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What are imaginary numbers, and why do we bother thinking about them if they don't exist?

When studying anything in Mathematics, it is very easy to get lost in the technical details and lose sight of what everything really means on a conceptual level - that's why these kinds of questions are so f...
SF
3606 Views

What is the definite integral of 2x^2 + 4x + 1 with a lower limit of 3 and a higher limit of 6?

When integrating we add one to the power of x and divide the number in front of the x by the new power for each part of the function. So 2x^2 becomes 2/3 x^3, 4x becomes 4/2 x^2, 1 becomes 1/1 x^1. Then we n...
EL
Answered by Ed L. • Maths tutor
3671 Views

A curve C is defined by the equation sin3y + 3y*e^(-2x) + 2x^2 = 5, find dy/dx

d(sin3y)/dx= 3cos3y*(dy/dx)d(3y e^(-2x))/dx = -6y e^(-2x) + 3(dy/dx) e^(-2x)d(2x^2)/dx = 4xd(5)/dx = 0so3cos3y (dy/dx) - 6y*e^(-2x) + 3(dy/dx) e^(-2x) + 4x = 0rearrange the equationdy/dx = (6y e^(-2x)-4x)/(3...
ZZ
Answered by Zhaohui Z. • Maths tutor
6067 Views

Based on structure, how is an enzyme's function affected by amino acids?

An enzyme is a type of protein, and proteins are made up of amino acids. The sequence of amino acids determines the shape of the enzyme, which in turns controls which substrates will or won't fit into the ac...
CC
Answered by Chester C. • Biology tutor
4101 Views

if a^x= b^y = (ab)^(xy) prove that x+y =1

ln(a^x) = ln(b^y) = ln((ab)^(xy)) xln(a) = xyln(ab) ln(a) = yln(ab) = y(ln(a) + ln(b)) y = ln(a)/(ln(a)+ln(b)) with same analysis for ln(b^y): ln(b) = x(ln(a) + ln(b))x = ln(b)/(ln(a)+ln(b)) x + y = (ln(a) +...
SC
Answered by Scott C. • Maths tutor
6189 Views