A cube has a volume of 27 cubic inches. What is the length of each edge of the cube?

I believe the given limit is

[tex]\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)[/tex]

Let

[tex]a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1[/tex]

Now rewrite the expression as a difference of cubes:

[tex]a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}[/tex]

Then

[tex]a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2[/tex]

The limit is then equivalent to

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}[/tex]

From each remaining cube root expression, remove the cubic terms:

[tex]a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}[/tex]

[tex](ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}[/tex]

[tex]b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}[/tex]

Now that we see each term in the denominator has a factor of x ², we can eliminate it :

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}[/tex]

[tex]=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}[/tex]

As x goes to infinity, each of the 1/x ⁿ terms converge to 0, leaving us with the overall limit,

[tex]\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}[/tex]

Transformation involves changing the location of a shape

The image of P after the transformation is: (-5,-2)

The vertices are given as:

[tex]\mathbf{P = (-8,6)}[/tex]

[tex]\mathbf{Q = (1,-3)}[/tex]

[tex]\mathbf{R = (-6,-3)}[/tex]

The rule of reflection across line y = 2 is:

[tex]\mathbf{(x,y) \to (x,4-y)}[/tex]

So, the image of P, after the reflection is:

[tex]\mathbf{P' = (-8,4-6)}[/tex]

[tex]\mathbf{P' = (-8,-2)}[/tex]

The rule of translation 3 units right is:

[tex]\mathbf{(x,y) \to (x + 3,y)}[/tex]

So, we have:

[tex]\mathbf{P" = (-8 + 3,-2)}[/tex]

[tex]\mathbf{P" = (-5,-2)}[/tex]

Hence, the image of P after the transformation is: (-5,-2)

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4+​(−​7)  is​ 7 units from​ 4, in the​ negative direction​ (that is, to the left of 4)

4 + (-7) is 7 (seven) units from 4, in the negative Direction.

The result of 4 + (-7) is -3. It represents a movement of 7 units in the negative direction from the starting point of 4.

In this context, "units" refer to a number-line, where positive values are to the right and negative values are to the left. Starting at 4 and moving 7 units to the left brings you to -3.

This calculation and explanation describes the concept of adding a negative value, which is equivalent to subtracting a positive value, resulting in a displacement in the specified direction on the number line.

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The given question is incomplete, the complete question is

4 + (-7) is _____ units from 4, in the _____ Direction. What will the answer be?

Answer:

Step-by-step explanation:

Just make an example

Answer:

159.29-159.29(5/100)=151. 3255

Answer:

(258÷3) - 10 = 76.

Step-by-step explanation:

You need to use this equation to find this answer even though I already wrote the answer there for you.

Answer:

Pencil on y: 5.5 then 3 down and 1 to the right. (You can trace a line with 2 points, but can continue the pattern: 3 down, 1 to the right)

Step-by-step explanation:

y- intercept = 1 - (3/2)(-3)

y-intercept = 1 + 9/2 = 11/2 = 5.5

y = 3/2x + 11/2

Using the uniform distribution, we have that:

a) The graph is sketched at the end of this answer.

b) 0.33 = 33% probability of generating a number between 0.01 and 0.34.

c) 0.05 = 5% probability of generating a number greater than 0.95.

An uniform distribution has two bounds, a and b.  

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

In this problem, uniformly distributed between 0 and 1, thus [tex]a = 0, b = 1[/tex].

Item b:

[tex]P(0.01 \leq X \leq 0.34) = \frac{0.34 - 0.01}{1 - 0} = 0.33[/tex]

0.33 = 33% probability of generating a number between 0.01 and 0.34.

Item c:

[tex]P(X > 0.95) = \frac{1 - 0.95}{1 - 0} = 0.05[/tex]

0.05 = 5% probability of generating a number greater than 0.95.

