contestada

A 11-inch candle is lit and burns at a constant rate of 1.3 inches per hour. Let t represent the number of hours since the candle was lit, and suppose f is a function such that f ( t ) represents the remaining length of the candle (in inches) t hours after it was lit. Write a function formula for f . f ( t ) = 11-1.3t Correct What is the domain of f relative to this context? Enter your answer as an interval. (0,8.46) Incorrect ( 0 , 8.46 ) = (0,8.46). What is the range of f relative to this context? Enter your answer as an interval. [11,0] Incorrect Solve f ( t ) = 6.4 for t . t = 3.53846 Correct What does your solution in part (d) represent in this context? Select all that apply. How many hours since the candle was lit when it is 6.4 inches long. The length of the candle (in inches) 6.4 hours after it was lit. How long it takes for the candle to burn out. Correct

Respuesta :

jolis1796

Answer:

Domain t ∈ [0, 8.4615]

Range d ∈ [0, 11]

t = 3.538 h    (d = 6.4 in)

d(6.4 h) = 2.68 in

t = 8.4615 h     (d = 0 in)

Step-by-step explanation:

Given

v = - 1.3 in/h

d₀ = 11 in

We use the formula

v = d/t   ⇒  d(t) = v*t + d₀  = - 1.3*t + 11

Domain t ∈ [0, 8.4615]

At the beginning t = 0 ⇒  d(0) = v*0 + d₀  = 0 + 11 = 11

At the end d(t) = 0  ⇒  0 = - 1.3*t + 11  ⇒ t = 8.4615

Range d ∈ [0, 11]

If  d(t) = 6.4 in

t = ?

6.4 = - 1.3*t + 11   ⇒   t = 3.538 h

If  t = 6.4 h

d = ?

d(6.4) = - 1.3*(6.4) + 11 = 2.68 in

If d = 0

t = ?

0 = - 1.3*t + 11   ⇒   t = 8.4615 h

MrRoyal

A function is the relationship between variables. The domain is the possible set of input while the range is the possible set of output values.

  • The function formula for f(t) is f(t) = 11 - 1.3t
  • The domain of f(t) is [0,8.46]
  • The range of f(t) is [0,11]
  • The value of t when f(t) = 6.4 is 3.54

Given that:

[tex]Length = 11-in[/tex]

[tex]Rate = 1.3in/hr[/tex]

The formula f(t) is calculated as follows:

[tex]f(t) = Length - Rate \times t[/tex]

[tex]f(t) = 11 - 1.3 \times t[/tex]

[tex]f(t) = 11 - 1.3t[/tex]

To determine the domain as it relates to this scenario, we set f(t) to 0, to calculate the time for the candle to completely burn out

[tex]11 - 1.3t = 0[/tex]

Collect like terms

[tex]- 1.3t = 0-11[/tex]

[tex]- 1.3t = -11[/tex]

Divide both sides by -1.3

[tex]t = 8.46[/tex] ----- This is the time it takes to burn the candle completely.

At [tex]t = 0[/tex], the candle is still whole

So, the domain as an interval is: [0,8.46]

To determine the range as it relates to this scenario

When

[tex]f(t) = 0[/tex] --- the candle has completely burnt out

[tex]f(t) = 11[/tex] --- the candle is still whole

So, the range as an interval is [0,11]

To solve for t when [tex]f(t) = 6.4[/tex]

We have:

[tex]f(t) = 11 - 1.3t[/tex]

[tex]6.4 = 11 - 1.3t[/tex]

Collect like terms

[tex]1.3t = 11-6.4[/tex]

[tex]1.3t = 4.6[/tex]

Divide by 1.3

[tex]t = 3.54[/tex]

The interpretation of the above solution is:

  • How many hours since the candle was lit when it is 6.4 inches long.

Read more about functions at:

https://brainly.com/question/13824428

Otras preguntas