A rectangle is placed inside a semicircle of radius r, with one side along the diameter. What is the largest area the rectangle can have? There are at least two ways to set up variables you can use the coordinates of the upper corner of the rectangle, or you could use the angle the arrow makes with the diameter. Here, r is a 'parameter', to be treated as a fixed constant.

Q: Find the area of rectangular plot if it's length is (5×+8y³) centimeters and it's width is (5×-8y

A: The area, A of a rectangle is given by A=lw, where l is the length and w is the width of the…

Q: 2. Express in radical form the length of the line segment joining the points whose coordinates are…

A: In a right triangle, the lengths of the sides of the triangle are related to each other by the…

Q: Find the equation of the smaller circle that touches the circles x2 +y2=1  and passes through the…

A:

Q: Calculatw the r for circle: 1. x^2 + y^2 = 4 2.X^2 /5+ y^2/5 = 125

A:

Q: nd the condit. on if the circle whose equation a x² + y² + c² = 2ax = 0 and x² + y² + c² = 2b y = 0…

A: The two circles are x2+y2+c2=2ax=0 and x2+y2+c2=2by=0.centers:C1(a,0),C2(0,b)radii:r1=a2=c2,r2=b2-c2

Q: What are the coordinates used to evaluate the following problem and how are they found?

A: Given that D is a region that lies below the sphere and above a cone.

Q: Suppose a cut is made through a solid object perpendicular to the x-axis at a particular point x.…

A: Given that a cut is made through a solid object perpendicular to the x-axis at a particular point x.

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: A cable car is to be built up the side of a hill. The coordinates of the bottom end of the are…

A: Let coordinates of the point  on the cable where tower will be placed is P(x,y,z)-

Q: A circle of radius √5 and centre at (4,q) passes through the point (2,-2). Find the values of q.

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Q: The employees of a company were asked how long it took (in minutes) to commute to work. The results…

A:

Q: Find the points of intersection of the following pair of curves. 29 X+5 y = ,x3 +3x2 +5, y= 9x2 -…

A: Given

Q: What is the ordered pair of the point that is located four units to the left of the origin and three…

A: Answer is  (4, 3)

Q: Find a point whose coordinates are integers and whose distance from (3, 2) is √41

A: To find:   a point whose coordinates are integers and whose distance from (3, 2) is √41 Consider the…

Q: If the distance between the points is (x,7) and (1,15) is 10 .find the value of x

A:

Q: The equation of a curved road is given as y = 100+6x–0.015x² +0.0000111? Determine the places where…

A: The equation of the curved road given is: y=100+6x-0.015x2+0.00001111x3 Measure of the "Sharpness of…

Q: A circle has center at the intersection of the two lines, 4x + y = 4 and x - y= 6.  If it passes…

A: two lines are system Ax=b is

Q: Find the area of the largest rectangle that can be bounded by the x-axis and the parabola y = a -…

A: The given problem is to find the area of the largest rectangle that can be bounded by x-axis and the…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.