Find the dimensions of the rectangle of maximum area that can be drawn within a semicircle of radius 3, if one side of the rectangle lies along the diameter of the semicircle. (Suggestion: draw your semicircle on the ry-plane as the top half of the circle 22 +y? = 9.) Solution

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4 – x². What…

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Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

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A: Solution:-   First we are draw a rough diagram based on the given problem.      Both towers are…

Q: A rectangle is inscribed in a parabola y^2 = 16x with the side of the rectangle along the latus…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: 6.Find the area for a circle that has a radius of 4x3y3

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Find the center and the radius of the sphere. x2 +y? +z? +5x + 6z = 0

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Q: 2.) %3 %23 a.) Give the most specific name for the quadrilateral b.) How do you know? What…

A: A polygon with four sides is a quadrilateral. There are different kinds of quadrilaterals. Each…

Q: Find the area of the region bounded by the semicircle with equation y = V4 – (x + 2)² + 1 and the…

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Q: 3 If A B 224 and D(3cos 0, 2sin ) are four points, then find the maximum area of quadrilateral ABCD,…

A: The diagonal divides the quadrilateral into two equal parts. Area of triangle is obtained as area of…

Q: A parabolic arch has an equation of 7x + y- 260 0. Find the maximum height of the arch. units

A: The equation of parabolic arch is: 7x2+y-260=0

Q: 5. Sketch the parabolas showing the intercept and the maximum/minimum points. a) y = 2x – 4x +7 b)…

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Q: A parabolic arch has an equation of 3x 2 + y – 300 = 0. a) What is the maximum height of the arch?…

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Q: The points of intersection of the graphs of xy = 20 and x2 + y2 = 41 are joined to form a rectangle.…

A: Given: xy=20                                              ..1x2+y2=41…

Q: A parabola has an equation of x²-4y-2x+8=0. Find the length of the latus rectum.

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Q: The points of intersection of the graphs of xy = 20 and x² + y? = 41 are joined to form a rectangle.…

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Q: The diagram shows a convex polygon. 3y 103° 2y 135° 72° What is the value of y?

A: find the value of y

Q: Let ABC be a right triangle with right angle ZA and hypotenuse |BC|| = a is a constant. Find the…

A: Maximization  of in radius of triangle

Q: Find the area of the largest rectangle with the lower base on the X-axis and the upper vertices on…

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Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: 26. Find the area of the largest rectangle that can be inscribed in the ellipse x²/a² + y°/b² = 1.

A: Topic- application of derivatives to find maximum area

Q: Find the point P on the parabola y = x? closest to the point (57, 0). (x, V) = ( y y =x 57

A: Let x, x2 be the point on the parabola y=x2 closest to the point 57, 0. Now the distance between x,…

Q: The base of a solid is the segment of the parabola y²=12x cut off by the latus rectum. A section of…

A: The base of a solid is the segment of the parabola y²=12x cut off by the latus rectum. A section of…

Q: Find the two values of c such that the area of the region enclosed by the parabolas y = x² – c² and…

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Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y=6-x² What is the…

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Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: 3. A piece of wire of length shape of an equilateral tr should the wire be cut sa a) a minimum? b) a…

A: L: length of the wirex: one piece of wire cut from length LPerimeter of the equilateral…

Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                ->Equation(1)Let (x,y) be the upper right corner of the…

Q: What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y =…

A: According to the figure, we have

Q: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

Q: A rectangle is inscribed with its base on the ?x-axis and its upper corners on the parabola y=2−x^2.…

A: Given, The equation of the parabola is y=2-x2

Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: Find the minimum distance from the point (4, 2) to the parabola y2 = 8x. A 4/3 B) 2/7 © V3 D 2/3

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x^2 - c^2 and y = c^2 -x^2…

A: Given parabolas, y=x2-c2y=c2-x2

Q: Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence in their field…

A: We have to find the area of the enclosed region.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

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Q: find the ends of the latus rectum, axis of symmetry of x2+20y=0

A: Given  x2+20y=0 Find the ends of lactus rectum and axis of symmetry.

Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

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Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: The parabolic antenna has an equation of y^2 + 8x = 0. Determine the length of the latus rectum.

A: Here we use the standard form of parabola.

Q: The area of the region below the parabola y = 9- x² and above the x-axis is a. 12 b. 24 с. 36 d. 48…

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Q: 6. KAWE is an isosceles trapezoid with midsegment LS. Determine the length of LS. 2 6 2x W. 4x-4

A: Given, KAWE is a isosceles trapezoid which means that it has congruent diagonals. We need to…

Q: hat is the shape of the vertical cross section of this solid figure that passes through the vertex?

A: We have to identify the shape of the cross-section.

Q: What is the Axis of Symmetry of the parabola represented by y = - = -x² – 3x + 7? O x = 3 O x = -3 O…

A: The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent…

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 11 –…

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Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: Find the vertex and length of the latus rectum for the parabola. y = (x - 2)2 - 9 Vertex: (x, y) = (…

A: Topic = Parabola