Equation 1 = 8
equation 2 = 8
equation 3 = 8
equation 4 = 6
so it’s 4 :)
Answer:
3750 strings.
Step-by-step explanation:
First we have 6 different letters to choose from (a, b, c, d, e, f) and we will make a string of length 5.
First, we would have to choose one of the letters, to do this we would have 6 choices.
For our second choice, we can only choose from 5 letters since we cannot choose the one that we already chose (no two consecutive letters can be the same).
Then, for our third choice, we would have to choose from 5 different letters (any letter but the one before).
Similarly for our fourth and fifth choice, we can choose 5 different letters.
Then, the total amount of strings would be:
6 x 5 x 5 x 5 x 5 = 6 x 5⁴ = 3750 strings.
Answer:
a)
b) (a,b) (c, d) As long as (a,b) and (c,d) are the endpoints of of the diameter.
Step-by-step explanation:
a)
1) The reduced formula of the Circumference is given by:
![(x-a)^{2}}+(y-b)^{2}=r^{2}](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%7D%2B%28y-b%29%5E%7B2%7D%3Dr%5E%7B2%7D)
2) Let's expand the factored one into one closer to the pattern above:
![x^{2}-8x+12+y^{2}+6y-55=0\Rightarrow x^{2}-8x+y^{2}+6y=43](https://tex.z-dn.net/?f=x%5E%7B2%7D-8x%2B12%2By%5E%7B2%7D%2B6y-55%3D0%5CRightarrow%20x%5E%7B2%7D-8x%2By%5E%7B2%7D%2B6y%3D43)
3) Completing the square for both trinomials:
![(x-4)^{2}+(y+3)^{2}=43+16+9\Rightarrow (x-4)^{2}+(y+3)^{2}=68](https://tex.z-dn.net/?f=%28x-4%29%5E%7B2%7D%2B%28y%2B3%29%5E%7B2%7D%3D43%2B16%2B9%5CRightarrow%20%28x-4%29%5E%7B2%7D%2B%28y%2B3%29%5E%7B2%7D%3D68)
4) In the Reduced Formula,
,
![C(a,b) \Rightarrow C(4,-3) \:the\:radius\:is\:r=\sqrt{68} \Rightarrow r=2\sqrt{17}](https://tex.z-dn.net/?f=C%28a%2Cb%29%20%5CRightarrow%20C%284%2C-3%29%20%5C%3Athe%5C%3Aradius%5C%3Ais%5C%3Ar%3D%5Csqrt%7B68%7D%20%5CRightarrow%20r%3D2%5Csqrt%7B17%7D)
b) Using the previous example to show this:
When we factor this way
![(x-a)(x -c) + (y -b)(y-d) = 0](https://tex.z-dn.net/?f=%28x-a%29%28x%20-c%29%20%2B%20%28y%20-b%29%28y-d%29%20%3D%200)
We are indeed, naming "a" and "b", the coordinates of (a, b) of the first endpoint and "b" and "d" the second endpoint as well.Id est, D (2, 5) and B (6,-11).
The radius, is ![\sqrt{68} \cong 8.25](https://tex.z-dn.net/?f=%5Csqrt%7B68%7D%20%5Ccong%208.25)
So yes, the equation of the circle can be written as
![(x-a)(x -c) + (y -b)(y-d) = 0](https://tex.z-dn.net/?f=%28x-a%29%28x%20-c%29%20%2B%20%28y%20-b%29%28y-d%29%20%3D%200)
As long as (a,b) and (c,d) are the endpoints of of the diameter.
![d_{AC}=d_{BC}=R](https://tex.z-dn.net/?f=d_%7BAC%7D%3Dd_%7BBC%7D%3DR)
Answer:
62 - 2v v represents vidya
Answer:
A fixed interest rate will always be the same rate of interest throughout a period of time no matter the amount of borrowed money. A variable interest rate can change over time based on the amount of money borrowed.