how do I complete the square with problems like: 3y^2 - 4y + 4x = 0 Thank you for your help!

Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: 1 A tank with a capacity of 400 gal initially contains 100 gal of water with 50 lb of salt dissolved…

A: 100gal=Initial amount of water in 400gal tank50lb=Initial amount of salt in the tank1lbgal=salt…

Q: Part 2: Exponential Growth and Decay and Logistic Growth Model (3) Suppose an experiment was…

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Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: 10. | x³(lnx+1)8x* dx

A: To evaluate the integral: I=∫xx(ln x+1)8xxdx=∫8xxxx(ln x+1)dx

Q: Find the limit. NOTE: Enter the answer using round brackets. 1 lim (12²2 +9.7) = (17.00) 9't

A: Given : A value that a function approaches the output for the given input values Here, it has been…

Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: 13-16 Sketch the region whose signed area is represented by the definite integral, and evaluate the…

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Q: a₁ = 5 9₁2=35 Find the common difference using arithmetic sequence.

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Q: Find T(t) and N(t) at the given point. r(t) = (t²- 2)i + tj; t = 2 T(2) N(2) = =

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Q: 9. (y³+4)√1- cos² (y4 + 16y) ». f (y ³. cos(y¹+ 16y) () 2. dy

A: Answer of the above integration is

Q: 37-38 Evaluate the integrals by completing the square and ap- plying appropriate formulas from…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: ​D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​…

A: Solution is here

Q: Evaluate the iterated integral. - y² I. L (x + y) dx dy

A: Take integration

Q: In (x² + y² ) = 2 arctan y' 9 X

A: We know that derivative of xn is nxn-1.     Here i attached the solution of this question.

Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,…

A: Since you have submitted multiple questions, according to Bartleby policy I'll solve the first…

Q: Find the derivatives of the following function (a) y=4²-3+2√ 2x+3 (b) y=2

A: We can answer the questions as below to find derivatives

Q: | 12 – 2 – 1 2x - (x − 1)²(x² + 1) dr

A:

Q: Given sin(a)= -and a is in quadrant IV and sin(B) = and π/2 <B<T. Use sum and difference formulas to…

A: Given sin(α) = - 8/9 and α is in quadrant IV and sin(β) = 5/8 and π/2&lt;β&lt;π Use sum and…

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: Activity 4: Determine whether the functions below are continuous or not on a given point or a given…

A: A function f(x) is continuous at a given point x=a   if following conditions are hold: (I)…

Q: C. ¡(4eª + x¹/³)dx

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Q: The sec√x dx is {A}=sec x³/2 + C {B} ²sec ³/2x + C 3 {C} 2 In sec √x + tan √x {D} In sec √x + tan √x…

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Q: 38. a10-49.5, a14 = -73.5

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Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: We have to calculate first and second number

Q: Evaluate the definite integral. √ (e19¹ ₁ + (e¹% i + e¯¹j+1 k)dt O e¹⁹ - 1 19 O el9 i-e²¹ j + ½ k 19…

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Q: lim (t i − 4 j + t² k) 1-9 ■im (t i − 4 j + t² k) = i →9 i+ i

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Q: y = 5x6 − 6x² + x +4

A: Follow the procedure given below.

Q: x²-3x - 7 √ - (x² + x + 2)(2x − 1) dx

A: Given: I=∫x2-3x-7x2+x+22x-1dx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: Find the derivatives of the following function (a) y=4²+2√²

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Q: 4x+10 1. S (x-2)(x-1)² dx

A: Given integral ∫4x+10(x-2)2(x-1)2  dx

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: A company can buy a machine that is expected to increase the company's net income by $10,000 each…

A: Given Continuous annual stream function R(t)=$10000 time t=10 year  ; M=10 Rate of interest r=6%…

Q: Given the expression below, set up (DO NOT SOLVE) the partial fraction decomposition. (Use A, B, C,…

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Q: 5. y = cos x sin²x What is the appropriate formula? Solution:

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Q: Use the graph of f to describe the transformation that yields the graph of g. f(x) = 6*, g(x) = 6x +…

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Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: d Calculate [ri(t) r2(t)] and Calculate[ri(t) r₂(t)] and [ri(t) × r₂(t)] first by differentiating…

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Q: Seatwork: Obtain the general solution of the following differential equations 1. (xy² + x) dx + (x²y…

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Q: y = = Ax is YBC Ycs YBS = 1 -1 0 1 1 0 - D IB XC IS

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Q: x +4 x² + 2x + 5 dr

A:

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: A company can buy a machine that is expected to increase the company's net income by $15,000 each…

A:

Q: b. √ ( 3 √ √x + ²) a dx

A: The given integral,      ∫3x+1xdx

Q: Decide whether the integral is improper. 00 [ In(x8) dx O proper O improper Explain your reasoning.…

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Q: Find the partial derivatives f(x,y)=e* sin(xy) of dx

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Q: find dy/dx of each equation using implicit differentiation. a. (x+y) / (x-y) = y2 b. 2xy - y2 = 3

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Q: the base of a three-dimensional figure is bound by the circle x² + y2 = 4. Vertical cross sections…

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