Tutor profile: Carlos H.

Find the equation of a circle that has its center on $$ (2, -4) $$ and has a radius of 7.

$$ (x-2)^2 + (y+4)^2 = 49 $$

The height of a football in feet $$ t $$ seconds after it is thrown can be modeled by the equation $$ f(t) = -x^2 + 5x + 6.4 $$ After how many seconds does the football reach its max height? What is that max height?

To find the point where the football's height goes from increasing to decreasing, we can use the derivative. $$ f'(t) = -2t + 5 $$ $$ 0 = -2t +5 $$ $$ t = 5/2 $$ After 2.5 seconds, the football reaches its max height, which can be calculated by plugging 2.5 back into the original equation. $$ f(2.5) = 12.65 $$

Jenny has a phone plan that starts at $10 per month but also charges her $0.05 for each call he makes. Her parents would like her to keep her monthly total below $15 a month. How many calls a month can Jenny make while staying within budget?

If "m" is how much her monthly bill will cost and "c" for number of calls, we can express this problem as a function: $$ m = 0.05c + 10 $$ If her parents wants the monthly cost to stay below $15, we would solve the inequality $$ 15 > 0.05c + 10 $$ $$ 5 > 0.05c $$ $$ 100 > c $$ Jenny can make up to 100 calls before she goes over budget!