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9966 [12]
3 years ago
11

How to solve a quadratic sequence

Mathematics
1 answer:
Luda [366]3 years ago
6 0
FIRST FIND THE THE FIRST AND SECOND DIFFERENCES ON THE GIVEN SEQUENCE OF NUMBERS.                                                                 FOR EXAMPLE IF YOU ARE GIVEN THIS SEQUENCE                                  2,4,6,8............AND YOU ARE ASKED TO FIND THE GENERAL FORMULA....  STEP 1:FIND THE FIRST DIFFERENCE  BY SUBTRACTING THE FIRST TERM FROM THE SECOND TERM,AND THE SECOND FROM THE THIRD AND SO ON.                                                                          STEP 2:FIND THE SECOND DIFFERENCE BY APPLYING STEP 1 TO THE ANSWERS OBTAINED.EG 4-2=2,6-4=2,8-6=2 THEREFORE THE SECOND DIFFERENCE WILL BE 2-2=0,2-2=0                                                                STEP 3:DIVIDE THE SECOND DIFFERENCE BY 2 TO GET THE VALUE OF (A).                                                                                                                STEP 4:WRITE 3a-b=the first term of the first term of the first difference which is the difference between 4 and 2.and solve for the value of b.3(0)-b=2 therefore b=-2                                                                                                    STEP 5:FIND THE VALUE OF c BY  term 1=a=b=c                                                                                                                                                               
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Remember that the equation of a circle is:
(x - h)^{2} + (y - k)^{2} =  r^{2}
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.

x^{2} - 6x +  y^{2} - 10y = 56

Complete the square. We must do this for x² - 6x and y² - 10y separately.

x² - 6x
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Square -3 to get 9. Add 9,
x² - 6x + 9

Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.

x^{2} - 6x + 9 + y^{2} - 10y = 65

Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.

y² - 10y
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Square -5 to get 25.
Add 25 on both sides.

(x - 3)^{2}+ y^{2} - 10y + 25= 90

Factor y² - 10y + 25 to get (y - 5)²

(x - 3)^{2}+ (y - 5)^{2} = 90

Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)

Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
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notsponge [240]

The question given is incomplete, I googled and got the complete question as below:

You are a waterman daily plying the waters of Chesapeake Bay for blue crabs (Callinectes sapidus), the best-tasting crustacean in the world. Crab populations and commercial catch rates are highly variable, but the fishery is under constant pressure from over-fishing, habitat destruction, and pollution. These days, you tend to pull crab pots containing an average of 2.4 crabs per pot. Given that you are economically challenged as most commercial fishermen are, and have an expensive boat to pay off, you’re always interested in projecting your income for the day. At the end of one day, you calculate that you’ll need 7 legal-sized crabs in your last pot in order to break even for the day. Use these data to address the following questions. Show your work.

a. What is the probability that your last pot will have the necessary 7 crabs?

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This is Poisson distribution with parameter λ=2.4

a)

The probability that your last pot will have the necessary 7 crabs is calculated below:

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b)

The probability that your last pot will be empty is calculated as:

P(X=0)=  {e-2.4*2.40/0!} = 0.0907

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Answer

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