Answer:
Step-by-step explanation:
ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.
Similar triangles so we can do .
Solve for it we get 44y = 6x
Differentiate relative to time t, we get 44y' = 6x'.
change in x (x') is equal to 5. And we get the answer y' = .
the ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.
is the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.
<em><u>Solution:</u></em>
The linear equation in slope intercept form is given as:
T = cx + k ------ (i)
Where "t" is the temperature at an elevation x
And x is in thousands of feet
<em><u>Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain</u></em>
Given, when c = 6 thousand ft and fahrenheit
This implies,
From (i)
76 = c(6) + k
76 = 6c + k
⇒ k = 76 - 6c ----- (ii)
<em><u>Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain</u></em>
Given, when c = 12 thousand ft and fahrenheit
This implies,
From (i)
49 = c(12) + k
49 = 12c + k
Substitute (ii) in above equation
49 = 12c + (76 - 6c)
49 = 12c + 76 - 6c
49 - 76 = 6c
6c = -27
Substituting the value of c in (ii) we get
Substituting the value of c and k in (i)
Where "x" is in thousands of feet
Thus the required linear equation is found