Ahot-air balloon is 150 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 40 mi/hr (58.67 ft/s). if the balloon rises vertically at a rate of 10 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 10 seconds later?

Answer-

Rate of change of the distance between the motorcycle and the balloon after 10 seconds is 57.89 ft/s.

Solution-

Let's consider an instance after t second,

Let D = Distance between the motorcycle and hot air balloon

As shown in the attachment, the situation represents a right angle triangle, hence applying Pythagoras Theorem,

After t=10 seconds,

Then, rate of change of the distance between the motorcycle and the balloon after 10 seconds will be,

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: