Rewrite the following polynomial in standard form -x2 + 1 + 2x
1 answer:
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Answer:
The equation for the curve is:
Step-by-step explanation:
We know that for a curve defined as:
y = f(x)
The slope of the curve at the point x is:
y = f'(x)
where f'(x) = df(x)/dx
Here we know that we have a function that passes through the point (0, 7)
We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))
Then we have two equations:
f(0) = 7
f'(x) = 2*f(x)
From the shape of the equation, we can assume than this is an exponential equation like:
Replacing that in the second equation, we get:
From that equation, we can conclude that k = 2
Then:
Now we can use the first equation:
f(0) = 7
With this, we can find the value of A.
Then we can conclude that the equation for the curve is:
Answer:
Largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.
Step-by-step explanation:
Design of a mural is 16 in. wide and 9 in. high.
Dimensions of the wall are 24 ft by 14 ft.
If we enlarge the size of the design along the width the wall, scale factor to be used,
Scale factor =
=
=
With the same scale factor, height of the design will be,
Width of the wall used =
= 13.5 ft
Therefore, largest possible mural that can be painted on the wall is 24 feet wide and 13.5 feet high.