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Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.

First, we factor out one (x+1). (1+x)^3 = (x+1)^2(x+1)= Then, we expand using the formula (a+b)^2 = a^2 + 2ab +b^2: =(x^2+2x+1)(x+1)= Then we multiply: = x^3 + 2x^2 + x + x^2 + 2x + 1 We sum the terms wit...

AI
8512 Views

Find dy/dx of the curve x^3+5xy-2y^2-57=0

3x2+5y+5x(dy/dx)-4y(dy/dx)=0

3x2+5y=(5x-4y)dy/dx

dy/dx=(3x2+5y)/(5x-4y)

SP
Answered by Steven P. Maths tutor
4193 Views

When should I use imparfait and passé composé?

Passé composé (AVOIR ou ETRE + participe passé) is used for ponctuel actions in the past which have been ended. Ce matin, j’ai mangé une tartine de pain.  On the other hand, imparfait is ...

CM
Answered by Charlotte M. French tutor
2827 Views

Given that y=x/(2x+5) find dy/dx.

Using the quotient rule: Let u=x and v=2x+5 then du/dx= 1 and dv/dx=2 Hence dy/dx=[(2x+5)x1- (2x)]/(2x+5)2             =5/(2x+5)2

SB
Answered by Shayna B. Maths tutor
3857 Views

How is information contained in the nuclear DNA of a cell converted into proteins? Outline the role of each molecule and enzyme involved in the process.

DNA is a double-stranded nucleic acid that consists of four different bases (A, T, C, G) which make up the 'language' of the genome. Sets of three bases on the coding strand of DNA, known as a triplet cod...

TL
Answered by Timothy L. Biology tutor
2533 Views

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