Terrell trucking company is in the process of setting its target capital structure. the cfo believes that the optimal debt-to-capital ratio is somewhere between 20% and 50%, and her staff has compiled the following projections for eps and the stock price at various debt levels: debt/capital ratio projected eps projected stock price 20% $3.00 $34.75 30 3.65 36.50 40 3.80 37.75 50 3.55 32.25 assuming that the firm uses only debt and common equity, what is terrell's optimal capital structure? round your answers to two decimal places. % debt % equity at what debt-to-capital ratio is the company's wacc minimized? round your answer to two decimal places. %
answer: conjunction and -20< x < 16 is answer.
it is a conjunction because it is and statement
|x+2|< 18 gives
[since l x-a l < b means x-a lies between -b and b ]
-18< x+2< 18
subtracting 2 in the whole inequality ,we get
-18-2 < x +2-2 < 18-2
-20 < x < 16
i'll go through the list of possible answers. anything marked as true i'll highlight in bold
choice a) the graph has a minimum. this is true. this is because there is a lowest point at the vertex (-1,-9)
choice b) the graph has a maximum. false. a parabola can have a min or a max but not both at the same time. choice a is true, so this contradicts choice b. the graph goes on forever upward so there is no highest point.
choice c) the graph has zeros at -4 and 2. this is true. the term "zeros" may be confusing. i like to think of them as x intercepts or roots. this is where the graph crosses or touches the x axis. they solve the equation f(x) = 0.
choice d) the vertex is located at (-1,-9). this is true. this is the lowest point of the graph. it's also where the axis of symmetry is located.
choice e) the graph has y intercepts at (-4,0) and (2,0). this is false. the parabola only crosses the y axis one time and it is at the location (0,-8) which is the y intercept. we can also say "the y intercept is -8". see choice g below. note that any function will have only y intercept. if it has more than one y intercept, then it won't be a function anymore because it fails the vertical line test.
choice f) the solution of the parabola is (-1,-9). false. a solution is another term for root or x intercept. it's where the graph crosses the x axis. in other words, it's the set of x values that make f(x) = 0 true. in this case, x = -4 and x = 2 do the trick. the vertex is not considered a solution point unless the vertex is on the x axis.
choice g) the y intercept is (0,-8). true. the graph crosses the y axis here. see choice e above.in summary, the four answers are: a, c, d, g