Prove by cases that 25x² + 35x is an even integer whenever 5x-7 is an integer. Note here that the variable x may not necessarily be an integer.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

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Q: 24 xp-

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A: Based on the general formula of eular's method we will solve the problem. Please follow the procedur...

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A: I am attaching image so that you understand each and every step.

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Q: Apply Differential Equation A lake has a volume of 458 cubic km, and its rate of inflow and outflow ...

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Q: Instructions for forms of answers in differential equation problems: For second order DEs, the roots...

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Q: 2. f (x) - 2x2 if メくQ 2- メ if x 2 2

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Q: 1 Evaluate the following integral. dx X4V9-x2

A: ∫vn dv = vn+1n+1+C

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Q: Select ALL possible answers if there is more than one. * 1 16 Let f(x) =- ifx<- 2 . If f(x) is conti...

A: Let's find. 

Q: Ax) = ,5-9,4+73 -5,2 -8x+1 is continuous on (-o, co) because fx) is a polynomia and polynomials are ...

A: The objective is to state true or false of the above question.

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Q: V -/1+/x - 1 1+/x +1 · IVx tan 2 tan dx 1+/x +1+//1+/x -1 -1

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Q: 1. find an equation of the line tangent to y = x-3 at point (O,-) %3D

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Q: C. Discuss the continuity of the following functions at/on the given point/interval. 4x 1. (6 points...

A: Continuous 

Q: ctivity 3: For each problem, use implicit differentiation to find in terms of x and y. d²y dx² a) 4y...

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Q: If f(4)= 3 and f'(4) = –5, find g'(4) when g(x)=² (4) Your answer

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Q: Let f(x) = /3r – 10. According to the definition, f'(r) = lim h0 (Enter the limit in reduced form)

A: f(x)=3x-10f'(x)=limh→0f(x+h)-f(x)h

Q: b) Show that y = 2sin (2x) is a solution to the differential equation: - 64 =0

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Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)², and passing throu...

A: slope m at (2,1)  m = 2(2+5)2 m = 2*49 m = 98 so line equation y - y0 = m(x - x0 ) y -1 = 98(x - 2) ...

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: (x'y – y+ 2) dy 1 II (x'y – y +2) dy dx 1

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Solve the following initial value problem. y"-2y'+ 2y 7x +4; y(0) = 3, y'(0) =0 The solution is y(x)...

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Q: Let f(x) = 5 + 9x -9. According to the definition, f'(x) = lim (Enter the limit in reduced form) h 0

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Q: Find the derivative of g(x)= using the limit definition

A: Solution:we have use formula g'x=limh→0gx+h-gxhgx=1x-1g'x=limh→0gx+h-gxhg'x=limh→01x+h-1-1x-1h=limh→...

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 16j as ...

A: Given,            The adjacent sides are i+j and i-16j.To find : Find the lengths of the diagonals o...

Q: Determine the point elasticity n of the demand equation pq+ p+ 50q = 10,000 when p = 200. On--0.820;...

A: Based on the general formula of elasticity we will solve the question. Please follow the procedure g...

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Q: 1 -dr. a In r| Find 3.

A: Let's find. 

Q: Q3 : Evaluate the following integral. x+V9-x2 xps

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Q: 10. Given the functions /(x) = 3x² + 2x + x+1 and g(x) = 2x² – 1, find (f - 9)x. a 3x +x b. 3x +x+2 ...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)² , and passing thro...

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Q: ity 5: Do what is asked. Show neat and complete solutions on your answer A Norman window is construc...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: x+2 8) Let f(x) = values of x at which the function is discontinuous. Determine the +x – 2 Determine...

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Q: 5. Which of the has a domain of (-o, +c0)? a. f(x) = x b. f(x) = x2 c. f(x) = x d. f(x) = x*

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