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Answer:

so we're dealing with negative numbers here so after learning negative numbers you have to add negative15 to -182 Wich is negative 197

Answer:

 2x^2 + 8x + 3

Step-by-step explanation:

The expression is not factorable with rational numbers.

Answer:

The sum is about 22

Step-by-step explanation:

When you round the values at the ones place, you get:

7 + 6 + 9 = 22

Answer:22

Step-by-step explanation:

The cauliflower for one portion cost $6.75.

The first step is to convert pounds to ounces. The unit of conversion of pounds to ounces is 1 pound is equivalent to 16 ounces.

1 pound = 16 ounces

Therefore, 16 ounces of cauliflower costs $18.

The cost of one ounce = 18 / 16 = $1.125

The cost of one portion of cauliflower is:

Cost of one ounce x number of ounces in one portion

$1.125 x $6 = $6.75

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y = -1/4x + 2

yeah

that's it

Answer:

1. 2x + 4= slope: 2 | y intercept: (0,4)

2. 2x + 4= slope: 2 | y intercept: (0,4)

3. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

4. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

Answer:

54

Step-by-step explanation:

the ladder need to be 54 feet high

Answer:

-28

Step-by-step explanation:

Answer:

the answer is -28

Step-by-step explanation:

-8 x 7 / 1 x 2

= 56 / 2

Answer:

yes bti dsnin s

Step-by-step explanation:

9514 1404 393

Answer:

  -2/a^3

Step-by-step explanation:

Anything (except 0) to the 0 power is 1, so b^0 = 1. This immediately simplifies the expression to -2a^-3. If you also want it with positive exponents, this will be ...

  -2/a^3

Hello there I think the measure of EBC is 58 degrees.

That's because angles EBC and DBE are complementary. it means that they add up to 90 degrees.

We are given that

DBE=32 degrees.

And we know that angles EBC and DBE add up to 90 degrees.

So we take 90 and subtract the measure of angle DBE (32 degrees)

90-32=58

Hope this helps!

Answer:60 miles.

Step-by-step explanation:

m=number of miles the bicycle can travel in 4 hours.

Set up a ratio of hours over miles.

2/30=4/m. Multiply both sides by m. (2m)/30=4. Multiply both sides by 30. 2m=120. M=60. You could also just realize that you are multiplying the numerator by 2 of the fraction 2/30 to get 4/m, so you would also have to multiply the denominator by 2 so that both of the fractions are equivalent. So then you’d just multiply the bottom by 2 to get the miles the bike travels in 4 hours.

the answer would be c because the angles are equal to each other

- tan(50) → Choice A

Step-by-step explanation:

tan(-α) = - tan(α)

tan(-50) = - tan(50)

Further more :

tan (-50) = - tan (50) ≈ 0,27

Answer:

2.222

Step-by-step explanation:

Hope this helps :)  

Pls make brainliest :3  

And have an amazing day <3

Answer:

2 2/9

Step-by-step explanation:

so if we want to be able to substract, we're gonna multiply the 1/3 times three so the result come out to 3/9 and now we are able to substract, so 6 3/9 - 4 1/9 is equal to 2 2/9

The graphical relationship of the demand and price of brie are given in the two graphs

Reason:

The given parameters are;

The graphs gives the utility-maximizing combinations of bread and brie chosen by Hayden

The price of the loaf = $1.00

The prices of the brie are $4.00 and $6.00 per wheel

Given that as the price increases from $4.00 to $6.00, the quantity

demanded increases, we have;

When the price is $4.00, the quantity of brie demanded 23.84 brie wheels,

and the quantity of bread demanded is 15.9 bread loaves

When the price increases to $6.00, the quantity of brie demanded

decreases to 7.49 brie wheels, while the quantity of bread demanded

increases to 25.2 loaves

Therefore; we have;

At point A, the price is $4.00 and the quantity demanded is 23.84

At point B, the price is $6.00 and the quantity demanded is 7.49

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Goodluck

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

#1

Solving by submitting method:

[tex]\sf \leadsto 5x - 4y = 9 \: \: - - - (i)[/tex]

[tex]\sf \leadsto x - 2y = -3 \: \: - - - (ii)[/tex]

By first equation,

[tex]\sf \leadsto 5x - 4y = 9[/tex]

[tex]\sf \leadsto 5x = 9 + 4y[/tex]

[tex]\sf\leadsto x = \frac{9+4y}{5}\\[/tex]

Now, we can find the original value of y from Eqⁿ (ii).

