Find the number in {x € R: – 2

Q: Among all pairs of numbers (x,y)such that 4x+2y=24find the pair for which the sum of squares, x2 +…

A: Given equation,4x+2y=24we have to find values of x and y such that (x2+y2) is minimum

Q: Find the number in (-5≤x≤1) such that the sum of thrice the number and its square is a maximum.…

A: let the x be the number in the  interval [-5,1]

Q: To show that ( n + a ) b = θ ( n b ) ( n + a ) b = θ ( n b ) for any real constants a a and b b…

A: Here we use the binomial expansion:

Q: Find two positive real numbers x and y such that they add to 120and x 2y is as large as possible.

A: Given: x+y=120and  y=120-xAlso given that z=x2ybut we have z=x2120-x=120x2-x3    ...(1)

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: ketch represents f(x) = x² + x – 6 and g(x) = -x - 3 M If MN = 3, calculate the possible length(s)…

A: Graph for a function is representation of function with respect to independent variable on axes.…

Q: For any real number xx the maximum value of 4−6a−a2 is, 4 7 9 13

A:

Q: Find two numbers whose sum is 20 and whose product is a maximum A None of the given choices B 10 and…

A: Using function,

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A:

Q: Find a positive number x such that the sum of 4x and is as small as possible. Does this problem…

A: Solution is given below:

Q: 6-Given P(x)=2x3+3x2+1 and Q(x)=8x-2, find all the possible values of so that Q(x)<P(X )state your…

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Q: (x – 1)°(x + 2)°(x – 3) < 0

A:

Q: n! Prove that the maximum value of when n. +n2 t+ nr =n n.! n.! na! ... is given by n, = na = = ny =

A: The expression n!n1!n2!...nr! will be number of different permutations of n objects with n1, n2...nr…

Q: Suppose that 4 < f '(x) < 5 for all values of x. What are the minimum and maximum possible values of…

A:

Q: solve the following rational inequality for x

A: Givenx+1x+3&lt;0solve the following rational inequality for x

Q: A cubic function can have at most, how many unique zeros? O 3 O 1 O 2 6.

A: As we know that a cubic function is degree 3 polynomial function.

Q: a) Solve for x in the following questior 7-x = 1 %3D

A:

Q: Find the maximum of f(x, y) = 4y + 7xy – 4x on the square domain 0 < x < 8, 0 < y < 8. (Give an…

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Q: Find the number in {x € R: – 2< x < 2} such that the sum of that number and its square is a maximum.…

A:

Q: Find a positive number a such that the sum of 25x and is as small as possible. Does this problem…

A:

Q: Find a closed-form formula for f(n)=...) k+1 II₁¹. (Write your answer in the form of: k

A: We will use definition of product notation to find closed form of given product form.

Q: 34. If both x and ++) are positive integers, what is the least possible value of x ? F. 21 G. 27 Н.…

A: x=?

Q: Given the interval (a, b) on the x-axis with the point c inside, find the greatest value for ð > 0…

A: on the given interval (a,b) on the x-axis with the point c inside, find the greatest value for…

Q: A rectangular area needs to be fenced in such that fencing on one side costs $15 per meter while the…

A: Given that, A rectangular area needs to be fenced in such a way that fencing on one side costs $15…

Q: Consider the following functions. f,(x) = x, f,(x) = x², f,(x) = 5x - 4x² g(x) = c,f,(x) + C2f2(x) +…

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Q: Find two positive numbers whose product is 193 and whose sum is a minimum. A 0,193 1,193 193 2/193,…

A:

Q: 11. Determine three positive numbers x, y and z whose sum is 10 that produce a maximum value for the…

A: x,y and z be the three positive numbers whose sum is 10that produce a maximum value for x2yz

Q: Given the interval (a, b) on the x-axis with the point c inside, find the greatest value for 8 > 0…

A: The objective is to find the correct option.

Q: 2. Let f(x) =-x°(x- 2)’(x+7)°. a) As x→ 0, f(x) → b) As x →-0, f (x)→ c) How many turns f(x) can…

A: The given function is fx=-x2 x-23 x+72. Note that the leading term will be -x2·x3·x2=-x7. Therefore,…

Q: Find the two positive integers x and y such that x + y = 60 an 2 xy is maximum

A: The equation is x+y=60 where x and y are two positive integers. The main objective is to find x and…

Q: 14. A 2x + 17 25 112 B 133 25 D 39

A: The converse of the Hinge theorem states that when two triangles have two congruent sides, then the…

Q: Solve the following rational inequality for x. Give your answer in interval notation. Provide your…

A: Let's solve for x.

Q: Find the value of a such that 1 0. 3 2 2 a- 2

A: I have solved the determinant

Q: Find the zeros of f(x), and state the multiplicity of each zero. (Order your answers from smallest…

A: Given, (x2 + x − 20)4(x2 − 16)5

Q: Find a positive number a such that the sum of 16x and is as small as possible. x = Does this problem…

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Q: Find the number in {xER: -2<x<2} such that the sum of that number and its square is a maximum. Write…

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Q: Find the number in {x € R: – 1 < x < 5} such that the difference of twice the number and its square…

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Q: Find a positive number a such that the sum of 36x and is as small as possible. Does this problem…

A: The sum of the number of 36x and 1x

Q: In the figure, find PR such that 0 ≤ PR ≤ 3 and m∠ is a maximum

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Q: Example: Given m(x) = x + 3, n(x) = x² – 9 , and p(x) = vx + 1 Find (n – m) (x) and write the domain…

A: Interval:- A interval is a set of real numbers that contains all real numbers lying between any two…

Q: Find the number in (x € R: - 2< x< 2} such that the sum of that number and its square is a maximum.…

A:

Q: Let a, b and c be real numbers that satisfy b a+== b+ C C = C +==2 a a - b (A) 3 (В) 5 Find the…

A: Let's find.

Q: A company finds that if they price their product at $ 30, they can sell 138 items of it. For every…

A: To find the maximum revenue possible

Q: 9) Find the Maximum or Minimum value of the following quadratic function:

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Q: Determine a constant k such that (kA)" (kA) = 1, where -2 A = Is there more than one value of k that…

A: Given: kATkA=1 A=-21-1

Q: Find positive constants a and n, such that n - 4 > an for all n > n,.

A: To find positive constants a and n0 such that n−4≥an for all n&gt;n0.

Q: Solve for x. (Enter your answers as a comma-separated list.) In(x) + In(x + 8) = 0 X =

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Q: Let a, b, and c be real numbers such that a + the maximum value of (ab + bc + ca).

A: