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,

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

y > 1/3x

y < = -x + 4

hope this : )