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4 years ago

Express 6^1/3 in simplest radical form.

Mathematics

1 answer:

seropon [69]4 years ago

6 0

<em>Greetings from Brasil</em>

From radiciation properties:

$\large{A^{\frac{P}{Q}}=\sqrt[Q]{A^P}}$

bringing to our problem

$\large{6^{\frac{1}{3}}=\sqrt[3]{6^1}}$

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We know that logarithmic functions are a bit more unusual than functions we’ve seen in the past, such as linear, exponential, qu

AnnyKZ [126]

Answer:

Step-by-step explanation:

can you re-phrase that please then i can answer

7 0

3 years ago

Assume that there are 365 days in a year, the probability that a person is born on any given day is the same for all days, and e

Artemon [7]

Answer:

Step-by-step explanation:

If each day equal chance then p = Prob that a person is borne on a particular day = 1/365

Each person is independent of the other and there are two outcomes either borne in July or not

p = prob for one person not borne in July = (365-31)/365 = 334/365

a)Hence prob that no one from n people borne in July = $(\frac{334}{365} )^n$

b) p = prob of any one borne in July or Aug = $\frac{(31+31) }{365} =\frac{62}{365}$ =0.1698

X- no of people borne in July or Aug

n =15

P(X>=2) = $15C2 (0.1698)^2*(1-0.1698)^{13} +15C3 (0.1698)^3*(1-0.1698)^{12} +...+15C15 (0.1698)^{15}$

=0.7505

3 0

3 years ago

In the last three years frederico's basketball team won 40 more games than they lost if they won 150 games what was their ratio

Westkost [7]

150 games won: 110 games lost

Ratios
150:110
150/110
150 to 110

3 0

3 years ago

What is 5x^2-7x-3=8 by solving using a graph???

Alinara [238K]

Hello!

Simplifying
5x2 + -7x + -3 = 8

Reorder the terms:
-3 + -7x + 5x2 = 8

Solving
-3 + -7x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8

Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0

Begin completing the square. Divide all terms by
5 the coefficient of the squared term:

Divide each side by '5'.
-2.2 + -1.4x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2

The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49

Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69

Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
x + -0.7 = 1.640121947

Simplifying
x + -0.7 = 1.640121947

Reorder the terms:
-0.7 + x = 1.640121947

Solving
-0.7 + x = 1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7

Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947

Simplifying
x = 2.340121947

Subproblem 2
x + -0.7 = -1.640121947

Simplifying
x + -0.7 = -1.640121947

Reorder the terms:
-0.7 + x = -1.640121947

Solving
-0.7 + x = -1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7

Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947

Simplifying
x = -0.940121947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}

3 0

3 years ago

A geometric sequence has first term 1/9 and common ratio 3. Which is the first term of the sequence which exceeds 1000?

Svetach [21]

$a_{n}= \frac{1}{9} (3)^{n-1}$
(We know this from a=1/9 and r=3)
Simplifying this, we get:
$\frac{1}{9} (3)^{-1} (3)^n$

Since we're finding the first term that exceeds 1000, let's set it equal to 1000.

$\frac{1}{27}(3)^n=1000$
Multiplying both sides by 27
$3^n=27000$

$log_{3}27000=n$

n≈9.2

We have to round n up, since if n=9, the value would be <1000.
Therefore n=10. Substituting n=10,
$\frac{1}{27}3^{10}$
=2187

Therefore the first term that exceeds 1000 is 2187, and it is the 10th term

3 0

3 years ago