APPLICATIONS
4. A steady snowfall is coming down outside. Prestel decides to measure the depth of the snow on the ground.
After 4 hours, the snow is at a depth of 9 inches an after 8 hours it is at a depth of 14 inches
(a) Express the information given in this problem (b) Find the slope of the line that passes through
as two coordinate pairs, (h, d), where h is the these two points. What are its units?
number of hours and d is the depth of snow.
(c) Find the equation of the line that pass
through the two points in d = mh + b form.
What was the depth when the snowfall began
(h=0)? What would the depth be after 12
hours?

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{14 - 9}{8 - 4}\\\\& = & \dfrac{5}{4}\\\\& = & \mathbf{1.25}\end{array}[/tex]

The slope of the line is 1.25 in/h

(c) Equation of the line

[tex]\begin{array}{rcl}d & = & mh + b\\9 & = & \dfrac{5}{4} \times 4 + b\\\\9& = & 5 + b\\b & = & \mathbf{4}\\\end{array}[/tex]

The y intercept is at (0,4)

d = 1.25h + 4

(d) Depth when snowfall began

[tex]\begin{array}{rcl}d &= &\text{0 h } \times \dfrac{\text{1.25 in}}{\text{1 h}} \text{+ 4 in}\\\\&= &\text{0 in+ 4 in}\\& = & \textbf{4 in}\\\end{array}[/tex]

The depth was 4 in when the snowfall began.

(e) Depth after 12 h

[tex]\begin{array}{rcl}d &= &\text{12 h } \times \dfrac{\text{1.25 in}}{\text{1h}} \text{+ 4 in}\\\\&= &\text{15 in+ 4 in}\\& = & \textbf{19 in}\\\end{array}[/tex]

The depth would be 19 in after 12 h.

The figure below is a graph of your function. It shows that the depth was 4 in at the start of the snowfall, that it increases by 5 in every 4 h, and predicts a depth of 19 in after 12 h.

eudora eudora · Answer 2 · 2021-12-06T17:15:05+01:00

Slope of the line passing through (4, 9) and (8, 14) will be [tex]\frac{5}{4}[/tex].

Equation of the line → [tex]d=\frac{5}{4}h+4[/tex]

Depths of the snow after 0 and 12 hours will be 4 inches and 19 inches respectively.

(a) It's given in the question,

Depth of snow was 9 inches after 4 hours.
Depth of snow was 14 inches after 8 hours.

If we plot 'Time' on x-axis and 'Depth of snow' on y-axis of the graph, (4, 9) and (8, 14) will be two points lying on the straight line.

(b) Slope of the line passing through these points (4, 9) and (8, 14) will be,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]=\frac{14-9}{8-4}[/tex]

[tex]=\frac{5}{4}[/tex]

Slope of the line will define the increase in depth of the snow with unit change in time.

Its unit will be inches per hours.

(c). Equation of the line will be,

d = mh + b

Here, m = slope of the line

By substituting the value of 'm' in the equation,

[tex]d=\frac{4}{5}h+b[/tex]

If the point (4, 9) lies on the line,

[tex]9=\frac{5}{4}(4)+b[/tex]

[tex]b=9-5[/tex]

[tex]b=4[/tex]

Therefore, equation of the line will be,

[tex]d=\frac{5}{4}h+4[/tex]

For h = 0,

[tex]d=\frac{5}{4}(0)+4[/tex]

[tex]d=4[/tex] inches

For h = 12 hours,

[tex]d=\frac{5}{4}(12)+4[/tex]

[tex]d=19[/tex] inches

Therefore, slope of the line will be [tex]\frac{5}{4}[/tex], equation of the line will be [tex]d=\frac{5}{4}h+4[/tex] and depths of the snow at h = 0 and h = 12 will be 4 inches and 19 inches respectively.

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https://brainly.com/question/13027828