When flying faster than the speed of light, an airplane that flies parallel to the ground forms sound waves in the shape of a cone behind it. The waves intersect the ground in the shape of a hyperbola, with the airplane directly above the center of this hyperbola. If you hear a sonic boom along the hyperbola x^2/81 - y^2/4 = 1, what is the shortest horizontal distance you could be to the airplane?

show work please!!

Which of the following expressions is equal to 2x^2+8

Ateacher brought a pack of 17 batteries . each calculator uses 3 batteries . how many calculator can the teacher fill with batteries

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.