SOLUTION: A diver jumps into the water, the function 11t^2-77t+110 represents the path the swimmer took underwater where t is the time in seconds. How long was the swimmer under water?

Algebra ->  Matrices-and-determiminant -> SOLUTION: A diver jumps into the water, the function 11t^2-77t+110 represents the path the swimmer took underwater where t is the time in seconds. How long was the swimmer under water?      Log On


   

Question 1200406: A diver jumps into the water, the function 11t^2-77t+110 represents the path the swimmer took underwater where t is the time in seconds. How long was the swimmer under water?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The given quadratic is in the form
at^2 + bt + c
where in this case:
a = 11
b = -77
c = 110

Use the quadratic formula to determine when 11t^2-77t+110 is equal to zero. This is when the swimmer is at the water's surface.
t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

t+=+%28-%28-77%29%2B-sqrt%28%28-77%29%5E2-4%2811%29%28110%29%29%29%2F%282%2811%29%29

t+=+%2877%2B-sqrt%285929-4840%29%29%2F%2822%29

t+=+%2877%2B-sqrt%281089%29%29%2F%2822%29

t+=+%2877%2B-++33%29%2F%2822%29

t+=+%2877%2B33%29%2F%2822%29 or t+=+%2877-33%29%2F%2822%29

t+=+%28110%29%2F%2822%29 or t+=+%2844%29%2F%2822%29

t+=+5 or t+=+2

t+=+2 or t+=+5

If t = 2, then,
11t^2-77t+110
11(2)^2-77(2)+110
11(4)-77(2)+110
44-154+110
-110+110
0
Showing 11t^2-77t+110 = 0 when t = 2
I'll let you check t = 5.

The swimmer is at the surface when t = 2 and t = 5
For the interval 2 < t < 5, the swimmer is underwater.
This is a timespan of 5-2 = 3 seconds

Graph:

Desmos and GeoGebra are two graphing options I recommend.

Answer: 3 seconds