[10] 3. If a rock is thrown upward on the planet Mars with a velocity of \( 10 m / s \) , its height (in meters) after \( t \) seconds is given by
\( H = 10 t - 1.86 t ^ { 2 } \)
a) Find the velocity of the rock after \( 1 \) second b) Find the velocity of the rock when \( t = a \) c) When will the rock hit the surface of the planet? d) With what velocity will the rock hit the surface?
H'(t) = v(t) = 10 - 3.72t ,
a) v(1) = 10 - 3.72 = 6.28 , b) v(a) = 10 - 3.72a , c) rock will hit when H(t) = 0 ,
t(10 - 1.86t) = 0 , t = 0 , 5.37 , hence at t = 5.37 s , rock will hit the earth ,
d) v(5.37) = 10 m/s
A linear function that models data is described below. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable. The linear function \( f ( x ) = - 0.41 x + 28.6 \) models the percentage of adults in a country who smoked cigarettes, \( f ( x ) \) , \( x \) years after \( 1997 \) .
The slope is \( \square \) . (Type an integer or a decimal.)
Use the quadratic formula or completing the square to determine the greater solution to
\( x ^ { 2 } + 4 x + 2 = 0 \) . Round your answer to the nearest hundredth. Record your answer and fill in the bubbles on your answer document.
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