prove that 2m+1 is composite.

A:

Q: Suppose P(t)represents the population of a certain mosquito colony, where tt is measured in days.…

A:

Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

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Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

A:

Q: suppose X=N(10, 1.924)Pr(X is less than or equal to 8.5)

A: Given a normal distribution with mean 10 and variance 1.924.the relationship between standard…

Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days.…

A:

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: 11. If AJKL AMKN, find the value of x. K 12 N 20 x + 1 L. 3x-2 J

A:

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

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Q: 7. (12) Show that the hypotheses of the Mean Value theorem are satisfied and find all values…

A: 1. For the testing of the hypothesis of mean value theorem we need to know whether the function f(x)…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.