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SOH CAH TOA (imagining each as a triangle)

S = sin

C = cos

T = tan

O = opposite

H = hypotenuse

A = adjacent

The product rule states that y=uv and dy/dx=(u)dv/dx + (v)du/dx. As the equation is in this form we can let u=2x and v=sinx. Therefore du/dx=2 and dv/dx=cosx. Substituting for u and v we get dy/dx=(2x)(co...

1. 5x + 3y = 41   2) 2x + 3y = 20 Subtract equation 2) from equation 1) to cancel the y's (3y-3y = 0) .  Next we subtract  the x's (5x - 2x = 3x) and then finally we have 41 - 20 = 21. We now have that...

Recognise that quadratic can be factorised:

(x+4)(x-1)=0

This gives the solutions x=-4 and x=1 by inspection.

First Simplify the numbers we know. Therefore we get:       x²=75/3      which is the same as     x²=25

Now find the square root of 25, which is 5 or -5. Therefore x=5 or -5