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3 years ago

Which of the following expressions is equivalent to the one shown below (3/2)^8

Mathematics

1 answer:

vichka [17]3 years ago

8 0

Option B is the right answer

Step-by-step explanation:

Given expression is:

$(\frac{3}{2})^8$

The exponent properties are used to solve these type of questions,

One of the property states that if an exponent is applied to a fraction, it can be applied to the numerator and denominator separately.

so,

for the given expression, the exponent 8 will be applied to 2 and 3 separately

$(\frac{3}{2})^8 = \frac{3^8}{2^8}$

Hence,

Option B is the right answer

Keywords: Exponents, fractions

Learn more about exponents at:

#LearnwithBrainly

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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

Last year a large trucking company delivered 5.5 x 10^5 tons of goods with an average value of $23,000 per ton. What was the tot

evablogger [386]

5.5*10^5 = 550,000 tons

$23,000 per ton

23,000 x 550,000 = $12,650,000,000 (total value)

Now to convert to scientific notation.

1.265 x 10^10

Hope that was useful :)

8 0

3 years ago

In a week karry ran 9.3 miles and Tricia ran 4.4 miles.Use mental math to find how much farther Karry ran than Tricia.Explain ho

sineoko [7]

Karry ran 4.9 miles more than Tricia. I determined the difference but subtracting the miles to see how many more karry ran.

6 0

3 years ago

Read 2 more answers

Simplify the following expression. show your work. (-y + 5.3) + (7.2y - 9)

Kitty [74]

Answer:

6.2y - 3.7

Step-by-step explanation:

−y+5.3+7.2y−9

Subtract 9 from 5.3 to get −3.7.

−y−3.7+7.2y

Combine −y and 7.2y to get 6.2y.

6.2y−3.7

6 0

2 years ago

What is the explicit rule for the sequence? 10.5, 9, 7.5, 6, 4.5, 3, ...

makvit [3.9K]

Answer: the rule is to add 1.5

3 + 1.5 = 4.5
4.5 + 1.5 = 6
6 + 1.5 = 7.5
etc...

6 0

3 years ago