Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is 9.05%. She kno
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Answer:
The derivative of the function does not exist.
Step-by-step explanation:
The alternative form of a derivative is given by:
Our function is defined as:
h(x)=|x+8|
i.e. h(x)= -(x+8) when x+8<0
and x+8 when x+8≥0
i.e. h(x)= -x-8 when x<-8
and x+8 when x≥-8
Hence now we find the derivative of the function at c=-8
i.e. we need to find the Left hand derivative (L.H.D.) and Right hand derivative (R.H.D) of the function.
The L.H.D at a point 'a' is calculated as:
Similarly R.H.D is given by:
Now for L.H.D we have to use the function h(x) =-x-8
and for R.H.D. we have to use the function h(x)=x+8
L.H.D.
we have a=-8
=
similarly for R.H.D.
Now as L.H.D≠R.H.D.
Hence, the function is not differentiable.
The area of the window is
The shape of the Norman window is described as a rectangle surmounted by a semicircle.
Let 'x' be the width of the window.
Then this width corresponds to the diameter of the semicircle.
That is, radius of the semicircle = x/2
Now given the perimeter of the whole window = 25 ft
This perimeter is equal to the sum of 3 sides of the rectangle and the perimeter of the semicircle.
Perimeter of the semicircle = , where r is the radius of the semicircle.
Now let 'y' be the length of the window.
Then sum of three sides of the window = 2y + x
So 2y + x + = 25
Therefore,
Area of the window = Area of the semicircle + Area of the rectangle =
So Area of the window =
Learn more about area of circle and rectangle at brainly.com/question/4694841
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