differential equations d^2y/dt^2-2dy/dt-15y=3e^2t Y(0)=0 Y’(0)=3/5

Q: Problem 6. Find the sum of the series Σan, wh n=1

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Q: f(x) dx, given than = 4 Find the value of 6 f(x) is odd, and ſ≤₂ ƒ(x) dx √₂ f(x) dx =

A: Integral

Q: 16. Find the length of the curve r(t) = (2 sin (t), 5t, 2 cos (t)) for -10 ≤ t ≤ 10.

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Q: 4.80. Find each of the following integrals:: (a) zcos 2z dz, (b) ſze=² dz.

A: Topic = Integration

Q: Calculate the area of the region bounded by the graphs of f(x)=√x - 1 and g(x) = x - 1.

A: Given data, fx=x-13 and gx=x-1

Q: Solve the equation. Write numbers using integers or simplified fractions. 4 cos2x = 2√2 Part: 0 / 2…

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Q: Evaluate the line integral, where C is the given curve. √(x²y³ - √x)dy, C is the arc of the curve y…

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Q: A boat is anchored offshore. From the bow of the boat, 40 ft of anchor line is out with 5 ft of line…

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Q: Use a definite integral to find the area under the curve between the given x-values. 1 f(x) = from x…

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Q: 12. Use Green's Theorem to evaluate ſxydx+x²y³dy, where C' is the triangle with vertices (0, 0),…

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Q: Let f(x) = e* and g(x) = Inx. Then O(A) x ER such that f(g(x)) = g(f(x)) O(B) Vx ER, f(g(x)) =…

A: The answer is given below:

Q: Consider the graph of f'(x) below. At what value (or values) of x does f(x) have a local minimum? -6…

A: The solution is given below

Q: Determine the radius and interval of convergence of the following power series. Σ(-1)*** 8k

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Q: Complete the table by finding u and du.

A: To find,  u and du

Q: A particle moves along the x-axis with velocity given by v(t) = sin(t) for time t> 0. If the…

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Q: Find the area (in square units) of the region under the graph of the function f on the interval [5,…

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Q: The graph of f(x) = -² 3r is shown alongside. a Use the graph to estimate the gradient of the…

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Q: 1. Find for the following by implicit differentiation: dy dx 18x9-5 cot y = y² - 18x

A: Given:  1) 18x9-5cot y=y9-18x Implicit differentiation:    Differentiating on both sides…

Q: 12r³6x²+62-6 x4+x² dz= +C

A: We need to solve integral.

Q: Q7: Can you solve this question with showing your work clearly please write clearly so I can see…

A: As per our guideline we are allowed to answer only three subparts of the given problem. Kindly…

Q: Problem and Computation Problem No. 1: In 2015, there were 233,040 Individuals living in Olongapo…

A: Let present number of people=x⇒dxdt=Rate of Expansion in number of people

Q: 1) Use the Substitution Method to find f 12x (3x² + 4) dx . O 20(3x^2+4)^10 +C O 0.2(3x^2+4)^10 +C…

A: The given integral is 12x(3x2+4)9.

Q: 3 Find the value of ³ ƒ(x) dx, given than ƒ(x) is even, ſ_¹₁ ƒ(x) dx = 9, and ſ³3 ƒ(x) dx = 6. 3 f²³…

A: Given :fx is even ∫-11fxdx=9∫-33fxdx=6

Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: The concentration of a medication in the plasma changes at a rate of h(t) mg/ml per hour, t hours…

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Q: Consider the following functions y = f(x) defined on x € [0, ∞). Currently x = 1. Calculate = f'(x)…

A: As per the rules, we are supposed to answer the first question.

Q: Determine the type of DE: x²y¹ = 4x²+7xy + 2y² O Homogeneous O Bernoulli's equation Both Homogeneous…

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Q: Find the indefinite integral. (Use C for the constant of integration.)      9x−3/2 dx       Evaluate…

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Q: y-|z²+3x - 11.

A: Given :                      y=x2+3x-1 To find : the derivative of y i.e. y' = ?

Q: differential equations 2ycos(2x)dx+(sen(2x)-2sen(y))dy=0

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Q: a) Find the eigenvalues of B b) Find three linearly independent solutions of x˙ = Bx. c) Find the…

A: The given matrix is: B=100100-2520

Q: Provide 1 real-life situation involving  a) Rational Function b) Exponential Function Make sure…

A: Let us provide examples of rational function and exponential function below.

Q: Suppose F(x, y) = (4x – 2y)i + 3xj and C is the counter- clockwise oriented sector of a circle…

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Q: Consider the function f(x) = 4x² - 6x + 5, 0≤ x ≤ 6. The absolute maximum of f(x) (on the given…

A: We need to find absolute max and min.

Q: Complete the table by finding u and du. [f(g(x))g'(x) dx 1./ (8. 2₁ / 1² √ ₁²³ + 1dx 1./ (8x² + 1)²…

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Q: Show that for motion in a straight line with constant acceleration a, initial velocity vo and…

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Q: For all positive numbers a and b with a>b ln(a−b)=ln(a)/ln(b)

A: given a,b positive numbers anda>b

Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

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Q: Determine whether the series 8 Σ n=0 cos 9nx converges or diverges. If it converges, find its sum.

A: The given series ∑n=0∞cos 9nπ. We have to find its convergence.

Q: 9x During the course of an illness, a patient's temperature (in degrees Fahrenheit) x hours after…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: a) Let f(x) = √5 + 132³. Find f'(x). f'(2) - O b) Let f(z) J'(x) = 0 evS+13³ Find f'(z). -e'

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Q: If C(x) = 9x² - 8, find the following. (a) C(0) (b) c(-1) (c) C(-3) (d) ((--)

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Q: The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)

A: Given: From the above graph, we can observe that the function is increasing in the interval (-1,…

Q: 3) Suppose I want to use a "u" substitution to find sec² (9x + 4)dx. What should I choose for u? O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is…

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Q: Mary invested in an account that grows 2.25% interest every month. If she invested Php 15,000 this…

A: Given grows 2.25% interest every month. r = 2.25% = 0.025 P = Php 15000 y = Php 20000

Q: Minimize the material needed to design a rectangular cubic box of volume 900 cm3.   Find the…

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Q: 8) Let y²-4x²-16x-2y-19-0. Find the center, vertices, foci, and asymptotes. Then graph.

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Q: Find an equation for the line that passes through the given point and satisfies the given…

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Q: What is the difference between the maximum and minimum of the quantity numbers such that x + y = 10?…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…