A disease has hit a city. the percentage of the population infected t days after the disease arrives is approximated by p(t)equ
als=7 t e superscript negative t divided by 127te−t/12 for 0less than or equals≤tless than or equals≤4848. after how many days is the percentage of infected people a maximum
We have been given that function that models the population to be: p(t)=7te^(-t/12) we are required to compute for the time taken for the percentage of infected people to be maximum. from the interval given, the maximum number will be at the point p'(t) from the function; p'(t)=-7/12e^(-t/12)(t-12) equating this to zero and solving for t we get: -7/12e^(-t/12)(t-12)=0 t=12 hence it will take a maximum of 12 days for infection to reach it's maximum percentage.
2) By definition of the midpoint point. If a point is in the middle of a segment, then the two resulting segment are equal. 3) Obvious, the point K is on the line MJ. 6) From statement 5 and the property of fractions. 8) SAS statement of congruent triangles (notice the two triangles share on common angle which is between the two proportional sides) 9) The two corresponding sides are congruent. 10) The constant of proportionality is 2. 11) From statement 10.
The parabola has an absolute minimum and its vertex is located at (1, 7).
Step-by-step explanation:
Since the directrix is below the focus, we infer that parabola has an absolute minimum, where there is a vertex, which is the midpoint of the line segment between (1, 10) and (1, 4). By definition of midpoint, we conclude that vertex is located at (1, 7).
