Solve the following equations 65. y” + 10y + 25y = xe-5x +4

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Q: Consider the basis S = {V₁, V₂} for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the…

A: Explanation of the answer is as follows

Q: (x - 2y - 1) dy = (2x - 4y - 5) dx

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Q: Find the solution of the given initial value problem. ty' + 4y = t² − t +7, y(1) = 2, t>0 Y

A: We know that a differential equation of the form y'+P(t)·y=Q(t) has Integrating Factor (I.F.) =…

Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it dx dr dr d.…

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Q: 4. Evaluate 12x+1 dx 5. Evaluate dx X 6. Evaluate [ 3x -¹ dx

A: To find the value of given integrals .

Q: Give the complete solution Find the derivative of f(x) = 5x6 - sec-1(x2)

A: Complete solution is given.

Q: 2. Evaluate Solve all parts or I'll dislike. If you can't solve all parts just skip it dx dx d. S S…

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: The given indefinite integral is: I=∫dx4x+3   ...1   As we know the common integral. ∫1xdx=lnx+C

Q: Y 3 -3 -2 -1 2 1 -5 1 2 3 4 -1 -2 -3 The function graphed above is: Increasing on the interval(s)…

A: If value of y increases as x increases then function is increasing in that interval. If value of y…

Q: Find the eigenvalues of A² for Enter the eigenvalues in increasing order. Eigenvalues of A² are: i A…

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Q: Two people on bikes are at the same place. One of the bikers starts riding directly north at a rate…

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Q: Find the area of the region bounded by: r = 5 cos(20) 0 ≤ 0 ≤ 2π

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Q: S 1 A box with a square base and open top must have a volume of 318028 cm³. We wish to find the…

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Q: dy dx = x+1 2(y+3)

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Q: # 2 1 -5 1 2 3 4 The function graphed above is: Increasing on the interval(s) Decreasing on the…

A: The objective is to find the intervals where the graph is increasing and decreasing.

Q: The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of…

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Q: The set S = [1,3] is not./compact. Which open cover of S 9.) {[1,3 + ¼/n) I nεN } b.) { C1-1/n,…

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Q: Find the eigenvalues of A³ for Enter the eigenvalues in increasing order. Eigenvalues of A³ are: i i…

A: Cayley Hamilton theorem and basic property of eigenvalues are used

Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…

Q: The function y = a. O a-3 O a = -2 ax4 ++has a minimum at the point (√(√)). D . Determine the value…

A: To find the minimum point of the function

Q: (xy² + y-x) dx + x(xy+1) dy = 0

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Q: (2x + 3y - 1) dx - 4 ( x + 1) dy = 0

A: Explained below

Q: Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural…

A: a) As a is a real number, then it can be written as sum of a natural number and a fraction.  Hence,…

Q: A lighthouse is on an island 300 meters off shore. The lighthouse beam makes a full turn every 7…

A: Let's solve.

Q: A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as…

A: Trigonometric ratio

Q: -3π/2 2. S TL √sinx + 1 cos x dx

A: We solve the given definite integral by using substitution method .

Q: Looking for some advice on this problem please! By using derivative, determine the intervals of x…

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Q: Q1: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: The task is to set up an iterated triple integral equal to the volume of H using spherical…

A: Given

Q: 1. Evaluate a) for²dr, 2. Evaluate fr+7r² dr. 3. Evaluate a) fe²dr, r/2 4. Find sin rdr. b) dr, c)…

A: 1. evaluate  a) ∫01x2dx = [x3/3]01 = 1/3   b) ∫231/x2dx [-1/x]23 = -1/3 +1/2 = 1/6   c) ∫12x2dx =…

Q: Find the values of x for which the given function has a maximum or a minimum value using the First…

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We can solve this as follows:

Q: (3x²2y²)y' = 2xy,when x = 0, y = -1

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Q: bacteria culture starts with 200 bacteria and triples in size every half hour. After 2 hours, how…

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Q: Find all numbers b such that the average value of f(x) = 7+ 8x - 6x2 on the interval [0, b] is equal…

A: Value of b is given.

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (8x…

A: Given

Q: 5. Let D be the region bounded by the lines y = x, x = 3 and the curve y = 1 (a) Sketch the region…

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Q: For each of the following, find (i) the direction of P₁P2 and (ii) the midpoint of line segment P₁…

A: Given, P1(1,4,5)P2(4,-2,7) Therefore position vector of P1 and P2 is p1=i+4j+5kp2=4i-2j+7k

Q: x²-5y²-3x-y +22=0 (y-2)(x-y-2) = 0

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Q: Find a line that is parallel to the line that passes through both P and Q and contains R.

A: We have to find the equation of line.   According to our guidelines we can solve only one question…

Q: Consider the function f(x) = x¹ − 50x² +11, x¹50x² This function has an absolute minimum value equal…

A: We need to find absolute max. and min. value.

Q: The width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

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Q: F Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

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Q: - Find the derivative of f (t) = (5t³ — 4t² + 1) 49 f' (t) =

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