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| Name | ARBELOS, Find area, the maximum area and the general expression| Maths | Leaving Cert Maths | |
| Video Uploader | Video From thinkeccel |
| Upload Date | This Video Uploaded At 10-03-2021 00:17:02 |
| Video Discription | 01:12 Q1: Prove that the shaded area of the arbelos is equal to the area of the circle with diameter k. 05:09 Q2: In general, for a fixed value of r1, say, P centimeters and r2 equal to x. Find an expression in x, for the area of the arbelos. 06:02 Q3: Find the maximum area of an arbelos, that can be formed, when the value of r1. is P centimeters. 09:19 Q4: Find the maximum area of an arbelos, that can be formed, when the value of r1. is 6 centimeters. For Question1, the area of arbelos is found by subtracting areas of inner semicircles from the outer circle. For the area of the circle with diameter k, we use the Pythagoras' Theorem in order to find the value of k in relation to radii r2 and r3. substituting value of k in ther area equation proves that the area of the red circle is the same as the area of the arbelos. For Q2, writing r2=x and r3=p-x, into the equation for the area of the arbelos yields the general expression in x. For Q3, we see that our problem involves find maxima of a quadratic function. One method for this task is to use calculus . we first found the critical point by setting the first derivative equal to zero. a second derative test showed that the second derivative is negative that means our quadratic function has a maximum point. Finally by substituting this x vlaue in the equation for the area gives us the maximum area. For Q4, set P =6 as before and follow the same steps. It is interesting to note that the second derivative of a quadratic function is constant. *************************************** Subscribe to support this channel. *************************************** #LeavingCertMaths |#Arbelos #Maths | |
| Category | Education |
| Tags | Arbelos | area | find maximum area | find general expression | Geometery | trigonometery | use calculus | find maximum of function | maxima of quadratic function | slope of line | Area of semicircle | Exam questions | A level | Junior and Leaving Certificate Maths | Leaving cert maths | Leaving cert | maths | junior cert | GCSE | GCSE maths | leaving cert notes | 3b1b | Leaving Cert Maths | khan academy |
