<h3>Answer: approximately 63.43 degrees</h3>
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Work Shown:
Locate the intersection points
f(x) = g(x)
x^2 + 2x + 1 = 1
x^2 + 2x = 1-1
x^2 + 2x = 0
x(x+2) = 0
x = 0 or x+2 = 0
x = 0 or x = -2
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Compute the derivative
f(x) = x^2 + 2x + 1
f ' (x) = 2x + 2
Then plug in each solution x value we found earlier
f ' (0) = 2(0) + 2 = 2
The slope of the tangent line at the intersection point (0,1) is m = 2
The tangent line is y = 2x+1
The angle between the lines y = 1 and y = 2x+1 is arctan(2) = 63.43 degrees approximately
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Plug x = -2 into the derivative function
f ' (x) = 2x+2
f ' (-2) = 2(-2)+2
f ' (-2) = -2
The slope of the tangent line at (-2,1) is m = -2
The tangent line here is y = -2x-3
The angle between the lines y = 1 and y = -2x-3 is also 63.43 through similar reasoning as before.
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See the diagram below.
Answer:
- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.
- The scientist can substitute these measurements into
and solve for the distance between the Earth and the Sun.
Step-by-step explanation:
Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.
Then:
The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.
The scientist can substitute these measurements into
, and solve for the distance "d".
Knowing that:
![\alpha=x\°\\adjacent=d\\hypotenuse=y](https://tex.z-dn.net/?f=%5Calpha%3Dx%5C%C2%B0%5C%5Cadjacent%3Dd%5C%5Chypotenuse%3Dy)
Then:
![cos(x\°)=\frac{d}{y}](https://tex.z-dn.net/?f=cos%28x%5C%C2%B0%29%3D%5Cfrac%7Bd%7D%7By%7D)
And solving for "d":
![ycos(x\°)=d](https://tex.z-dn.net/?f=ycos%28x%5C%C2%B0%29%3Dd)
As we know that the area of a rectangle is -
length × Breadth
So, here length = (3n+1)
Breadth = (2n-5)
Area of rectangle
= (3n+1)(2n-5)
= 3n(2n-5)+1(2n-5)
= 6n² - 15n + 2n - 5
= 6n² - 13n - 5
Answer) Area of rectangle is 6n² - 13n - 5
Come, sphere, and I’m not sure what else