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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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What is the attachment theory?

The attachment theory was developed by Mary Ainsworth. This theory is used to describe the relationships that children between the ages of 1-2 develop with their primary caregiver (usually the mother). This ...
AC
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How would you increase 400 by 7%

First, we'd want to find out what 1% of 400 is. If 400 is the total number, that would make 400 the whole 100%. In order to find out 1% we'd want to divide the number by 100 which is 4. Now that we know 1% i...
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Answered by Tharani T. • Maths tutor
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