Consider the parabola r(t)equalsleft angle at squared plus 1 comma t right angle, for minusinfinityless thantless thaninfinity, where a is a positive real number. Find all points on the parabola at which r and Bold r prime are orthogonal?

t=0

Step-by-step explanation:

r=<+1,>

by differentiating the r vector component by component

r' = <2at, 1>

Two vector are orthogonal when the dot product between them is zero, so:

r'·r=0

<+1,>·<2at, 1>=2+2at+t=0

common factor

t(+2a+1)=0

Then, the only real value for t is zero.

-> t=0

which expression represents the approximate length of bc?

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: