Question

1. the slope of a hill is an average of 0.64. how many metres will it rise for a horizontal distance of 32 metres?
2. hazuki needs to calculate the slope of the water - table—the elevation at which water is found under the ground. one well has water at 752 m elevation and the another has it at 895 m elevation. if the wells are 1.2 km apart, what is the slope of the water table?
3. calculate the slope of the roof and of the diagonal trusses.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{\text{rise}}{\text{run}}$, where $m$ is the slope, $\text{rise}$ is the vertical change and $\text{run}$ is the horizontal change.

Step2: Solve for rise in question 6

Given $m = 0.64$ and $\text{run}=32$m. Rearranging the slope formula for $\text{rise}$, we get $\text{rise}=m\times\text{run}$. So, $\text{rise}=0.64\times32 = 20.48$m.

Step3: Prepare data for question 7

First, convert the distance between wells to meters. Since $1.2$km = $1200$m. The vertical change (rise) is $\Delta y=895 - 752=143$m and the horizontal change (run) is $\Delta x = 1200$m.

Step4: Calculate slope in question 7

Using the slope formula $m=\frac{\text{rise}}{\text{run}}$, we substitute $\text{rise}=143$m and $\text{run}=1200$m. So, $m=\frac{143}{1200}\approx0.119$.

Step5: Calculate slope for roof in question 8

For the roof, the total rise is $3.2$m and the total run is $\frac{16}{2}=8$m. Using the slope formula $m=\frac{\text{rise}}{\text{run}}$, we have $m=\frac{3.2}{8}=0.4$.

Step6: Calculate slope for diagonal trusses in question 8

For the diagonal trusses, the rise is $1.6$m and the run is $4$m. Using the slope formula $m = \frac{\text{rise}}{\text{run}}$, we get $m=\frac{1.6}{4}=0.4$.

Answer:

1. 20.48 m
2. $\frac{143}{1200}\approx0.119$
3. Slope of roof: 0.4; Slope of diagonal trusses: 0.4