4. A line has the equation \( 5 x + 6 y = 35 \) What is the equation of the perpendicular line going through the point \( ( 8 , - 1 ) ? \) The equation is given by \( A x + B y = C \) where \( A = \square \) and \( C = \)
\( * \) Remember, when writing an equation in standard form you must simplify until the x-coefficient is positive.
A= 1.2
B= -1
C = -10.6
Find the solution of the exponential equation \( 16 e ^ { x } = 12 \) in terms of logarithms, or correct to four decimal places. \( x = \)
Certain radioactive material decays in such a way that the mass remaining after \( t \) years is given by the function
\( m ( t ) = 100 e ^ { - 0.01 t } \)
where \( m ( t ) \) is measured in grams. (a) Find the mass at time \( t = 0 \) . Your answer is (b) How much of the mass remains after \( 20 \) years? Your answer is Round answers to \( 1 \) decimal place.
