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what function models the height of the periscope lens at time t? If the periscope reaches its maximum Heught after ascending for 22 seconds, what is the maximum height in feet? ( 24 inches above the surface and ascends at 6 inches per sec.)​

Respuesta :

Answer:

Step-by-step explanation:

First we are going to find the function which models the height of the

periscope lens at time t.

Let the 2 be height of the periscope.

The height of the periscope at the beginning is 24 inches. It ascends at 6

inches per second. The expression which describes how much it has raised,

at the moment, is 6t.

The function is sum of beginning height and how much it has raised, 2 = 24 + 6t.

To find maximum height of the periscope, we need to evaluate function

for + = 22.

2 = 24 + 6(22)

= 24 + 132

156

Substitute 22 for t.

Multiply.

Maximum height in inches is 156.

We know that 1 foot is 12 inches.

So the function that describes converting feet to inch is y :

= 12x. Where y

represents number of inches and a number of feet.

U = 12.2

156

12x

12

-n=

156

12

2 = 13

Substitute 156 for y.

Divide both sides by 12.

Maximum height in feet is 13.

MrRoyal

The height function modeled by the periscope is an illustration of a linear function.

  • The height function modeled by the periscope is  [tex]\mathbf{h(t) = 24+ 6t}[/tex]
  • The maximum height is 156 inches

The given parameters are:

[tex]\mathbf{Start = 24\ inches}[/tex]

[tex]\mathbf{Rate = 6\ inches/second}[/tex]

The function model of the height is calculated using:

[tex]\mathbf{h(t) = Start + Rate \times t}[/tex]

Where: t represents the time in seconds

So, we have:

[tex]\mathbf{h(t) = 24+ 6\times t}[/tex]

This gives

[tex]\mathbf{h(t) = 24+ 6t}[/tex]

After 22 seconds, the height of the periscope would be

[tex]\mathbf{h(22) = 24+ 6 \times 22}[/tex]

Multiply

[tex]\mathbf{h(22) = 24+ 132}[/tex]

Add

[tex]\mathbf{h(22) = 156}[/tex]

Hence, the maximum height is 156 inches

Read more about linear functions at:

https://brainly.com/question/21107621

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