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2 years ago

5

Select the correct answer. What is the value of x? log^2(x+ 7) = 2

1 answer:

Delvig [45]2 years ago

3 0

Answer: x=-3

Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.

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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

Aliens spotted! They have pulled up 97 chickens, 47 cows, and 77 humans. What is the probability, if they randomly select from a

emmainna [20.7K]

The answer would be 0.34. Theres 77 humans out of 221 beings, which means 77/221. Simplifying this fraction gives us 0.34.

4 0

3 years ago

What is the classifications of polynomials -gh4i+3g5

Step2247 [10]

Answer:

The polynomial -gh⁴i + 3g⁵ is a binomial, since it has two terms

Degree of polynomial: degree of a polynomial is the term with highest of exponent.

Degree of binomial -gh⁴i + 3g⁵ = 6

1st term(-gh⁴i ) = (power of g = 1, power of h = 4, power of i = 1)

2nd term(3g⁵) = (power of g = 5)

the polynomial -gh⁴i + 3g⁵ is a 6 degree binomial.

5 0

3 years ago

a fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively, by weight. what fract

musickatia [10]

2/10 or 1/5, which is 20%

6 0

3 years ago

Can someone help me out please

lbvjy [14]

16 is the answer jxhsjcjaks

5 0

2 years ago