[tex]\sf \leadsto x - 2y = -3[/tex]

[tex]\sf \leadsto \bigg(\frac{9+4y}{5}\bigg) - 2y = -3\\[/tex]

[tex]\sf \leadsto \frac{9+4y-10y}{5} = -3\\[/tex]

[tex]\sf \leadsto \frac{9-6y}{5}= -3\\[/tex]

[tex]\sf \leadsto 9-6y = -3(5)[/tex]

[tex]\sf \leadsto 9 -6y = - 15[/tex]

[tex]\sf \leadsto -6y = - 15 - 9[/tex]

[tex]\sf \leadsto -6y = -6[/tex]

[tex]\sf \leadsto y = \frac{\cancel-6}{\cancel-6}\\ [/tex]

[tex]\sf \leadsto y = \dfrac{ 6}{ 6} \\[/tex]

[tex]\sf \leadsto y = 1[/tex]

Now, we can find the original value of x , from Eqⁿ (I)

[tex]\sf \leadsto 5x-4y = 9[/tex]

[tex]\sf \leadsto 5x - 4(1) = 9[/tex]

[tex]\sf \leadsto 5x - 1 = 9[/tex]

[tex]\sf \leadsto 5x = 9+1[/tex]

[tex]\sf \leadsto 5x = 10[/tex]

[tex]\sf \leadsto x = \frac{10}{5}\\[/tex]

[tex]\sf \leadsto x = 5[/tex]

Therefore, the values of x and y are 5 and 1 respectively.

#2

Solving by Eliminating method:

[tex]\sf \leadsto 4x + 6y = 12\:\:- - - (i)[/tex]

[tex]\sf \leadsto 6x+9y = 12 \:\: - - -(ii)[/tex]

Step 1: Multiply Eqⁿ (I) by 3 and Eqⁿ (ii) by 2 to make the coefficients of y equal. Then we get the equations.

[tex]\sf \leadsto 12x + 18y = 36\:\: - - - (iii) [/tex]

[tex]\sf \leadsto 12x + 18y = 24\:\:- - - (iv)[/tex]

Step 2: Subtract Eqⁿ (iii) from Eqⁿ (iv) , we get

[tex]\sf \leadsto (12x + 18y)-(12x + 18y) = 36-24[/tex]

[tex]\sf \leadsto 0 =12, Which is a false statement. [/tex]

Therefore, the pair of equations has no solution.

Hope this helps!!

Answer:

Bro it is simple,see when the 2 numbers are multiplying in 1st number decimal is before 2 digits and in 2nd number decimal is before 1 digit and in product decimal is before 3 digits so to place the decimal you need to + the digits afer decimal of numbers eg. in 0.43 there are 2 digits afer decimal and in 0.2 there is 1 digit after decimal and in answer there are 3 digits after decimal

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer: SEE BELOW

Step-by-step explanation:

Decimals are multiplied as if they were whole numbers, and then the decimal point is placed in the product. To find out where the decimal point should be placed, count the number of decimal places after the decimal point in each factor.

0.43......... 2 decimal place(s) Add your decimal places = 3

0.2......... 1 decimal place(s)

0.086 Place decimal 3 decimal places in answer like so.

hope this helps you! Smile ; )

Step-by-step explanation:

think it is 1.0000100011000 x10 rise the power negative 3

Answer:

where is the graph?........

Step-by-step explanation:

Hope this helps you ☺️☺️