Use Separation of Variables to find the general solution. 30x² y³ y' - = 0 (Express numbers in exact form. Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.)

Q: -2 CS -1 J1 2 x cos(x² + y2) dy dr

A: ∫-11∫12xcosx2+y2dydx

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Q: 1. The function S(t) (where t is measured in weeks starting with t = 0) approximates the stock…

A: Numerical integration

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Q: Find the interest rate needed for an investment of $5000 to grow to an amount of $9500 in 4 years if…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = t-√√t, [-1,…

A: ft=t-t3

Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) 9x³…

A: We have to find asymptotes.

Q: Doesn't seem like any of these answers work.

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Q: Find the antiderivative of the function f(x) = 7. That is, find a function F(x) for which F'(x) =…

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Q: Find the Laplace transform of the following given: 3. g(t) = e²t cos² t 4. f(t) = e¹t[(sin2t)(cost)]

A: To find the Laplace transform of the following functions. (3) gt=e2t cos2 t (4) ft=e4tsin2tcos t

Q: 8. Write the equation of the ellipse given that the vertices are at (0,−4), and (0, 2); and the…

A: NOTE: Refresh your page if you can't see any equations. . the given vertices are the center of the…

Q: Suppose f'(x) = cos(x²) and f(0) = 2. A. Use a graph of f'(x) to decide which is larger: A. f(0) OB.…

A: Given information: f'x=cosx2 and f0=2 To find: a) Use the graph of f'x, estimate where the function…

Q: Find    F/ (x) (2x+3) (x+1)

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In a town whose population is 3000, a disease creates an epidemic. The number of people, N, infected…

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Q: The table gives the price t, in dollars, of a round-trip flight from Denver to Chicago on a certain…

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Q: Calculate u, the normalization of the vector v = -6i + 2j + 5k. (Write your solution using the…

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Q: Find lim r(t) t →∞ 3t if r(t) = (2+e¯³)i + 2tan ¹tj + - 4t³ – t 2t - t³ k

A: If rt=2+e-3ti+2 tan-1 tj+4t3-t2t-t3k, then to find limt→∞ rt.

Q: The coordinates of B' after a reflection across the line y=-2 are

A: The coordinates of B' after a reflection across the line y=-2

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Given: h(r,s,t)=ln(3r+6s+9t) We are required to find: The directional derivative of h at (1,1,1) in…

Q: day the scenano and complete the questions that follow. Rate of change of Rainfall In the rainy…

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Q: Find parametric equations for the tangent line to the curve r(t) = (t² +e²t)i + (2+e¯³)j + (t³ −…

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Q: Work. An open tank has the shape of a right circular cone. The tank is 5 feet across the top and 20…

A: Work = Distance*density*volumeVolume of…

Q: Determine whether the infinite series 3n² n+4. Σ tan n=1 converges or diverges, and if it converges,…

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Q: K Find the area under the given curve over the indicated interval. y=x²; [0.2] The area under the…

A: y=x2;      [0, 2]

Q: 3. Express the A. the integral D. •√4-x² px²+y²+1 [²√√**²*² 0 ²+1 ² ² ²*¹ x 2²³ rdz dr de 0 π/2 2 B.…

A: ∫02∫04-x2∫0x2+y2+1xz2dzdydx

Q: If f is a continuous function on (-4, 4) whose graph is in 1. ƒ"(x) > 0 on (-4,-2) 2. (0, 1) is an…

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Q: 3 1 1 Use the transformation u = 3x+4y, v=x+3y to evaluate the given integral for the region R…

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Q: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,800 bacteria. Find an…

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Q: 5dv 7e +3

A: The given integral is 5/(7e-v+3).

Q: For the function graphed below, estimate the point of greatest curvature to

A: NOTE: Refresh your page if you can't see any equations. .

Q: 110 1.0

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Q: Calculate the following sums. Use symbolic notation and fractions where needed.) (2) Σ 9 = i=1 (b) Σ…

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Q: 12 +6 18 to 12

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Q: 2. Let f,g: R → R³ be differentiable functions. Show that d dt (f(t) × g(t)) = d d f(t) × g(t) +…

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Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n = 10 over the…

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Q: A cylinder is inscribed in a right circular cone of height 4.5 and radius (at the base) equal to 8.…

A: We have given radius and height of cone. We have to find the radius and height of cylinder which has…

Q: swer: ________________________ B. Use your calculator to estimate the 'exact' amount. (Your…

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Q: 5. h(t) = 6e5t cos(2t) – e¹t -

A: ht=6e5tcos2t-e7tformula used : Leatcosbt=s-as-a2+b2Leat=1s-a

Q: 5.2 Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Evaluate the following limit using L'Hospital's rule. limx→0+ (e9x+6x) (1/2x)

A: To evaluate the following limit by using L'Hospital's rule. limx→0+e9x+6x12x

Q: A graphing calculator is recommended. For a camera with a lens of fixed focal length F to focus on…

A: ⇒1x+1y=1F

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 8. π…

A: The given function is fx,y=ycosxy. Evaluate the gradient of the function at the given point.…

Q: a floor is covered with 8 multicolored tiles and 91 plain red tiles wht is the raio of red tiles to…

A: Number of red tiles ( R ) = 91 Number of multi color tiles ( M ) = 8

Q: Find the curvature of the curve r(t) = (cos(2t), sin(2t), 2t) at the point t = 0 Give your answer to…

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Q: Find positive numbers x and y satisfying the equation xy=9such that the sum 3x+y is as small as…

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Q: Find the interest rate needed for an investment of $4,000 to triple in 10 years if interest is…

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Q: Let F(t) = fF(t)dt ( dt (don't include the +C) Find f(t)dt = Calculator Check Answer

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Q: Find the length of the curve. r(t) = t² i + 9tj + 4ť³/2k, 1≤t≤4

A: Given vector function is: r(t)=t2i+9tj+4t3/2k We have to find length of curve for the interval [1,4]

Q: Determine the value of f"(1) when f(x) 3 ln (2x + 1). 1. f"(1) = 813 5. f"(1) = = 2. f" (1) 3. f"(1)…

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Q: State whether the following is true or false by differentiation. 7√1+x² X True False [x²√²+x²° 1 dx…

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