4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

Q: Solve for a. 8. 9a = 16 - a² 9. 54 = a¹ 10. a² - 16 = 32

A:

Q: Evaluate the line integral r(t) = (sin t, cos t, t), F · dr, where F(x, y, z) = −3xi + 2yj + 4zk and…

A: Given:- Fx,y,z=-3xi+2yj+4zk rt=sint,cost,t To find:- ∫cF.dr , where c is given vector rt ,0≤t≤3π2

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Q: You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents…

A:

Q: Write an equation of the plane with normal vector n (7,5, -4) passing through the point (1, −5, 1)…

A: Given; n=<7,-5,4> Point (1,-5,1).

Q: Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a A. THE…

A: We can find the slope at the given point in the following steps.

Q: 5) Prove that : tanz 올n(를) i-z

A: tan-1z=i ln[(i+z)/(i-z)]/2.

Q: 4. < y:5

A:

Q: Given the DE as 2xy² + 4 = 2(3-x²y)y'. A. prove or disprove if the given D.E. is exact. B. If it is…

A: The given differential equation 2xy2+4=23-x2yy' Exact differential equation:    The differential…

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A: Given query is to perform indicated function operation and simplify.

Q: Fill in the blanks: As x → 5, f(x) → , meaning the graph of f(x) has a asymptote. The equation is…

A: By using the graph of fx to answer each of the question that follows. i To fill in the blanks:As…

Q: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Draw the graph of…

A: Solution is given below:

Q: 9. 54 = a¹

A:

Q: Given f(x)=x²-2x+1, g(x)=√7-x, h(x) = 2-5x² J

A: Given 1. fx=x2-2x+1 2. gx=7-x 3. hx=2-5x2

Q: Find the exact value of the expression for the given value of 0. Do not use a calculator. COS COS ()…

A: Given that  : theta= 7π/4 and we find the value of cos(theta/2).   We know that : cos(2π-x)= cos(x).…

Q: Find the set of all solutions of each of the following differential equations.  y" =32.

A:

Q: What is the range of the function shown? Y 1 1≤x≤3 1≤ y ≤3 -3 ≤x≤3 -3 ≤ y ≤ 3 I -2- 4

A:

Q: ASAP

A: Please refer to the image below

Q: 1. The general formula for a sequence is t = 3t₁ - ₁ - n, where t₁ = 3 Find the fourth term.

A:

Q: 1. Find the G.S. and P.S. of y" = 6x, y'(0) = 2, y(0) = 1.

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Q: A] Are these functions? 1. {(2,3), (-3,4), (-3,5)} 2. ((-2,4), (-3,4), (-4,4)} 3. f(x) = 4x + 5 4. À…

A:

Q: upward. flux = Compute the flux of the vector field F = 5xzi + 2yk through the surface S, which is…

A:

Q: Because of the curvature of the earth, the maximum distance D that you can see from the top of a…

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

Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: For each pair of functions f(x) and g(x), find the following. P(x) = x²³² +6; g(x) = = (a) f(g(x))…

A:

Q: 3x² + 3y² - 6x − 24y + 24 equation of a circle with center (h, k) and radius r for: h = and k = and…

A: We have to find the center and radius of given circle.   According to our guidelines we can solve…

Q: Procedures and Problem Solving Library of Parent Functions In Exercises 5-8, use the graph of the…

A:

Q: Find the slope of the line through P and Q: P( – 2, 2) and Q( – 4, 5). -

A: Given query is to find the slpe of the line passing through P and Q.

Q: (2) Determine the intersection points of y=-x² +9 and y = 5. Then find the area bounded by this…

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Q: What form of the particular solution is appropriate for the differential equationy" - y'=4?

A:

Q: (1) Sketch these four lines y = 2x + 1, y = -x, and x = 0 and x = 2. Then use integrals to find the…

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Q: When a business sells an item, it receives the price paid by the consumer (this is normally greater…

A: We need to answer revenue and cost model.

Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

A:

Q: Find the integral. (Note: Solve by the simplest method - not all require integration by parts. Use C…

A:

Q: Which of the following is the complete set of roots of the auxiliary equation fory""-3y+3y'-y = 0.

A: Given y'''-3y''+3y'-y=0

Q: At what points is the following function continuous? 3 x - 125 x²2²-25 f(x) = 7.5, 4, X#5, x# -5 x =…

A: Given function:- fx=x3-125x2-25x≠5,x≠-57.5x=54x=-5 Condition for continuity at x=a…

Q: -5 -4 -3 -2 -1 O 3 2 1 7 -2 -3 -4 5 2 3 Write the domain of the function above using interval…

A: Domain is the set of  x-values for which function is defined.

Q: H] Example: If an amount of $5000 is invested at 3% compounded quarterly, what is the amount after 3…

A: The objective of the question is determine the amount after the given year end .

Q: 3. What is the general term of the sequence: 5, 15, 45, 135, 405, ... a. t₁ = 3(15) b. t₁ = 3(5)n-1…

A:

Q: the properties of the cross product to ma following calculations. (a) ((j + k) × j) × k = (b) (i +…

A: We will find the required.

Q: Let CCR² be the circle with radius 6 centered at the origin. Let F: R² → R² be the vector field…

A: The objective of the question is determine the flux of given F under C

Q: Let A = (3, 4, 2), B = (-1, 4, 4), C = (-2,−1,0), and D = (2,−1, -2). Find the area of the…

A:

Q: 3. Determine the Present Value of an annuity which provides payment of $1200 every month for 6…

A: Concept: Future value: Amounts of money or streams of cash flows that are anticipated in the future…

Q: ∞ Use the equation = Σ x” for |x| < 1 to expand the function in a power series with center c = 0.…

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Q: f(x)= = √16 − x^2

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

Q: 32. ³+x²+x+2 + 1)(x² + 2) dx

A:

Q: The derivative of e" is e. What is the derivative of e? There are two functions named 'sinh' and…

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Q: Q. 1. a) Find the area of the region enclosed by the curve y = x² -2 and by the line y = 2. y=x²-2…

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Q: u սյ # P Express numbers in exact form. Use symbolic notation and fractions where needed.) ||U₁v ||…

A:

Q: For each pair of functions f(x) and g(x), find the following. F(x) = x³ +6; g(x) = = (a) f(g(x))…

A: