A missile is fired vertically upward such that its distance, \( s \) (in metres), above the ground is given by.
\( s = 50 + 90 t - 4.9 t ^ { 2 } , \)
where t is time (in seconds). (a) When will the missile hit the ground? (b) What is the maximum height of the missile?
a) When the missile hits the ground, s = 0
So, quadratic equation will be
-4.9t^2 + 90 t + 50 = 0
t = ( -90 \(\pm\)\(\sqrt{90^2 - 4 (- 4.9) (50)}\) ) / 2 * -4.9
On solving the above, we get t = 18.907 seconds
b) For max. height, differentiate 's' w.r.t t and equate to 0
\(\dot{s}\) = -9.8 t + 90 = 0
t = 90 /9.8 = 9.183
Max height occurs at t = 9.183 seconds
So s at t = 9.183
Max height = s(9.183)= 50 + 90 9.183 - 4.9 (9.183^2)
Max. Height = 463.325 metres
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.
