An implicit equation for the plane passing through the points (–4, 0, –4), (–6, 1, –4), and (−3, 5, −7) is .

Q: A 50-gal tank initially contains 10 gals of fresh water. At t = 0, a brine solution containing 1 lb…

A: The objective is to find the amount of time required for overflow to occur.

Q: Find MID(2) and TRAP(2) for f -5(1 – e−²x) dx. е MID(2) = TRAP(2) = = Sketch the function f(x) =…

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Q: Let ƒ (x) = tan(x) defined on the interval (-3,7) and let ƒ¯¹(x) = tan−¹(x). From the 2 following…

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Q: 2. (D³ – D² – 12)y = 0

A: To find the solution of the following Homogeneous Linear DE of Higher Order. D3-D2-12y=0

Q: Let x - 9 f(x) = 32+3 520+5 Find an equation for the tangent line to the graph of f at x = 9.…

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Q: At noon, ship A is 110 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing…

A: Given query is to find rate of change of distance.

Q: Find a and b so that the function s both continuous and differentiable. a = f(x) = = 5x³ - 3x² + 4,…

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

Q: In the question they said without determine the numerical values of the coefficients

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Q: 5) Determine convergence or divergence using any method covered so far (up to section 10.5.) Justify…

A: Note:- Since you asked multiple Questions ,According to our policy we can solve only first question…

Q: Which of the following represents the same point as (3,-)? Select all that apply. (-3,5) ㅁ (3, 뽕) □…

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Q: 1. (y-2)dx - (x − y − 1)dy = 0. -

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Q: True or false: At the point where x = , the tangent line to y = sin(x) is perpendicular to the…

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Q: Sove for the differential equation. (9xy - 2y²) dx - (bx² - xy ) dy = 0

A: To solve the following differential equation. 9xy-2y2 dx-6x2-xy dy=0

Q: Find the exact length of the curve. x = 4 + 6t², y = 5 + 4t³, 0≤t≤2

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Q: S JO e¹4x 4+e7x dx

A: Please see the below picture for detailed solution.

Q: If f(x) = x + 2 and g(x) = x = x - 2, (a) f(g(x)) (b) g(f(x)) = = (c) Thus g(x) is called an f(x)…

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Q: Evaluate the limit: r(t + h) - r(t) h for r(t) = (t-2, sint, 7) lim h→0 r' (t) = 100)

A: The objective is to solve the above question.

Q: Use the Chain Rule to find dz/dt. dt z = x² + y² + xy, x = sin(t), y = 5et = 2 sin(t) cos(t) + 5e…

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Q: The combined electrical resistance R of two resistors R₁ and R₂, connected in parallel, is given by…

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Q: Problem 6: Find the function values of sin² TT Given: TT sin²: 12 Required: Apply the half-angle…

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Q: Use the Implicit Function Theorem to find ∂z/∂x and ∂z/∂y if y3z2 = ln(x5+ z). Assumez is a…

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Q: Plot the point with the given polar coordinates. (−3, — ) 0 0 0 0 ਜੋ --

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Q: Find Vf at the given point. f(x,y,z)=x² + y² - 4z² + z ln x. (1,5,3)

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Q: Find the surface area of revolution about the y-axis of y = 8 - 2x² over the interval 0 ≤ x ≤ 2.

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Q: a³ = 9, f(a)=3, f'(a)=2, f'(a³) = 10

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Q: Find the present value of the investment (Round your answer to the nearest cent.) funding $8,000…

A: Given: Withdrawl amount is $8000.            Rate of interest is r=5.25%.           The interest is…

Q: The following equation e³ + Zxy = x³ describes a curve in the plane, where Z is an unspecified…

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Q: Evaluate the following limit: 2x²-xy-y² lim (x,y)-(1,1) x² - y² (Hint: factor both the numerator and…

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Q: Use the Chain Rule to find the indicated partial derivatives r= y + x cos(t), s = x + y sin(t) when…

A: Given that , u=r2+s2 , r=y+xcost , s=x+ysint Use the chain rule to the find the partial derivatives…

Q: True or false: For any constant C, d [tan(x) + C] = [sec(z)]²

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Q: Evaluate the integral. rπ/2 5 + 9 cot(x) dx Jπ/4 9-5 cot(x)

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Q: The circle (x − 8)² + (y – 5)² = 25 can be drawn with parametric equations. Assume the circle is…

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Q: (5) Consider the polar equation (a) Find r corresponding to r=2 sin 0-2. 0=0, π/6, 1/3, π/2. What…

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Q: Let f(x) = = x + 2 9+x ƒ−¹(−9) =

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Q: [s sec³ x tan5 x dx

A: The given integral is sec3x tan5x.

Q: f(t)=−2t^2+t+1 Find the equation of the line tangent to the graph of f(t) at t=9 y=

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Q: Q4// Find the distance between (0,1) and the line 6x - 3y = 5.

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Q: 3. Two forces F₁ and F2 push on an object with an angle of 70° between them. If |F f|F₁| = 170N and…

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Q: Fill in the multiplicity table with the provided graph or factors. 6. 19 7. 5 Fy N

A: here we have to find the multiplicity of the roots.

Q: Find the volume of the parallelepiped determined by the vectors a = (3, 4, -1), b = = (2, 4, 1).…

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Let f'(x) = f(x) = tan ¹(cos(8x))

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Q: A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0…

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Q: Find the general solution of the differential equation. Then, use the initial condition to find the…

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

Q: z = 1+2 cost, y = 8+2 sint, π/2 < t < 3/2

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Q: The total cost (in hundreds of dollars) of producing a slide rules per day is C(x): = 8+ √2x + 25.…

A: Given: C(x)=8+2x+25

Q: Find the surface area of revolution about the x-axis of y = 5x + over the interval 0 ≤ x ≤ 3.

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Q: Let f(x) = Evaluate f'(x) at x = 4. ƒ'(4) = J 4√x 4x² + 3x - 9

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Q: Let A be a positive constant. The equation of the line tangent to the curve sec(y) + x³ - 9 = Ay at…

A: Equation of tangent to the graph y=f(x) at point x1,y1 is given byy-y1=dydxat x=x1,y=y1×(x-x1)   The…

Q: Use substitution to find the Taylor series at x = 0 of the function 5 sin (-x). What is the general…

A: We have to solve given Questions.

Q: Let v = =(-4, 2, 3) Calculate: v xi= vx j = ( v x k = (

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