All categories

3 years ago

How can you write the expression with rationalized denominator? 2+sqrt3(3)/sqrt3(6)

1 answer:

8 0

So we have a 6 at the bottom, and the root is 3, so hmm how to take it out, simple enough, just let's get something to make the 6 a 6³, so it comes out of the root

so

$\bf \cfrac{2+\sqrt[3]{3}}{\sqrt[3]{6}}\cdot \cfrac{\sqrt[3]{6^2}}{\sqrt[3]{6^2}}\implies \cfrac{(2+\sqrt[3]{3})(\sqrt[3]{6^2})}{(\sqrt[3]{6})(\sqrt[3]{6^2})}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{3}\cdot \sqrt[3]{36}}{\sqrt[3]{6^3}}
\\\\\\
\cfrac{2\sqrt[3]{36}+\sqrt[3]{3\cdot 36}}{6}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{108}}{6}\implies \cfrac{2\sqrt[3]{36}+\sqrt[3]{3^3\cdot 4}}{6}
\\\\\\
\cfrac{2\sqrt[3]{36}+3\sqrt[3]{ 4}}{6}$

You might be interested in

What is 1 tenth of 2.0

timofeeve [1]

O.2 0.2 0.2 the answer is 0.2
yeah

6 0

3 years ago

Read 2 more answers

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0

3 years ago

What set of reflections would carry hexagon ABCDEF onto itself?

Marianna [84]

When a set of reflections that carry a shape onto itself, it means that the final position of the shape will be the same as its original location

Reflections (a) y=x, x-axis, y=x, y-axis would carry the hexagon onto itself

First; we test the given options, until we get the true option

(a) y=x, x-axis, y=x, y-axis

The rule of reflection y =x is:

$(x,y) \to (y,x)$

The rule of reflection across the x-axis is:

$(x,y) \to (x,-y)$

So, we have:

$(y,x) \to (y,-x)$

The rule of reflection y =x is:

$(x,y) \to (y,x)$

So, we have:

$(y,-x) \to (-x,y)$

Lastly, the reflection across the y-axis is:

$(x,y) \to (-x,y)$

So, we have:

$(-x,y) \to (x,y)$

So, the overall transformation is:

$(x,y) \to (x,y)$

Notice that, the original and final coordinates are the same.

This means that:

Reflections (a) y=x, x-axis, y=x, y-axis would carry the hexagon onto itself

Read more about reflections at:

brainly.com/question/938117

4 0

2 years ago

I NEED HELP ASAP ITS A QUIZ Jim's uncle is four times as old as his nephew Jim. In ten years, Jim's uncle's age will be twenty y

Dmitrij [34]

Answer:

Jim's uncle is 20 years old right now

Step-by-step explanation:

The number of times Jim's uncle is as old as Jim = 4 times

The age of Jim's uncle in 10 years = 20 + 2 × Jim's age

Let Jim's age = A, and Jim's uncles age = B;

Therefore, from the information in the question, we have;

B = 4 × A........................................(1)

B + 10 = 20 + 2 × A......................(2)

Therefore, by substituting the value of B from equation (1) into equation (2), we have;

B = 4 × A

∴ B + 10 = 20 + 2 × A, gives;

4 × A + 10 = 20 + 2 × A

4 × A - 2 × A = 20 - 10 = 10

A × (4 - 2) = 10

2 × A = 10

A = 10/2 = 5

A = 5 years

Therefore, Jim's age = A = 5 years

Jim's age = 5 years

B = 4 × A = 4 × 5 years = 20 years

B = 20 years

Jim's uncles age = B = 20 years

Jim's uncles age = 20 years

Therefore;

Jim's uncle is 20 years old right now.

4 0

3 years ago

Find the length of the rectangle. A. 10 in. B. 20 in. C. 27 in. D 70 in.

Dmitriy789 [7]

10 in

This is a answer

6 0

3 years ago

Read 2 more answers