Find the general solution of the differential equation: y+4y = 3 sin(2t) Use lower case c for the constant in your answer.

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Q: Find the general solution to the following differential equations. 1. y"-8y'+16y=0 2. y"+y'=0 3. ...

A: As per our company guidelines we are supposed to answer only the first three questions. Kindly re Po...

Q: 3. The fractal C is constructed as follows. (i) Begin with the line segment Io = [0, 1]. (ii) Remove...

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Q: QUESTION 1 For the following differential equations, - Classify whether the equation is ordinary or ...

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Q: Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let an = In(2n + 1) – In(2n – 1). Does {an}...

A: We have to check the given sequence and series is convergent or divergent.

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Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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A: Given, the function                     f(x)=ex-2 The horizontal line  y=-4, and the vertical lines ...

Q: For what values of h are the given vectors linearly dependent? -6 -24 Vectors are linearly dependent...

A: Vectors, lindearly dependent and independent

Q: Find the set of all positive integers n with the property that the set  M={n,n+1,n+2,n+3,n+4,n+5} c...

A: A very good problem based on a nice application of quadratic residues

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Q: Theorem 11. Let f be a continuous function on R such that f(x+y)Df(x)+fy) vx, yER. Show that f(x)3Dc...

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Q: L Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) ...

A: Introduction: An infinite series is classified as convergent when the sum of the series is finite. W...

Q: H.W: Estimate the root of the equation for the following equation usmu ivewton- Raphson method: f(x)...

A: Since you have asked multiple questions so as per guidelines we will solve the first question for yo...

Q: Let a be a real number. Consider the series an Σ cos(n7); An, where An = 2n + 1 n=0 (a) Is it possib...

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Q: 2k 8∞ Ek=072k) ! Lk%3D

A: Let us consider the function f(x)=ex The expansion of the exponential function is  ex=∑n=0∞xn(n)!=1+...

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Q: х, у, Z) %3D ху rection of Ff to two d

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Q: (1) E(-1)n+1 (3n)! 3n+1 n=1

A: (f). Given series is ∑n=1+∞(-1)n+1(3n)!3n+1

Q: Prove the following statements using the Principle of Mathematical Induction (PMI). 3.) 2. 7" +3. 5"...

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Q: dH RH² /1 + R² dR In H

A: The given problem is to solve the given differential equation. We can solve by using separation of v...

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Q: In this exercise, we suggest the use of technology. Round all answers to two decimal places. Maximiz...

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Q: _2 _8 .8 00

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Q: 1. Consider the function f(x) = x"e-2x for x > 0, where n is some unknown constant greater than 2. A...

A: Introduction: The point where a function attains its extremum, at that point, there is no change in ...

Q: An advertising company offer three types or mediums: television, newspaper and radio . The cost for ...

A: Given:The radio constraint is that atmost 46% of the total number of advertisement should be on radi...

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A: Introduction: The exponential function is a real-valued function. It is one of the basic functions t...

Q: Find the area of the region cut from the first quadrant by the cardioid r =1+ sin 0.

A: The area bounded by a polar curve r=f(θ) in the domain: a<θ<b is calculated using the formula:...

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Q: cosQ -sinQ Rotation matrix on the plane (2n - 2). R = sinQ cosQ : : -W RWR' = w W = show me that the...

A: Given R is rotation matrix such  that R=cosQ-sinQsinQcosQ also there is matrix  w^=0-ww0 we have to ...

Q: 1.) Water is pouring into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top....

A: step by step clear explanation is given .Have a look 

Q: B. Prove the Triangle Inequality Theorem using Indirect Method. Given: AABC. Prove: AC + AB > BC

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Q: fx3 - x - 3 = 0 f the starting of tho root

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Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 , ar...

A: Equation of the surface of revolution of a curve x=f(y), about y axis is given by x2+z2=fy2Here fy i...

Q: A company is divided into 50,000 shares. An investor purchases 2,500 shares. What percent of the com...

A: Introduction: The percentage is very important in mathematics. The figure x% means that out of 100, ...

Q: 900x50

A: Given that  900 × 500

Q: 7x If the function y= e' O on the interval (-co,00), determine is a solution of y" -ay+ 14 y = a) 5 ...

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Q: Your uncle has $90,000 that he wishes to invest now in order to use the accumulation for purchasing ...

A: Given: The total amount available for investment is $90,000. Investment A is available every year an...

Q: Please explain your answer in detail. Use Cramer's rule to solve the system. 2x, + X2 = 12 - 3x1 + X...

A: The given question is related with system of equations. Given that                2x1 + x2 = 12-3x1 ...

Q: I. Write True if the statement is true. If the statement is false, explain briefly why it is so. 00 ...

A: The given question is related with series. Given three statements.      (a) Suppose the infinite ser...

Q: -3, axy + bx°y"; with a and b constant. P is a point given by (1, -1) and it is Let known that dz (P...

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Q: 4. Find the domain of the function f(x) = Write your answer using interval notation in the x – 7' | ...

A: Given: The function, fx=4-xx-7   To find: The domain of the given function.  

Q: ACTIVITY If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5,6}, B = {1,2,3,5,7}, C = {2,4} and D = {8,9}....

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Q: Approximately, what percent of the data is less than the third quartile? O 75% O 0% 50% 25%

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Q: polar integral rIn 2 V(In 2)²–y² x dx dy c) dx dy

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Q: Detemmine whether each pair of triangies is similar. If similarity exists, identify the similar tria...

A: We have to show that pair of triangles  is similar or not similar.

Q: Apply forward elimination to transform the matrix 2 1 -1 2 4 5 -3 6 -2 5 -2 6 4 11 -4 8] into an upp...

A: Forward elimination method

Q: Exe use ing di fferent orders of in tegration, write six integral of SIC dv , where E is the solid s...

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