Search over 10,000 free study notes

a,y=5xfinding the inverse: x=5y - dividing by 5 (1/5)x=y f^-1(x)=(1/5)x
b,5x(7²+1)=250

We'll apply the quotient rule using "u = ln(x² + 1)" and "v = x² + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see &quo...

y^-1 dy = xcos(x) dx∫y^-1dy = ∫xcos(x) dx ln(y) = ∫xcos(x) dx [using integration by parts to integrate the right hand side] therefore, ln(y) = xsin(x) - ∫sin(x) dxln(y) = xsin(x) + cos...

Step one: As the fractions are mixed fractions we need to convert them into top heavy fractions to multiply. 2 3/4 is equivalent to 11/4 ( as 2 3/4 = 4/4 + 4/4 + 3/4 = 11/4). 1 1/2 is equivalent to 3/2 (a...

The initial mass is found by putting t=0 into the given equation, so the initial mass is 300g. When the mass has decreased to half its value, M=150g. This gives us 150=300e^-0.05t, so e^-0.05t=1/2. Natura...