What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the interval -1 sx< 2? O 0.5 O 1.25 O 2.25 O 2.75

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: 3. Find the right triangle of largest area inscribed under the parabola y = 4 – r² with its base…

A: Given: y=4-x2 Vertex of the parabola will be at 0,4 and the points where parabola intersect the…

Q: ind the point P on the line y = 5x that is closest to the point (78,0). What is the least distance…

A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: How to use the trapezoidal rule to approximate distance travel?(with a t of 1min)

A: The trapezoidal rule is used to estimate the area under a curve. The expression for the trapezoidal…

Q: What is the shortest distance from the curve x^2+xy+y^2=16 to the origin?

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Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Find the largest rectangle (that is, the rectangle with largest area)that fits inside the graph of…

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Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: Which integral computes the circumference of the ellipse +y? = 1? 2 216-322 16 – 4x2 dx 16 — З2? -…

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Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

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Q: Explain the steps required to find the length of a curve x = between y = c and y = d. g(y)

A: Given the curve x=g(y). We need to explain the steps required to find the length of a curve between…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

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Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: The tangent to the circle x? + y? +3x+3 y = 38 at the point (2 ,4) is Select one: O11 y- 7x = 58 011…

A: Equation of the circle is : x2 + y2 + 3x + 3y = 38 at point (2,4)

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: 8.) Find the exact length of the curve y= over the interval (0.4]. 2 %3D -

A: Given,          The exact length of the curve y=x22 over the interval 0,4 .

Q: Find the values of y where the straight line y = x+1 intersects with the parabola y = 4x? + 3.…

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Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

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Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

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Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: Find the area bounded by the curve y=- 16 A 10 square units B) 16 square units Ⓒ 8 square units (D)…

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Q: ind the exact length of the curve. X = 8 4y2' 1sys 2

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Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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Q: Which integral computes the circumference of the ellipse + y° = 1? %3| 2 16 — За? dx 16 — 4г2 2 -2 2…

A: As we know the differential arc length of a curve is ds=dxdθ2+dydθ2dθ  The parametric equations of…

Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Consider the circle, x2+y2=25 find the equation of the tangent line,…

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: 13. Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y,…

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Q: Find the length of the curve 3y = (x² + 1) ? from x = 0 to x = 3.

A: Given:

Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: Find the length of the curve y =1+6x?on the interval 0<x<1.

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Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: What is the largest vertical distance between the graphs of the functions y = Vx and y = x² in the…

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