For the differential equations dy/dx = squareroot y^2 - 81 does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point 1. (-1, 83)? 2. (1, 87)? 3. (2, -9)? 4. (0, 9)?

Point r divides in the ratio 1 : 3. if the x-coordinate of r is -1 and the x-coordinate of p is -3, what is the x-coordinate of q? a. b. 3 c. 5 d. 6 e. -9

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.

Darcy deposited $390 into a savings account. as long as the account balance remains at or above $150, she does not have to pay a service fee for the account. for how many months can she withdraw $40 a month without having to pay service fees? a) 3 b) 5 c) 6 d) 9