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balu736 [363]
3 years ago
13

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(

t), in feet, at different times, t, in seconds:
f(t) = −16t^2 + 32t + 384

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is _____ feet per second.
Mathematics
1 answer:
ehidna [41]3 years ago
7 0
Seven seconds is the answer any more
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The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.
pantera1 [17]

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:

m_{1}\times m_{2}=-1

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

m_{normal} \times m_{tangent}=-1

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.

m=\frac{y_2-y_1}{x_2-x_1}

         =\frac{8-4}{-6+6}

          = ∞

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

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