from a base elevation of 9800 feet a mountain peak in colorado rises to the summit elevation over a horizontal distance of 15,842 feet. find the grade of the peak

You need to provide the summit elevation.

what are the x and y intersepts of the equation 50x+ 20y= 20,000

To find the grade of the peak, we need to calculate the vertical rise of the mountain in relation to the horizontal distance traveled.

Grade is typically expressed as a percentage or a ratio. If the grade is given as a percentage, it represents the vertical rise relative to the horizontal distance, multiplied by 100. If the grade is given as a ratio, it represents the vertical rise relative to the horizontal distance.

In this case, we have the base elevation of 9800 feet and the horizontal distance of 15842 feet. We need to calculate the vertical rise.

The vertical rise can be found by subtracting the base elevation from the summit elevation:

Vertical rise = summit elevation - base elevation

However, since the summit elevation is not given directly, we can calculate it using the Pythagorean theorem, as we have a right triangle formed by the base elevation, summit elevation, and horizontal distance.

Using the Pythagorean theorem, we have:

(summit elevation)^2 = (base elevation)^2 + (horizontal distance)^2

Let's calculate the summit elevation using this formula:

(summit elevation)^2 = (9800 feet)^2 + (15842 feet)^2

(summit elevation)^2 = 96,040,000 feet^2 + 250,432,164 feet^2

(summit elevation)^2 = 346,472,164 feet^2

Taking the square root of both sides:

summit elevation = sqrt(346,472,164 feet^2)

summit elevation ≈ 18,614.03 feet

Now we can calculate the vertical rise:

Vertical rise = summit elevation - base elevation
Vertical rise ≈ 18,614.03 feet - 9800 feet
Vertical rise ≈ 8,814.03 feet

Finally, we can calculate the grade:

Grade = (Vertical rise / Horizontal distance) * 100

Grade = (8,814.03 feet / 15,842 feet) * 100

Grade ≈ 55.63%

Therefore, the grade of the peak is approximately 55.63%.