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choli [55]
3 years ago
8

What is the end behavior of the polynomial function graphed below?

Mathematics
1 answer:
Afina-wow [57]3 years ago
5 0

Answer:


Step-by-step explanation:

The answer is C

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Find the general term of sequence defined by these conditions.
disa [49]

Answer:

\displaystyle  a_{n}  =     (2)^{2n -1}   -   (3) ^{n-1 }

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0  \:  \: where :  \:  \:a_1 = 1 \: ,a_2 = 5,

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

  • {x}^{n}  =  c_{1} {x}^{n - 1}  + c_{2} {x}^{n - 2}  + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}

the steps for solving a linear homogeneous recurrence relation are as follows:

  1. Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
  2. Solve the polynomial by factoring or the quadratic formula.
  3. Determine the form for each solution: distinct roots, repeated roots, or complex roots.
  4. Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

{x}^{2}  - 7x+ 12= 0

Step-2:Solve the polynomial by factoring

factor the quadratic:

( {x}^{}  - 4)(x - 3) =  0

solve for x:

x =  \rm 4 \:and \: 3

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

\displaystyle a_{n}  = c_{1}  {x} _{1} ^{n }  + c_{2}  {x} _{2} ^{n }

so substitute the roots we got:

\displaystyle a_{n}  = c_{1}  (4)^{n }  + c_{2}  (3) ^{n }

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

\begin{cases}\displaystyle 4c_{1}    +3 c_{2}    = 1  \\ 16c_{1}    + 9c_{2}     =  5\end{cases}

solve the system of equation which yields:

\displaystyle c_{1}  =  \frac{1}{2}     \\  c_{2}   =   - \frac{1}{3}

finally substitute:

\displaystyle  a_{n}  =  \frac{1}{2}   (4)^{n }   -  \frac{1}{3}  (3) ^{n }

\displaystyle \boxed{ a_{n}  =    (2)^{2n-1 }   -   (3) ^{n -1}}

and we're done!

7 0
3 years ago
A group of 30 bikers went on a trip. some rode bicycles and the others rode tandems. if the total number of bicycles and tandems
Marina CMI [18]
10 Tandems or 63 Tandems
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2 years ago
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Hey if I could get some help it would be great
noname [10]

Answer:

One solution

Step-by-step explanation:

7 0
3 years ago
Which expression makes the equation true?
valina [46]
Equation is y^20 = (   )^2

Answer: 

y to the power of 10. 
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3 years ago
Hi.i need help with this.i will apreciate the answer:)))
Anvisha [2.4K]
Here is how to work 2, 3 , and 4.

7 0
3 years ago
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