10. The organizers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize of $25. The total prize money distributed is $3000. Find the number of winners, if the total number of participants is 63.

Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Eu, by Pupıng the…

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Q: 4. Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find…

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A: Please see the attachment

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Q: (1-x)y" - 2xy + n(n+i)y =0 [ Legendre Equation] |

A: We will solve it by power series method

Q: Problem #7: (a) Solve the initial value problem (x - 1)y' - *y = 16(x – 1)², y(2) = 0 %3! (b) Write…

A: The given differential equation is                                       x-1y'-2xx+1y=16x-12,…

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Q: nKen puzzle

A: 1). Given,

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Q: 125 Evaluate the formula z= when p= pq n= 410, p= 0.25, and q = 1-p. 3D(Round to two decimal places…

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Q: Establish that if a is an odd integer, then 2" aʻ = 1 (mod 2" *2) for any n 2 1.

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Q: Let D be the region in the plane bounded by the parabola x = y – y and the line x = y. Find the…

A: To calculate the center of mass of a thin plate of constant density

Q: Is there a way to solve this w/o using L'Hospital's rule?

A: Solution

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

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Q: 10. Solve 4y' + 8y = 7, y(0) = -2 by any method that we have learned this semester. Make sure to…

A: Given differential equation is a linear differential equation of first order. Linear differential…

Q: 3.х + у +z-5 2х + Зу + 5z %3 8 4х + 5z %3D 2

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Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

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Q: 7 In the interval T, 27|the equation sin x = - 8 O (a) has no solutions (b) has one (and only one)…

A: We are given sin2x=78 and we need to find the number of solution in interval [π, 2π]

Q: Find the minimum distance. a. Locate at 1:5 is_km away. b. Locate at 1: 7 is_km away. km away. km…

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y = eV1--, y(0) = 0…

A: Given equation: y'=e1-t2-y2 with condition y(0)=0   To find: Maximal interval of existence and…

Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

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Q: Solve the equations. Sketch the circle with triangle(s) & 0 & length of each side in its proper…

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Q: The following conclusion is based on which assumption:               Gregory had studied all night…

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Q: 1. What is the integral that describes the enclosed region between y = 4x- x and the x - axis ? A.…

A: We will use the properties of definite integral and area function to solve the given problem.

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Q: A revolving beacon of light is situated 925m from a straight shore. It turns at a rate of 2…

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Q: N(-3, 3*) 3. Find the equation of the line in polar coordinates that passes and the pole.

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Q: The bus is late or my watch is fast.

A: Solution

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about…

A: Solution-Lets draw the curve and the lines and identify the bounded area.

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A: When x tends to 2- then the sign of derivative is negative since it is decreasing from left side of…

Q: How many distinguishable permutations are possible with all the letters of the word ELLIPSES?

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

A: We will draw graph of given functions and identify the region bounded then will find range of…

Q: Problem : (i) Can we find nonzero symmetric 2 x 2 matrices H and A over R such that [H, A] = µA %3D…

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Q: Evaluate the double integral over the given region. II (x + Vy) dA, R: 0<xs1, 0<ys1 R

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Q: The sum of three numbers is 6. If we multiply the third number by 2 and add the first number to the…

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Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: Use Shell Method only Find the volume generated by revolving the area bounded by the given curve and…

A: To find: Volume generated by revolving the area bounded by the curves y=x3 , x=0, y=8 about the…

Q: Let F = yz?i+6y j+8Ē, and let S be the surface of the solid region bounded between the planes z - y…

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Q: find The complete SoLution of The differential eqution y+2y+4y=asX Subjected to The Condioin y…

A: The given differential equation is                                   y''+2y'+4y=cos x with the…

Q: t will be the domina ?

A: Given: Z is a complete graph with n vertices. To find : Domination number of R.

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Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

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Q: can you also answer no. 3.

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Q: Sketch the graph of a function which satisfies each of the following conditions: g'(-2) DNE g'(x) >…

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