Alice's magical cake in the shape of a half-sphere was placed in a box as shown. When she took her pill that night the cake and box grew at rates to maintain tangency. Find the rate at which the space between the cake and the box is growing when the top of the cake box has an area of 100ft2 and the perimeter of the top of the cake box is growing at 32ft/min. (Vsphere = 3 4 π r 3 )

Yuto and hila attempted to solve the same inequality. their work is shown below. which statement is true about the work shown above? yuto is correct because he isolated the variable correctly and reversed the inequality symbol. yuto is incorrect because he should not have reversed the inequality symbol. hila is correct because she isolated the variable correctly and reversed the inequality symbol. hila is incorrect because she should not have reversed the inequality symbol.

Write the expression as a single natural logarithm. 2 in a - 4 in y

(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.