Answer:
.
Step-by-step explanation:
The equation of a circle of radius centered at is:
.
.
Differentiate implicitly with respect to to find the slope of tangents to this circle.
.
Apply the power rule and the chain rule. Treat as a function of , .
.
.
That is:
.
Solve this equation for :
.
The slope of the tangent to this circle at point will thus equal
.
Apply the slope-point of a line in a cartesian plane:
, where
- is the gradient of this line, and
- are the coordinates of a point on that line.
For the tangent line in this question:
- ,
- .
The equation of this tangent line will thus be:
.
That simplifies to
.
<h3>
Answer: B. 62 degrees fahrenheit</h3>
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Explanation:
x = elevation in feet
y = temperature in fahrenheit
The temperature goes up 1/10 = 0.1 degrees for every 100-foot increase of elevation. So the slope is 0.1/100 = 0.001, which tells us how fast the temperature is increasing. In other words, the temperature goes up 0.001 degrees each time the elevation goes up by 1 foot.
The ground temperature is 60 degrees, which is our starting temperature. It's the value of y when x = 0. Therefore, 60 is the y intercept.
We have a slope of m = 0.001 and a y intercept of b = 60. The equation y = mx+b becomes y = 0.1x+60
Now plug in x = 2000 to find the temperature at this elevation
y = 0.001x+60
y = 0.001*2000+60
y = 2+60
y = 62