Determine the equation of the plane in the form z=f(x,y) that passes through the points P(−5,9,−6),Q(3,8,9)andR(8,−6,−3).

Q: The total cost (in dollars) of producing x food processors is C(x) = 2500 +90x-0.3x². (A) Find the…

A: The given cost function is: C(x)=2500+90x-0.3x2

Q: Differential Equations:  Solve the following problem for y(t). dy/dt + 2y(t) = 2x(t);    x(t) = u(t)…

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Q: 1. f(x) = 4x² -5x

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Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t²k, u(t) = 4ti + t²j…

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Q: 3. Determine whether the following function y=c₁x + ₂x³ + 2x²e* - 2xe* is a solution to the…

A: We have to determine given function whether solution of given differential equation.

Q: Jse any of these formula (an = 1/2 (a₁ + an ) or an = 1/2 [2a₁ + (n − 1)d] to solve for the sum of…

A: As per the guidelines I am supposed to do the first question among multiple questions, So here I am…

Q: x²y' = 4x² + 7xy + 2y²

A: We use homogeneous method to solve the given differential equation.

Q: 2 cos 9. S X 4 dx X sin 4

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Q: Write the first five terms of the sequence: [11]nn] ¹ n Jn-1 Determine whether the sequence…

A: The given sequence is 11 ln nnn=1∞ we have to find the limit of the sequence.

Q: Evaluate ∫ (3x2 − 20x )dx .

A: Given, ∫3x2-20xdx

Q: The cost, in dollars, to produce a designer dog leashes is C(x) in dollars per leash, is p(x) = 117…

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Q: Problems 6-7. Find all the real zeros of the polynomial. Use the quadratic formula if necessary. 6.…

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Q: Question Determine the point of intersection of the following two lines. L₁ : L2: Enter your answer…

A: Question:- Determine the point of intersection of the following two lines: L1: x=3-14s, y=-19+3s ,…

Q: y²dx + x(x + y)dy = 0

A: This question is based on Solution of Homogeneous Differential equation.

Q: 5. Y=√√4x+ 3

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Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. I k(k+…

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Q: The unit cost, in dollars, to produce bins of cat food is $15 and the fixed cost is $15470. The…

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Q: 1. y' = e²x-y

A: Given y'=e2x-y

Q: The measurement of the edge of a cube is measured to be 8 inches, with a possible error of 0.02…

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Q: w!! [[x-h]] +xh X> -4° x² + 3x-4 Will [[x-h]] + xh X>-4² x²+3x-4

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

Q: Determine the degree of the differential equati 3/2 2/3 (3x² ² 2 + 4xy) ¹ ² = (2y³d² - 4xy)" d²y dx²…

A: The given differential equation is; (3x2d2y/dx2 +4xy)3/2=(2y3d3y/dx3-4xy)2/3

Q: Find the point of intersection of the lines below. Then find the equation of the plane containing…

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Q: F(x,y) = 5 x+y sin²x 4 x +y 0 2 if (x,y)=(0,0) , , if (x,y)=(0,0)

A: Please see the below picture for detailed solution.

Q: Given the curve r(t) = 4t (4) i + (4 cos(t)) j find the acceleration vector at t = ㅠ 3

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Q: Find the limit of the following:  a) lim x→∞ (sin2x / x2) b) lim x→∞ (x - √x)

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: lim X→ +∞o (√9x² -5x+1 +3x

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Q: lim »- oolv 9x²-21x+10 +3x + 3x)

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Q: please solve   401,411

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: The solution of the differential equation y' : y+√√x² + y² = c y + 2√y² = x² = cx y+√√y²-x²=c y+…

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Q: 1. f(x) = 4x² -5x

A: Topic = Derivative

Q: Find the slope of the line through P and Q. P(3, −3), Q(−1, 6)

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Q: Which of the equation: Show your A. following is the general solution of the differential X ady - y…

A: The given differential equation is; x3dy - y(x2-y2)dx=0

Q: The degree of the equation is Blank 1. Blank 1 Add your answer d'y + (1)²-34/+ +y=9 :

A: We have to find the degree of the given differential equation.

Q: Which of the following = differential equation y' Show your solution A. y = 5 tan is the particular…

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Q: Let f(x,y,z) = x²-tany² 2xyz Solve for fxyz.

A: We need to find fxyz

Q: Find the radius of convergence and the interval of convergence. Radius of convergence: O A=0 k+5…

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Q: 4. The function f(x)=x²-x² - 2x + 1 has three zeros on the real line. For each of these zeros, find…

A: We have to locate all 3 real roots of f(x) = x3-x2-2x+1 on the real axis. Given f(x) is continuous…

Q: Identify the inside function, u = g(x), and the outside function, y = f(u). y = (x2 – 5x + 7)2 u =…

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Q: Solve for x: x - √9-8x = 0

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ?

A: A detailed solution is given below.

Q: 8. f(tan 2x + cot 2.x)² dx

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Q: For f(x) = √ (x^2 − 1) and g(x) = √( x − 3), determine the subset of the domain of g on which the…

A: For fx=x2-1 and gx=x-3, to determine the subset of the domain of g on which the composition f∘g is…

Q: Find the limit of the following:  a) lim x→∞ (sin2x / x2) b) lim x→∞ (x - √x) *please do in hand…

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Q: If the distance between (b, 6) and (5, 6) is 2.5 units, find all possible values of b. (Enter your…

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Q: Enter the exact answers. (a) Find the average rate of change of y = rave 1 rinst = with respect to x…

A: Given query is to find average rate of change and instantaneous rate of change.

Q: Which of the following functions is a solution of (x² +1)y' + y² + 1 = 0 ?

A: We have to solve the differential equation.

Q: 89. f(x)=√x-2 [Hint: Rationalize the numerator.]

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Q: Determine whether the following equations are linear, separable, Bernoulli, or nonlinear homogenous.…

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Q: b. Explain what The formula for the above graph that passes through the two coordinates she…

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Q: 12. Find f d dx du In(x+u)

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