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3 years ago

What does this mean???

Mathematics

1 answer:

LenKa [72]3 years ago

3 0

Answer:

A lot of things to be honest!

Step-by-step explanation:

I don't know what you are being asked to do but these are some possibilities...

You could graph it. I have the graph linked below.

You could Convert it to Interval Notation

[ 0, $\frac{1}{e}$ ]

You could Evaluate it.

log (8 )

log 2 ( 16 )

√ 2

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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

Chin canned a number of quart jars and a number of pint jars of tamoatoes from his garden a pint is 16 ounces and a quart us 32

natulia [17]

The total volume of the canned tomato sauce is equal to the sum of those canned in quart jars (32 ounces) and the number of pint jars (16 ounces). If we let p and q be the number of pints and quarts canned, the equation that would best represent the given is,
32q + 16p = 1280
Simplifying the equation by dividing by 16 will give us the final answer of,
2q + p = 80

7 0

3 years ago

Read 2 more answers

Charlene bought a used.It cost $43.00.A new skateboard costs 3 times as much as the used one Charlene bought.How much does a new

vovangra [49]

Multiply it by 3.
43.00*3=129=priceNewSkateboard

6 0

2 years ago

Tatesville had x inches of rainfall in April, (x + 1.3) inches of rainfall in May, and (2x + 0.5) inches in June. If x=2 inches,

inna [77]

Answer: 9.8 inches

Step-by-step explanation: