Use the vertex (h, k) and a point on the graph (x, y) to find the Standard Form ( f(x) = a(x − h)² + k) of the equation of this quadratic function. (h, k) = ( − 1, 0), (x, y) = (0, – 3) f(x) = Preview TIP Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c Be sure your variables match those in the question

Q: y' = ysecx

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Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: Solve the Differential Equations. 3.44 Test for homogeneity 3. f(x, y) tanx - sec²x - cosy

A: Let's find function is homogeneous or not.

Q: Evaluate each limit or state it does not exist a) lim 6x²-5x-1 x →1 2x² - x - 1 b). x²³_8 lim X-2…

A: a3 - b3 = (a-b)(a2+ab+b2)

Q: Define R as the region that is bounded by the graph of the function f(x) = 1-2, the z-axis, a = -1,…

A: Given problem:- Define R as the region that is bounded by the graph of the function ⇒fx=1-x22the…

Q: Evaluate lim f(x) if f (x) x-5- A B -10-4 D 0 ∞ ∞ = 1 (x - 5) 4

A: To find out the limit.

Q: Toflow (2) y = √sinh √tan x

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Q: Considering the definition of f(x) below, find lim f(x). (If the limit does not exist, enter Ø.)…

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: [x + y) dy = (x - y) dx x²

A: We need to solve D.E.

Q: Solve the differential equation. y' + 2xy = 23x A There is no correct answer from among the given…

A: To solve the differential equation. y'+2xy=23x

Q: Find the area of the parallelogram whose diagonals are represented by the vectors a =(3,-3,1) and b…

A: See this solution in below

Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: Bioavailability is a term that refers to the fraction of an antibiotic dose taken orally that is…

A: Given problem:- Bioavailability is a term that refers to the fraction of an antibiotic dose taken…

Q: Prove the identity. sin (x-y) cosx cosy tan.x - tany Note that each Statement must be based on a…

A: We can prove the given statement as per the example in the below steps.

Q: Find the solution to the given Differential Equation y dx + (2x-y) dy = 0

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Q: 5. Sketch a graph of a function of that satisfies each of the following. (Feel free to use the…

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Q: Find the Differential Equation of the Family of Ellipses with its center at the origin.

A: Here is the solution:

Q: You borrowed money and need to pay interest on the loan. You must pay 5% of the $6700 loan to remain…

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Q: 4. f(u) = 3u² +2u-6, g(x) = x + 2 5. f(u)=u², g(x)=x²-₁ Find the indicated composite function 6. f(x…

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Q: Evaluate the integral|5x-1| dr. Answer:

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Q: Find the angle between in the two planes a = (1,2,3) and b =(4,-5,6)

A: Let's find angle between two plane.

Q: 55. + -3 -2 -1 2 O -1 y -2 1 2 3 Graph of f' Let f be a differentiable function with f(1) = 3. The…

A: Let f be a differentiable function with f1=3. The graph of f', the derivative of f, is shown below.…

Q: Solve the differential equations 1. (3x²2y²)y' = 2xy 2. (y² - xy)dx + x²dy = 0

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Q: Which statements are true about matrix A if a ‡ 0 and a² #b²? b b a A = a [8 There is a unique…

A: Please see the below picture for detailed solution.

Q: Estimate the slope of the tangent line to f(x) = x³ at x=2 by finding the slope of the secant line…

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Q: 20. f(x) = sin a for a < 0 cos x for 0≤x≤ ³T tanx for 37 < x < 2π for 27 < x < 5 cot a Let f be the…

A: A piecewise continuous function is continuous on a given interval in its domain if the function…

Q: J. (1+vx), √x dx

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Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: You are planning to donate exactly 5% of your income to charity. Your weekly paycheck is $753.98.…

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Q: Eliminate the arbitrary constant. 2x -X y=c₁e + c e 1 2 A B с D y" y'- 2x=0 y"-y'- 2y=0 2y"-y-2x=0…

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Q: x²y = 1 + cx

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Q: Test for homogeneity 3. f(x, y) = tanx - sec²x - cosy 4. f(x, y): x²+3xy

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Q: Refer to the images, then Choose all descriptions that apply of how the tank filling on Tuesday…

A: Given information Function for Monday:- Mx = 5 x3 Graph is   Function for Monday:- Tx = 5 x-153…

Q: You are calculating a tip on a restaurant bill. The service was good, so you would like to tip about…

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Q: The graph below is the function f(x) -5 -4 -3 -2 -1 lim 5 4 3 x→2 12 A -1 -2 -3 -4 -5+ Select all…

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Q: 1. You leave Morgantown at noon and your distance traveled in miles after t hours is given by the…

A: Solution )a) f(t) = -10t2 + 85t  150 = -10t2 + 85t -10t2 + 85t - 150 = 0 10t2 - 85t + 150 = 0 5 (…

Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xdy +…

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Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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Q: Solve (xy + 4a²y)dy = √(xy-5a³ + ax - 5a²y)dx

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Q: <++ 10 -10-9-8-7-6-5-4-3-2-1 9+ 8- 7 1 6+ 10 4 3 Y 2- L -2- 3 -4- 5 -6+ -7+ -8+ -9+ -10+ 2 3 4 5 6 7…

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Q: Graph and find the domain and range for y= sin²x + 1

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Q: v − 1) dx + (x + 1) dv=0. If v= 2 when x = 1 determine v when x =

A: The given differential equation is; x(y+1)dx+(x+1)dy=0

Q: (y²_xy) dx + x² dy =O

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Q: Let F = (2x, 2y, 2x + 2z). Use Stokes' theorem to evaluate the integral of F around the curve…

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Q: Find the following limit Select the correct answer below: 8 88 0 -1 lim x18 -3x3 + 7x² - 6x + 4 -3x²…

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Q: A There is no correct answer from among the given choices. differential equation by separation of…

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Q: Find the area of the segment cut off from the curve y = sin x, 0≤x≤ n by the line y = 1/√2. H4 34 y…

A: Let's find area of segment.

Q: Q2/Solve the following equation from t=0 to 1 with step size is 0.5 using E Method. dy -= y sin³ (t)…

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Q: Find the following limit. 1 x+6 Provide your answer below: 1 3 lim x--3 x + 3 Give your answer as a…

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