Provide an appropriate response.Graph the equation 
for several values of a in order to get an idea of what these curves look like. (Try both 
and 
Show that the graph will have an inner loop for every a such that 
and find the values of ? that correspond to the inner loop.
What will be an ideal response?
For any a, the graph will be traced out as ? varies from 0 to 2?. The loop will occur when r is negative. For 
for all ? so there is no loop. For 
when 
For 
when 
and 
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When the graph of directed distance reaches a maximum (at a peak), what can be said about velocity at this point?
A. Velocity is a linear function. B. Velocity reaches a minimum. C. Velocity reaches a maximum. D. Velocity is 0.
Determine whether the polynomial is a perfect square trinomial, a difference of squares, or neither.x2 + 6xy + 9y2
A. Difference of squares B. Neither C. Perfect square trinomial
Solve.An express and local train leave Grays Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.
A. Express's rate = 50 mph and local's rate = 25 mph. B. Express's rate = 25 mph and local's rate = 12.5 mph. C. Express's rate = 60 mph and local's rate = 30 mph. D. Cannot be determined with information given.
A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.It costs the company $1.58 to make each dog and $1.00 for each dinosaur. What is the company's minimum cost?
A. $277 B. $150 C. $312 D. $258