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3 years ago

I need help please....

Mathematics

2 answers:

Alex Ar [27]3 years ago

8 0

Answer:

3/10

Step-by-step explanation:

Zina [86]3 years ago

5 0

Answer:

1/10

Step-by-step explanation:

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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:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
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

If f(x) = -3x+1 then f^-1(x) =

elena55 [62]

Answer:

please mark me brainliesf if it helps you

f(x) = -3x+1

or, y = -3x + 1

Interchanging the position of x and y, we get,

x = -3y +1

or, 3y = 1 - x

or, y = 1 - x /3

: . f^-1(x) = 1-x / 3

8 0

2 years ago

5.) -6x – 29 = 5x – 7

Umnica [9.8K]

Answer: x= -2

Step-by-step explanation: first step is to add 7 to both sides. You’re left with -6x-22=5x. After this you’re going to add 6 to both sides. You get -22=11x. Now you divide both sides by 11 to get X by itself. You’re left with -2.

6 0

3 years ago

Read 2 more answers

if the radius of one of the semi-circles is 7 meters what is the circumference of one of the semi-circles

Yanka [14]

Answer: 43.96 m

Step-by-step explanation:

the circumference of one of the semi circle radius of one of the semicircles is 7 meters is 7 meters

ur welcome

3 0

3 years ago

How do you find the angle of a slope

oksian1 [2.3K]

Answer:

Rise over Run, the slope in this graph would be 3/4

Step-by-step explanation:

You count the number of spaces it takes to move up, then you move right, towards the line. You write the rise number on top and the number moving right (run) on the bottom, (rise over run).

I hope this helps you, if not let me know in the comments :)

7 0

3 years ago