An iron ball is bobbing up and down on the end of a spring. The maximum height of the ball is 50 centimeters and its minimum height is 14 centimeters. It takes the ball 2 seconds to go from its maximum height to its minimum height.

Which model best represents the height, h, of the ball after t seconds?

h(t)=25sin(πt)+7

h(t)=50sin(πt / 2)+14

h(t)=18sin(πt)+32

h(t)=18sin(πt /2)+32

Step-by-step explanation:

Let us examine all options:

(a)

Lets verify for t = 0:

h(t = 0) = 7

This isn't allowable as 14 cm is the lower limit for the ball's motion.

This is rejected.

(b)

Let's verify for t = 0:

h(t = 0) = 14

Since at t = 0 sec, the ball is at its minimum, after 2 seconds, it should be at its maximum.

But h(t = 2) = 14, which doesn't satisfy the condition.

Hence, this is rejected.

(c)

Now, let's see at what time instance, the ball is at minimum in this case:

h(t) = 14 = 18sin(πt) + 32

∴ sin(πt) = -1

∴ πt = 3π/2

∴ t = 3/2 seconds

Hence, after 2 seconds, i.e. at 3.5 seconds, the ball should be at its maximum.

h(t = 3.5) = 18sin(3.5π) + 32 = -18 + 32 = 14, which doesn't satisfy the condition.

Hence, this is rejected,

(d)

Now, let's see at what time instance, the ball is at minimum in this case:

h(t) = 14 = 18sin(πt/2) + 32

∴ sin(πt/2) = -1

∴ πt/2 = 3π/2

∴ t = 3 seconds

Hence, after 2 seconds, i.e. at 5 seconds, the ball should be at its maximum.

h(t = 5) = 18sin(5π/2) + 32 = 18 + 32 = 50, which satisfies the condition.

Hence, option (D) is the right answer

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!