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Find the point of intersection of the lines y=2x-7 and 4y-2=3x

Substitute y into 4y-2=3x 4(2x-7)-2=3x -> 8x-28-2=3x -> 8x-3x=28+2 -> 5x=30 -> x=30/5 -> x=6 subsitute x into y=2x-7 y=2(6)-7 -> y=12-7 -> y=5 Point = ( 6 , 5 )
IG
Answered by India G. • Maths tutor
4489 Views

Differentiate y=(3+sin(2x))/(2+cos(2x))

dy/dx = (4cos(2x) + 6sin(2x) + 2)/(2+cos(2x)) 2
MB
Answered by Matthew B. • Maths tutor
9407 Views

Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x)) -1 . Next, find dy/dx in terms of cos(x) and sin(x). Again, we are f...
NL
Answered by Noah L. • Maths tutor
18093 Views

Solve the inequality x^2 > 3(x + 6)

In order to solve this inequality, it is helpful to have all the terms on the left-hand side of the equation. To do this, we can subtract 3(x + 6) from both sides of the equation. This gives us: x^2 - 3(x+6)...
JM
Answered by Joseph M. • Maths tutor
19182 Views

Find the value of dy/dx at the point where x = 2 on the curve with equation y = x^ 2 √(5x – 1).

Here we must use the product rule to differeniate because x appears in both terms of the equation, therefore both parts must be differentiated. So we will set u= x 2 and v= (5x-1)^(1/2) written like this mak...
LT
Answered by Lucy T. • Maths tutor
13395 Views