Question

Write a linear function, x(t), for the total distance in miles hiked in terms of total time hiking in hours using the data from the table.
Write a quadratic function, y(t), for elevation in terms of the total time hiking in hours using the data in the table. Find a system of three equations and three unknowns to write the equation
pls help! I'm super confused! here is the table

Answer 1

The system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

Equation

Given:

Elevation              Travel time

6990 feet                    0 hours

8290 feet                    10 hours

10875 feet                   21 hours

Using this formula

y(t)=at²+bt+c

Where:

At:

t=0; y=6990

6990=a(0)²+b(0)+c

c=6990 Equation 1

At:

t=10; y=8290

8290=a(10)²+b(10)+6990

1300=100a+10b Equation 2

At:
t=21; y=10,875

10875=a(21)²+b(21)+6990

3885=441a+21b Equation 3

Using equation 2 and 3 to solve for a and bc

1300=100a+10b

1300-10b/100=a

13-0.1b=a

Plug into equation 3

3885=441(13-0.1b)+21b

3885=5733-14.1b+21b

b=80

a=13-0.1(80)

a=13-8

a=5

Hence:

Write the Equation by plugging a,b and c

y(t)=5t²+80t+6990

Therefore the system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

Learn more about equation here:https://brainly.com/question/2972832

#SPJ1