(a) what can you say about a solution of the equation y' = - (1/4)y2 just by looking at the differential equation? 1. the function y must be decreasing (or equal to 0) on any interval on which it is defined. 2. the function y must be increasing (or equal to 0) on any interval on which it is defined. (b) verify that all members of the family y = 4/(x + c) are solutions of the equation in part (a). (c) find a solution of the initial-value problem. 3√12x+ 0.008 12

Step-by-step explanation:

a) We can state that the value of y' is negative on an interval because y^2 is positive in any interval (except in y(0), in which y'(0)=0). If y' is negative, as it is the slope of the tangent of the function y in any point, we can conclude that y is decreaing or equal to zero on any interval on which is defined.

b) First, we calculate y'

Then we replace in the differential equation and get the same result

c) The question is not readable, so I am going to solve this initial-value problem:

10x

step-by-step explanation:

the greatest common factor 30 and 20 is 10

5 is a common factor of 30 and 20 but 10 is also a factor and 10 is greater than 5 so 5 will definitely not be apart of our answer

now the most amount of x's you factor our is just 1 factor of 1

so 10x the gcf of the terms in the polynomial

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.