3. Find the right triangle of largest area inscribed under the parabola y = 4 – r² with its base along the x axis (as shown).

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Let L be a tangent line to the hyperbola xy=4at x=7. Find the area of the triangle bounded by L and…

A: Given: L is a tangent line to the hyperbola xy=4 at x=7. To determine: The area of the triangle…

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

A: Please see the below picture for detailed solution.

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

A:

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

A:

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

A:

Q: Let L be a tangent line to the hyperbola xy 32 at x3 Find the area of the triangle bounded by L and…

A: Find the equation of the hyperbola,

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

A:

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: 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: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

A:

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: 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: 5.Find the area of the surface generated by revolving the given curve about the y-axis. x = /9- y, -…

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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.…

A:

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

A: Please see the below picture for detailed solution.

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

A:

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

A:

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

A: We have to calculate the area of the smaller region bounded by x+52=2y from left sides,and bounded…

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

A:

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

A:

Q: 4. Find the area of the surface generated when the given curve is revolved about the y-axis. y=(2x)"…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If the infinite curve y = e-2x, x 2 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: Question 12 Calculate the area of the smaller region (to the left of the parabola) bounded by…

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Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

A:

Q: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

A:

Q: 5. Find the exact area of the surface generated by revolving the given curve about the y- axis, Draw…

A: Application of integration

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

A: Find the slope of the tangent to the curve x2+y2=25 at (3,4). 2x+2ydydx3,4=0dydx3,4=-xydydx3,4=-34

Q: Find the area of the surface generated when y² = 12x is revolved about the x- axis from x = 0 to x =…

A: Given curve,y2 = 12xRevolved about x-axis from x=0 to x=3.

Q: QUESTION 14 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: We need to find area.

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

A:

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: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

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: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

A:

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

A:

Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: -8x If the infinite curve y = e8x, x 2 0, is rotated about the x-axis, find the area of the…

A: Given curve is y=e-8x, x≥0 is rotated about x axis.

Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2