Find rates of change until you find a constant.
dy/dx=1,2,3,4,5,6
d2y/dx2=1,1,1,1,1
So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
a(n)=(x^2-x+2)/2
Answer:
A. 4/24
Step-by-step explanation:
If you convert to a common fraction which is 24. Then you get 16/24 - 12/24= 4/24. And if you simplify you can get 1/6. Have a great day, let me know if correct, and hope this helps!
Answer:
<u><em>C. </em></u>
<u><em> cm</em></u>
Step-by-step explanation:
<u><em>First, we can start out by stating that this is a </em></u><u><em>right triangle</em></u><u><em>, since </em></u><u><em>it has a right angle</em></u><u><em>, shown by the marker square in the corner of the triangle. </em></u><u><em>The x part, is called the hypotenuse</em></u><u><em>. When finding the value of the hypotenuse, we use a thing called the </em></u><u><em>Pythagorean Theorem.</em></u><u><em> This theorem is :</em></u>
<u><em>a^2 + b^2 = c^2</em></u>
<u><em>a is one side length, and b is the other. c is the hypotenuse.</em></u><u><em> To find x, the hypotenuse, we simply </em></u><u><em>plug in the values, and solve.</em></u>
<u><em>8^2 + 5^2 = c^2</em></u>
<u><em>64 + 25 = c^2</em></u>
<u><em>89 = c^2</em></u>
<u><em>To get c alone, we do the </em></u><u><em>square root of 89.</em></u>
<u><em></em></u><u><em> = c</em></u>
<u><em>9.43398113 = c</em></u>
<u><em>So, the answer is </em></u><u><em>C. </em></u><u><em> cm</em></u>
Answer:
The roots are 2, 5 and 6.
Step-by-step explanation:
As the last term is 60 we could see if one root is 2:
2^3 - 13(2)^2 + 52*2 - 60
= 8 - 52 + 104 - 60
= 112 - 112 = 0
So x = 2 is one root and x - 2 is a factor.
Long multiplication:
x - 2 (x^3 - 13x^2 + 52x - 60 ( x^2 - 11x + 30 <--- Quotient
x^3 - 2x^2
- 11 x^2 + 52x
- 11x^2 + 22x
30x - 60
30x - 60
So x^2 - 11x + 30 = 0
(x - 6)(x - 5) = 0
x = 6, 5.
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