how can i solve this by Putting the expression 250 within m

how can i solve this by Putting the expression < 250; within means <, i need to solve by factoring; so that it sets up two regions, one true and one false - which region states the speed within which the car can stop in 250ft?

Solution

Since distance is within 250, it must be less than or equals to 250.

Also distance is a postive quantity, so it will also be greater than or equals to 0.

So basically find the value of v for which 0<=0.06v^2+2v<=250

The work you have uploaded is correct,

Thus, speed should be between 0 to 50 including to stop within distance of 250 ft. Answer in interval noation is [0,50]

You can also solve only

0.06v^2+2v<=250

but solve it only for nonnegative value of v