Derive the formula for the area of a circle of radius r by evaluating an appropriate definite integral. (Hint: the equation y = square root {r^2 - x^2} gives a semicircle of radius r.) Calculate the integral either directly or using Fundamental T...
asemicirclewitharadiusof4m.Thevehiclecanonlytravel atonesideofthecenterlineoftheroad.Canatruckwith awidthof2.7mandaheightof3Mbeabletodriveintothe tunnel? [drawing]:drawingDepartment [studentactivity]:trytowritetheequationofthecurve(the stepsoftheequationofthecurveandthedefinitionofthe circle) Solution:asemic...
equationofcircle Choosethepropercoordinatesystemtosolvethepractical problemsrelatedtothecircle 3.Teachingprocess (1)creatingsituations(enlighteningthinking) Problem1:itisknownthatthecrosssectionofthetunnelis asemicirclewitharadiusof4m.Thevehiclecanonlytravel onthesideofthecenterlineoftheroad.Canatruckwith awidthof...
A rectangle is inscribed in a semicircle of radius 2. What is the area of the largest rectangle possible? What is the area of the largest rectangle that can be inscribed in a semicircle of radius r? What is the largest area of the rectangl...
A function y of variable x can be defined in parametric form where both x and y are functions of a third parameter t. Then, using first derivatives, the first derivative of y with respect to x can be calculated as the ratio of the...
Find parametric equations for the semicircle x^2 + y^2 = a^2, y 0, using as parameter the slope t = \frac{dy}{dx} of the tangent to the curve at (x, y). Consider the parametric curve: x = 9 + 6 cos t, y =...
Answer to: Use the equation A=\frac {1}{2} \ \int_c \ x \ dy-y \ dx to calculate the area of the circle of radius 3 centered at the origin. A=...