3. Evaluate y² x² dA where R is the part of the annulus a² ≤ x² + y² ≤ 6² lying in the first quadrant and below the line y = x.

Q: Calculate the are bounded by the curves: C. y = e2x and x - 2y + 5 = 0

A: Introduction: The formula of the area between the curves y=f(x) and y=g(x) is given by,…

Q: Q.1 Determine the centroid - 240 mm- r= 90 mm 120 mm

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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: 1.) Find the area bounded by the regions given by the graphs of y 3x2-10x and y x2+2x. Make sure you…

A: There are multiple unrelated questions. I will address the first one.The curves are:y = f(x) = 3x3 -…

Q: Find the surface area of the cone frustum generated by revolv-ing the line segment y = (x/2) +…

A: Consider the given line segment,The surface are of the cone frustum generated by revolving the line…

Q: Q: A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular…

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Q: Draw the image of quadrilateral ABCD under the dilation with scale factor -0.5 and center of…

A: Let (x,y) be a vertex of the figure.Translate so the origin becomes center of the dilation (1,2),…

Q: Distinguish briefly the Parametric and non-parametric analysis

A: There are two types of analysis in the testing of the hypothesis. they are: 1) Parametric analysis.…

Q: 6. Show that the area of the triangle intercepted from the co ordinate axes by the tangent to the…

A: We have to show that the area of the triangle intercepted from the coordinate axes by the tangent to…

Q: 2. Find the dimensions of the largest area rectangle that can be inscribed in the region bounded by…

A: Step 1: Draw a diagramFirst, draw a diagram of the region bounded by the curve and the line . Step…

Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: 2. Let ~v = h3,-2,1i and w = h-1,4,2i. (a) Find cos(0) where 0 is the angle betwen ~v and w.

A: Given,   v→=3,-2,1 and w→=-1,4,2

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

A: Given,The line passes through the point .Aim: To find the equation of the line that passes through…

Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

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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: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3