dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

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Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: Please confirm if the selected answer is correct ?

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Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Let f (x) = 1x² +6x+8. Find the x-coordinate for the parabola's vertex. Round your answer to the…

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

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Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: Given f(x, y) = x² – 4y, the parabola x - 4y = 8 = 0 is the level curve o -8 None of the given…

A: The solution is given below

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A: first we have to draw the sketch of y = 1-x2 and draw a rectangle beneath it From the graph we can…

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

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Q: Write the equation (f (x)) of the parabola satisfying the points a, (a + b) / 2 and b. where the…

A: Consider the given Simpson’s 13 rule: The objective is to find the equation fx of the parabola…

Q: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

A: Ggg

Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: The parabola y = Px² + Qx + R_passes through the coordinate (1,1) and has b. Determine the values of…

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Q: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

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Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse

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Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: The a value in the function f(x) = 2x2 makes the parabola %3D O more wider moves it left

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Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

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Q: Find the x-intercept(s) and the coordinates of the yertex for the parabola y =x´ +4x+4. If there is…

A: The given parabola is: y=x2+4x+4 To find the x-intercept and the coordinate of the vertex for the…

Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…

Q: Determine the axis of symmetry for the graph of the following parabola: f (x) = 3x2 + 24x - 54 - Ox…

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