Atortoise and a hare are competing in a race around a 1600-meter track. the arrogant hare decides to let the tortoise have a 950-meter head start. when the start gun is fired the hare begins running at a constant speed of 9.5 meters per second and the tortoise begins crawling at a constant speed of 4 meters per second. a. define a formula to determine the distance (in meters) of the tortoise from the starting line, t , in terms of the number of seconds, n , since the start gun was fired. b. preview define a formula to determine the distance (in meters) of the hare from the starting line, h , in terms of the number of seconds, n since the start gun was fired. c. preview define a formula that determines the number of meters the tortoise is ahead of the hare, d , with the number of seconds, n , since the start gun was fired. d. preview who finishes the race first?

A. t=4n+950

B. h=9.5n

C. d=9.5n-(4n+950)

D. The tortoise will finish first.

Step-by-step explanation:

To find the first two equations, we put the rate at which they are traveling in front of the n, and then add where they start. Since the tortoise gets a 950 meter head start, we add 950. The hare is starting at the start line so we don't need to add anything.

For answer c, we need to subtract the two equations from each other to figure out when they would pass each other. d=(equation h)-(equation t).

For the final answer, all you need to do is plug the first two equations into a graph, and then find where each line is at the point of y 1,600. (To make the graphs I replaced the n with x and the t and h with y.) Using this, we are able to see who got there first, which was the tortoise.

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.