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This question: 1 point(s) possible
Assume the following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the given question. Be sure you clearly identify the independent and de
variables. Then briefly discuss whether a linear model is reasonable for the situation described.
A snowplow has a maximum speed of 30 miles per hour on a dry highway. Its maximum speed decreases by 1.7 miles per hour for every inch of snow on the highway. According to this model, at what s
will the plow be unable to move?
Select the correct choice below and fill in the answer box to complete your choice.
(Simplify your answer.)
OA. The independent variable is speed (s), in miles per hour, and the dependent variable is the depth of snow (d), in inches. The linear function that models this situation is d=
OB. The independent variable is the depth of snow (d), in inches, and the dependent variable is speed (s), in miles per hour. The linear function that models this situation is s
The snowplow will be unable to move when the snow is inch(es) deep.
(Round to the nearest inch as needed.)
Is a linear model reasonable for the situation?
OA. The linear model is most likely not reasonable, because it is unlikely that the plowing rate is a constant.
B. The linear model is most likely not reasonable, because the plowing rate should not change, regardless of the amount of snow.
OC. The linear model is most likely not reasonable, because the plowing rate should increase as the depth of snow increases.
OD. The linear model is reasonable, because the plowing rate is always constant for any snowplow.
Time Remaining: 01:25:47
Nex
Jun 2
9:49

Sagot :

GinnyAnswer
Let's approach this step-by-step to understand the question and find the correct solution.

### Step 1: Identify the Independent and Dependent Variables

In this situation, we need to identify the two main variables involved:

- Independent Variable: The depth of snow, [tex]\( d \)[/tex] (in inches), because it is the variable that we consider changing.
- Dependent Variable: The speed of the snowplow, [tex]\( s \)[/tex] (in miles per hour), because it depends on the depth of the snow.

Hence, the correct choice is:

OB. The independent variable is the depth of snow ([tex]\( d \)[/tex]), in inches, and the dependent variable is speed ([tex]\( s \)[/tex]), in miles per hour.

### Step 2: Formulate the Linear Function

The problem tells us that the snowplow has a maximum speed of 30 miles per hour on a dry highway and that this speed decreases by 1.7 miles per hour for every inch of snow on the highway.

We can express this relationship with the following linear equation:

[tex]\[ s = s_{\text{max}} - k \cdot d \][/tex]

where:
- [tex]\( s \)[/tex] is the speed of the snowplow (dependent variable)
- [tex]\( s_{\text{max}} \)[/tex] is the maximum speed of the snowplow on a dry highway (30 mph)
- [tex]\( k \)[/tex] is the rate at which the speed decreases per inch of snow (1.7 mph per inch)
- [tex]\( d \)[/tex] is the depth of snow (independent variable)

So, the linear equation becomes:

[tex]\[ s = 30 - 1.7 \cdot d \][/tex]

### Step 3: Determine When the Snowplow Will Be Unable to Move

The snowplow will be unable to move when its speed drops to 0 mph. We need to find the depth of snow [tex]\( d \)[/tex] at which [tex]\( s = 0 \)[/tex]. Therefore, we set the equation to 0:

[tex]\[ 0 = 30 - 1.7 \cdot d \][/tex]

Now, solve for [tex]\( d \)[/tex]:

[tex]\[ 1.7 \cdot d = 30 \][/tex]

[tex]\[ d = \frac{30}{1.7} \][/tex]

After performing the division:

[tex]\[ d \approx 17.647058823529413 \][/tex]

When rounded to the nearest inch:

[tex]\[ d \approx 18 \][/tex]

Thus, the snowplow will be unable to move when the snow is approximately 18 inches deep.

### Conclusion

So, the correct choice to complete the statement is:

OB. The independent variable is the depth of snow ([tex]\( d \)[/tex]), in inches, and the dependent variable is speed ([tex]\( s \)[/tex]), in miles per hour. The linear function that models this situation is:

[tex]\[ \boxed{s = 30 - 1.7 \cdot d} \][/tex]

The snowplow will be unable to move when the snow is [tex]\( \boxed{18} \)[/tex] inch(es) deep.

### Reasonableness of the Linear Model

As for the reasonableness of using a linear model for this situation:

OD. The linear model is reasonable because the plowing rate is always constant for any snowplow. Given the constraints described, it is logical to assume that the reduction in speed per inch of snow is consistent up to the point where the snow depth is too much for the plow to handle.

Therefore, the most reasonable answer for the linear model is:

[tex]\[ \boxed{\text{OD}} \][/tex]
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