Tutor profile: Ayush V.

Perimeter of a △ with integer sides is equal to 15. How many such triangles are possible?

Let us assume a ≤ b ≤ c. a = 1, Possible triangle 1, 7, 7 a = 2, possible triangle 2, 6, 7 a = 3, possible triangles 3, 6, 6 and 3, 5, 7 a = 4, possible triangles 4, 4, 7 and 4, 5, 6 a = 5, possible triangle is 5, 5, 5 There are totally 7 triangles possible.

Mary sold 15 widgets last week. The median sale price of all widgets was $130 and the average sale price of all widgets was $150. What will be the least possible sale price for the most expensive widget?

The sum of 15 widgets CP will be = 15 X 150 = 2250 As median is 130 so there will be 7 items whose CP will be less than or equal to this. To get the least greatest price, assume all are 130 then 8*130 = 1040 The remaining will have a sum of = 7 X A(Avg price) Now 2250 – 1040 = 7 X A Answer = 172

If y is a function of x and log(x + y) = 2xy, then the value of y’(0) = ?

As y is a function of x, value of the equation when x=0, log(y) = 0; Hence y= 1. Now differentiating the euqation wrt x. 1/(x+y)*(1+dy/dx) = 2y*1 + 2xdy/dx dy/dx = (1-2y(x+y))/(2x(x+y)-1) dy/dx (at-0,1) =1