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differentiate x^2 + y^3 + xy respect to x

2x + 3y 2 * dy/dx + x * dy/dx +y
XJ
Answered by Xianming J. • Maths tutor
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dx/dt=-5x/2 t>=0 when x=60 t=0

dx/dt=-5x/2 Int(x, dx)=Int(-5/2, dt) ln(x)=-5t/2+c x=60 when t=0 ln(60)=c ln(x)=ln(60)-5t/2 x=e ln(60)-5t/2 x=60/e 5t/2
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Answered by Felix D. • Maths tutor
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A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

dy / dx = 9x^2 + 2ax + b x = 2, dy / dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b x = 1, dy / dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b 36 + 4a + b = 2(9 + 2a + b) b = 18 x = -1, dy / dx = 0 = 9(-1)^2 + 2a(-1) + 18 9 - ...
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Explain why an ice cube submerged in a drink melts faster than an ice cube on a kitchen surface (the drink, surface and room temperature are all equal). (3 marks)

(1) In the drink, all six faces are in contact with the liquid (or) On the kitchen surface, only one of the faces is in contact with a solid and the rest are in contact with the air (or) On the kitchen surfa...
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Answered by Alistair R. • Physics tutor
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Solve the simultaneous equations x^2 + y^2 = 9 and y = 3x + 3

y 2 = (3x + 3) 2 = 9x 2 + 18x + 9 x 2 + 9x 2 + 18x + 9 = 9 10x 2 + 18x = 0 (root a: x = 0) 5x + 9 = 0 (root b: x = -1.8) For x = 0, y = 3(0) + 3 (root a: y = 3) For x = -1.8, y = 3(-1.8) + 3 (root b: y = -2....
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Answered by Alistair R. • Maths tutor
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