Question

zane is dangerous fellow who likes to go climbing in active volcanoes. One time while inside a volcano, heheard some rumbling, so he decided to climb up out of there as quickly as he could. he climbed up at a rate of 4 meters per second. after 3 seconds, he was 13 meters below the edge of the volcano. how far was zane below the edge of the volcano when he started climbing? the n toltal how long did it take zane to reach the edge of the volcano ​

Answer 1

25 meters below the edge; 6.25 seconds

Explanation:

We can represent this with a linear function in slope-intercept form.

We know the rate of change is 4, since he climbs up at 4 meters per second. We do not know the value of b, the y-intercept.

This gives us

y = 4x + b

We know that he is 13 meters below the edge after 3 seconds. Using -13 for y and 3 for x,

-13 = 4(3) + b

-13 = 12 + b

Subtract 12 from each side:

-13-12 = 12+b-12

-25 = b

This gives us the equation

y = 4x - 25

He started out 25 meters below the edge of the volcano.

To find how long it took him to reach the edge, substitute 0 in for y:

0 = 4x - 25

Add 25 to each side:

0+25 = 4x-25+25

25 = 4x

Divide both sides by 4:

25/4 = 4x/4

6.25 = x

It takes him 6.25 seconds to reach the edge.