A campground owner has \( 2500 \) m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let \( x \) represent the width of the field.
(a) Write an expression for the length of the field as a function of \( x \) . (b) Find the area of the field (area = length \( x \) width) as a function of \( x \) .
(c) Find the value of \( x \) leading to the maximum area.
(d) Find the maximum area. (a) \( \ell ( x ) = \square\)
(a)2500-2x
(b)x(2500-2x)
(c)x=625
(d)781,250
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.
