Write the slope-intercept form of the equation of the line described.
2 answers:
Answer:
Step-by-step explanation:
<u>Slope-intercept form:</u>
y= mx +c, where m is the gradient and c is the y-intercept.
The product of the gradients of perpendicular lines is -1.
-4m= -1
m= -1 ÷(-4)
m= ¼
Substitute m= ¼ into the equation:
y= ¼x +c
To find the value of c, substitute a pair of coordinates.
y= ¼x +c
When x= -4, y= -4,
-4= ¼( -4) +c
-4= -1 +c
c= -4 +1
c= -3
Thus, the equation of the line is y= ¼x -3.
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Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
