Ineed ! a diver made this table to show the relationship between time, x, and depth, y, for his last dive.

time (sec) 0 12 24 30 36
depth (ft) −18 −12 −6 −3 0
question 1
part a

what is the initial value for the function represented in the table?

−18

0.5

2

36
question 2
part b

what is the rate of change for the function represented in the table?

−18

0.5

2

36
question 3
part c

which statements about the situation are true?

select all that are correct.

it took the diver 18 seconds to reach the surface.

the diver ascended 12 foot per second.

the diver started 18 feet below the surface.

the diver descended 12 foot per second.

it took the diver 36 seconds to reach the surface.

Part A = -18

Part B = 0.5ft/sec

Part C =The diver started 18 feet below the surface and It took the diver 36 seconds to reach the surface.

Step-by-step explanation:

Here if we observe the Given function

Time(sec)   0   12   24   30   36

Depth(ft)   -18  -12   -6   -3    0

Part A

we can clearly observe from the table that at the initial value ie. at Time=0sec

the value of the function is nothing but the depth at the given time value which is -18 ft at time=0sec.

Part B

The rate of change of the given equation is

Take any two points in the given funtion like (0 , -18) and (30 , -3)

Now the rate of change is =

therefore the rate of change is 0.5 ft/sec

Part C

Clearly option C is correct which is the diver started at 18 feet below the surface . because At time =0 sec the diver's depth is -18ft Here the negative sign implies that the diver is below the surface of water.

Also it took 36 seconds to reach the surface because the diver's depth is zero at Time = 36 sec (from the graph).

The diver ascended at the rate of 0.5 ft/sec.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!