Given f(x)=x2, g(x)=x+6, h(x)=7 find f{g[h(x)]}.
1 answer:
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Answer:
a)
b)
c) They'd have lost $1000 if they had sold no calendars.
Step-by-step explanation:
a) The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
In this case we know that "y" represents the profit of loss and "x" the number of calendars sold.
Then, according to the exercise, the line passes through these two points:
and
Then, we can find the slope of the line with the formula
Now, we can substitute the slope and one of those points into and solve for "b":
Then, subtituting values, we get that the equation that describes the relation between the profit of loss and the number of calendars sold, is:
b) The slope of the line is the profit they made from selling each calendar
c) The y-intercept is the amount they would have lost if they had sold no calendars:
They'd have lost $1000 if they had sold no calendars.
Answer:
y = 8 is the equation of tangent.
Step-by-step explanation:
The equation of the tangent to the circle at (-6,8) is of the form:
y = mx + c
where m is the slope of the tangent and c is the y-intercept.
The point (-6,8) lies on the circle and the tangent line as well.
Hence (-6,8) satisfies the line equation:
8 = m(-6) + c ⇒ c-6m = 8 -------------1
We know that slope of two perpendicular lines are related as:
At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.
Hence :
We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.
= ∞
Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0
Hence m=0
Putting m=0 in equation 1 we get:
c = 8
The equation of tangent line at (-6,8) is:
y = 8