Find a parabola with equation y=ax^2+bx+c that has a slope 10 at x=1, slope -26 at x=-1, and passes through the point (2,29)
1 answer:
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Answer:
y = 9x^2 -8x +9
Step-by-step explanation:
The given equation has derivative ...
y' = 2ax +b
The requirements on slope give rise to two equations:
2a(1) +b = 10
2a(-1) +b = -26
Adding these equations together gives ...
2b = -16 ⇒ b = -8
Then we have ...
2a -8 = 10
a = (10 +8)/2 = 9
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The given point lets us find the constant term c.
y = 9x^2 -8x +c
c = y -(9x -8)x = 29 -(9(2) -8)(2) = 29 -20 = 9
The equation of the parabola is ...
y = 9x^2 -8x +9
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You would begin by choosing which trigonometric function to use.
In this case, you would use sine.
Sine is opposite over hypotenuse.
Opposite of the 35 degree angle is 18, and you want to find the hypotenuse which is x.
sin(35) =
(multiply x to both sides)
x sin(35) = 18 (divide sin(35) to both sides)
x = 31.38204...
So, therefore x = 31.38. I don't know what decimal point you're supposed to round to, so I'm gonna guess the hundredths place. :)
In this case, you would use sine.
Sine is opposite over hypotenuse.
Opposite of the 35 degree angle is 18, and you want to find the hypotenuse which is x.
sin(35) =
x sin(35) = 18 (divide sin(35) to both sides)
x = 31.38204...
So, therefore x = 31.38. I don't know what decimal point you're supposed to round to, so I'm gonna guess the hundredths place. :)
Answer:
Assuming you're referring to the sides of a right triangle, the missing side X would be 12.
Step-by-step explanation:
The Pythagorean Theorem states that the two legs of a right triangle squared and added together is equal to the hypotenuse squared. is 169,
is 25, 169 - 25 = 144. Take the square root of 144 and you'll get 12, which is the missing side of the right triangle.