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Is AB perpendicular to BC where A =(2,0,-1), B=(4,3,-6) and C = (9,3,-4)

AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2) If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + (-5x2) =...
SU
Answered by Syed Usman B. • Maths tutor
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How do i use the chain rule twice when differentiating?

Ok so for this question we'll use this example: y = (e -2x^2 + 2) 1/5 We start off by making the expression inside the brackets equal to u. In other words u = e -2x^2 + 2. This also means y = u 1/5 Using the...
IL
Answered by Indiya L. • Maths tutor
5663 Views

∫2x(x+2)^(1/2) dx evaluated from 0->2

First make a substitution so we can apply the power rule ∫x n dx = (x n+1 )/(n+1) + C more simply. Can see u=x+2 means (x+2) 1/2 -> u 1/2 and so will help us apply this rule. Change dx/du=1 implies dx = d...
LP
Answered by Luke P. • Maths tutor
13612 Views

Find the equation of the normal of the curve xy-x^2+xlog(y)=4 at the point (2,1) in the form ax+by+c=0

differentiating: xy'+y-2x+(x/y)y'+log(y)=0rearranging: y'=y(2x-y-log(y))/x(1+y)at (2,1): y'=3/4 so gradient of normal at (2,1) is -4/3so the equation of the normal is y-1=(-4/3)(x-2)which is equivalent to 4x...
SL
Answered by Sam L. • Maths tutor
3576 Views

Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2

First express as a single logarithm as follows. The number in front of the logarithm remembering log rules can be rewritten as the power of the number in the bracketsSo rewriting the LHS log 3 (x 2 ) - log 3...
TS
Answered by Theranjit S. • Maths tutor
9433 Views