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4 years ago

I dont understand this question.

Mathematics

2 answers:

WITCHER [35]4 years ago

6 0

combine liked terms the 7 and 2 y3. and then arrange them in exponential order

grigory [225]4 years ago

3 0

Add them all together and you should get the answer

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Someone please help me

Aleonysh [2.5K]

Step-by-step explanation:

Part A: $u^6$ can be written as the square of u³, or $(u^3)^2$ . Similarly, $v^6=(v^3)^2$ . Hence, we can write this as a difference of two squares by writing it as

$(u^3)^2-(v^3)^2$

Part B:

<h3>Difference of Two Squares</h3>

<u>We can first factor a difference of two squares a² - b² into </u><u>(a+b)(a-b)</u>. Here, <em>a</em> would be u³ and <em>b</em> would be v³.

$(u^3+v^3)(u^3-v^3)$

<h3>Sum and Difference of Two Cubes</h3>

We can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:

$a^3+b^3=(a+b)(a^2-ab+b^2)\\a^3-b^3=(a-b)(a^2+ab+b^2)$

Since u³ + v³ is a sum of two cubes, let's rewrite it.

$u^3+v^3=(u+v)(u^2-uv+v^2)$

Since u³ - v³ is a difference of two cubes, we can rewrite it as well.

$u^3-v^3=(u-v)(u^2+uv+v^2)$

Now, let's multiply them together again to get the final factored form.

$u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)$

Part C:

If we want to factor $x^6-1$ completely, we can just see that x to the sixth power is just $x^6$ and 1 to the sixth power is just 1. Hence, x can substitute for <em>u </em>and 1 can substitute for v.

$x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)$

We can repeat this for $x^6-64$ , as 64 is just 2 to the sixth power.

$x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)$

7 0

2 years ago

Hi can anyone help me with this question please. <br> It is the combination fraction lesson.

lyudmila [28]

Answer:

it's so easy.................

8 0

3 years ago

Read 2 more answers

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate th

katen-ka-za [31]

Answer:

Part (A): The correct option is true.

Part (B): The null and alternative hypothesis should be:

$H_o: \mu =0 ; H_a:\mu \neq0$

Step-by-step explanation:

Consider the provided information.

Part (A)

A random sample of 100 students from a large university.

Increasing the sample size decreases the confidence intervals, as it increases the standard error.

If the researcher increase the sample size to 150 which is greater than 100 that will decrease the confidence intervals or the researcher could produce a narrower confidence interval.

Hence, the correct option is true.

Part (B)

The researcher wants to identify that whether there is any significant difference between the measurement of the blood pressure.

Therefore, the null and alternative hypothesis should be:

$H_o: \mu =0 ; H_a:\mu \neq0$

7 0

3 years ago

Solve the following system of equations.

sasho [114]

X is minus 2
y is equal to 1

4 0

4 years ago

A statistician chooses 27 randomly selected dates, and when examining the occupancy records of a particular motel for those date

Anni [7]

Answer:

Confidence interval variance [21.297 ; 64.493]

Confidence interval standard deviation;

4.615, 8.031

Step-by-step explanation:

Given :

Variance, s² = 34.34

Standard deviation, s = 5.86

Sample size, n = 27

Degree of freedom, df = 27 - 1 = 26

Using the relation for the confidence interval :

[s²(n - 1) / X²α/2, n-1] ; [s²(n - 1) / X²1-α/2, n-1]

From the chi distribition table :

X²α/2, n-1 = 41.923 ; X²1-α/2, n-1 = 13.844

Hence,

[34.34*26 / 41.923] ; [34.34*26 / 13.844]

[21.297 ; 64.493]

The 95% confidence interval for the population variance is :

21.297 < σ² < 64.493

Standard deviation is the square root of variance, hence,

The 95% confidence interval for the population standard deviation is :

4.615 < σ < 8.031

3 0

3 years ago

I dont understand this question.​

I dont understand this question.