Given two nonnegative numbers p and q such that p+q=6, what is the difference between the maximum and minimum of the quantity p2q2/84? (Enter your answer as a fraction.)

Q: Consider two nonnegative numbers x and y such that x+y=3. What is the difference between the maximum…

A: The given  equations are x+y=3 and the maximum and minimum quantity is 4x2y2 to find the maximum and…

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

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Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

A: A point x is said to be an interior point of S if there exists a neighborhood N(x) of x such that…

Q: What is the particular solution for y′=5ex −6x3 +4x such that y(0)=−8? Do not include "y=" in your…

A: The given differential equation is, y′=5ex −6x3 +4x.

Q: If p(x) = (x + 2)(x + k) and if the remainder is 12 when p(x) is divided by x – 1, then k =

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Q: Express the following in Partial fractions 9x2 + 48x + 18 (2x +1)(x2 + 8x + 3) Question

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Q: Solve. k = npv, for v

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Q: Two negative integers are 8 units apart on the number line and have a product of 308. Which…

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Q: What is the difference of two positive numbers whose sum is 16 such that the product of one number…

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Q: Find and show on the real number line the solutions set of the in equality. 1. l 7 - 4x l ≤ 9 2. l…

A: Since you have posted two questions, we will solve first question for you. To get another question…

Q: Solve for r in terms of P, n, and t: P = (1 + =) ² Or=(nP-1) Or=In(P)-1 Or = n(P-1) Or="(P-1) T=…

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Q: How many positive integer solutions are there to x1 + x2 + x3 + x4 < 50 ?

A: We want to find the number of tuples x1, x2, x3, x4 that satisfy the given inequality. Note that for…

Q: (ii) Find the set of values of k for which |(x- 4)(x+2)|=k has four solutions.

A: Let's find.

Q: Given the line f(x) = mx + b passing through the origin and the point (10, 9), find the values of m…

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Q: - Find two positive even consecutive integers such that the square of the smaller integer is 10 more…

A: Consider the first even positive integer be 'x'. The second consecutive even positive integer be…

Q: Use the fact that x'-6x = 2 has no integer solution to prove there do not exist 3 consecutive…

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Q: Show that for the d-cube, fk = 2ª-k (%) k.

A: It is required to show that for the d-cube: fk=2d−kdk

Q: Show that there is no rational number r satisfying 2r = 3.

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Q: 5 Suppose f(x)= )dr AV 4x-3 +C, for constants A and C, what is the value of A? 4x -3 Write the…

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Q: What is the largest number k for which 2x+3y=20 and 3x+4y=k have the same number if positive integer…

A: Given that, there are two equations following, 2x + 3y = 20…

Q: if the operaton ☆ is cde fined on the set of rational numbers by solve the equation X * 4= fx*…

A: Solution :  Given that the operation * is defined in the set of rational numbers by    x * y = x + y…

Q: For any numbers a andb and an even natural number n, show that the equation x" + ax + b = 0, x in R,…

A: Here, to prove this result we have to use Rolles theorem.

Q: A positive integer is 4 less than another. If 6 times the reciprocal of the smaller integer is…

A: Let the smaller integer is 'x' and larger integer is 'y'.A positive integer is 4 less than…

Q: When P(x) is divided by (x-1), the remainder is 3. When P(x) is divided by (x+1), the remainder is…

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Q: What is the sum of all critical numbers of 8(x) =2r+3x-36x+ 87 A) -2 B c) o D) 1

A: given functiony=2x3+3x2-36x+8dufferentiate w.r.t. xy'=6x2+6x-36let…

Q: does the eqations |2x+1|=|3x+4| and |2x+1|=3x+4 have the same solutions

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Q: Show, by using the discriminant, how many solutions 2x2-x-5=0  has. must show all work

A: The discriminant of a quadratic equation ax2+bx+c=0 is given by D=b2-4ac.  We have h quadratic…

Q: 23. Which of the following satisfies 2x² + 5x = 7? i) x=1 ii) x= -2 iii) x= 5 iv) x= 0

A: 23. Given equation is: 2x2 + 5x = 7 We have to solve for x. Then we get, 2x2 + 5x = 7 2x2 + 5x - 7 =…

Q: 3. Suppose f(x) =. ) dr=AV 5x-4 +C, for constants. %3D If 5x-4 A and C, what is the value of A?…

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Q: Suppose X=N(10, 1.924)Pr(7.6 less than X less than 9.3)

A: In this question we have X as random variable which follows normal distribution with mean = 10 and…

Q: Determine the values of m and n for f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero,…

A: Given that f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero, and when divided by (x-2)…

Q: A box with no top that is twice as long as it is wide has a volume of 36 m3. If x is the width of…

A: A box with no top that is twice as long as it is wide has a volume of 36 m3.

Q: If r(x) = In (3x³ +x + 6), find r' (æ). Select the correct answer below: In (9x? + 1) 9x2 +1 3x3…

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Q: Given two nonnegative numbers a and b such that a+b=4, what is the difference between the maximum…

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Q: Determine the number of integer solutions to the equation below: X1 + x2 + x3 + X4 + x5 = V subject…

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Q: The cost per unit, C(x)C(x), when manufacturing xx units is given by the formula C(x)=2x^2−24x+76…

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Q: The sum of values of x for which the equation x0929 + x. 3o92 * = xl092 15 holds true is

A: The graph is shown below:

Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

A: From the given information we want to find How many positive integer solutions are there to x1 + x2…

Q: How. Solve the following PDES OP-x² =Dq+y² 2. q=P-PX

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Q: How many nonnegative integer solutions of x₁ + x2 + x3 + 4 = 12 are there in which no r; exceeds 4?…

A: The given problem is to find that number of nonnegative integer solutions for the given equation…

Q: Translate this statement into its symbolic form: "For every rational number x, there exists a real…

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Q: Similarly, for F2, since the middle third of each side of F1 is removed and replaced with two line…

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Q: The nth term formula for the maximum number of pieces of baked cheese cake, Pn, that can n(n+1) be…

A: Given that , Maximum number of pieces of baked cheese cake Pn=nn+12 where n is number of straight…

Q: Show that if r is a rational number, then 2r2+3r+ 1 is rational as well.

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Q: 1. Joseph wants to find the side length of a square that has an area of 150 feet. Should his answer…

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Q: The sides of a rectangle are (x + 1) mand (2x + 5) * m . If the perimeter is 36 m, find the value…

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Q: 2. If f(x) = (x + 13)² +(x - 5)° + (x +5) , find f(3)- If necessary, use the Math Editor x to write…

A: our objective is to find f(3)

Q: A(n) ______ number is a real number that cannot be expressed as a ratio of two integers

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Q: How many integer solutions are there to the equation x + y + z = 10 for which a. x, y, and z are all…

A: We Know that The number of non-negative integers solutions to x1+x2+x3+. . .+xn = r is equal to C(n…

Q: What is the difference of two positive numbers whose sum is 16 such that the product of one number…

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