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2 years ago

Explain why the cubed root of -8/27 is -2/3

Mathematics

2 answers:

Len [333]2 years ago

4 0

Help me and I’ll help you

Kazeer [188]2 years ago

4 0

Answer:

Because the cubed root of the numerator and denominator equals the answer

Step-by-step explanation:

alright, we are trying to understand WHY $\sqrt[3]{\frac{-8}{27} } = -\frac{2}{3}$

You can actually rewrite the first number as $-\frac{\sqrt[3]{8} }{\sqrt[3]{27} }$

you must look for the number, which three times itself, equals 8...

...and the same thing for the bottom: a number, which three times itself... equals 27.

What number cubed equals 8? The answer is 2

What number cubed equals 27? The answer is 3

...so now we have -2 over 3. You can double check this answer.

$-\frac{2}{3} * -\frac{2}{3} = \frac{4}{9}$

$\frac{4}{9} * -\frac{2}{3} = -\frac{8}{27}$

we get the original number that we were looking for the cubed root... SUCCESS.

You might be interested in

(50 points) Which graph is defined by the function given below?

marta [7]

Answer:

Graph B

Step-by-step explanation:

y = (x - 3)(x - 3)

The x intercepts are at 3

Since both intercepts are at 3, the vertex is at 3

We know it is an upwards facing parabola since it is quadratic and the constant out front is positive

5 0

2 years ago

Need help asap, the answer I picked I think is wrong but idk

BigorU [14]

Answer:

Reflected about the y-axis and then rotated 90° counterclockwise

Step-by-step explanation:

(x , y) to (-x , y) --> reflected over y-axis

then (-x , y) --> (-y, -x) -->90 degrees rotation counterclockwise

So answer is the last one

Reflected about the y-axis and then rotated 90° counterclockwise

8 0

3 years ago

Determine n between 0 and 19 such that (2311)(3912) ≡ n mod 20.

sleet_krkn [62]

You can write 2311 and 3912 in the form $20q+r$ :

$2311=115\cdot20+11$

$3912=125\cdot20+12$

Then

$2311\cdot3912=(115\cdot20+11)(125\cdot20+12)$

$2311\cdot3912=115\cdot125\cdot20^2+(11\cdot125+12\cdot115)\cdot20+11\cdot12$

Taken modulo 20, the terms containing powers of 20 vanish and you're left with

$2311\cdot3912\equiv11\cdot12\equiv132\pmod{20}$

We further have

$132=6\cdot20+12$

so we end up with

$2311\cdot3912\equiv12\pmod{20}$

and so $n=12$ .

###

If instead you're trying to find $2311^{3912}\pmod{20}$ , you can apply Euler's theorem. We can show that $\mathrm{gcd}(2311,20)=1$ using the Euclidean algorithm. Then since $\varphi(20)=8$ , and 8 divides 3912, we have

$2311^{3912}\equiv2311^{489\cdot8}\equiv(2311^{489})^8\equiv1\pmod{20}$

To show 2311 and 20 are coprime:

2311 = 115*20 + 11

20 = 1*11 + 9

11 = 1*9 + 2

9 = 4*2 + 1 => gcd(2311, 20) = 1

3 0

3 years ago

Three square flower beds with side of 2m are dug in a rectangular piece of land whose length is 5.2 m and width is 4.8 m. What i

belka [17]

Answer: 12.96 m²

Step-by-step explanation:

The area of the piece of land that the flower beds were dug in is:

= Length * width

= 5.2 * 4.8

= 24.96 m²

The flower beds were 3 in number and all had the shape of a square.

Their area is:

= 3 * (Length * width)

= 3 * ( 2 * 2)

= 3 * 4

= 12 m² for all three flower beds

Remaining land:

= 24.96 - 12

= 12.96 m²

8 0

2 years ago

Which expression is equivalent to 10√5

mixer [17]

Answer:

A. √500

Step-by-step explanation:

Since 500 = 5·100 = 5·10² you can move the 10² out of the √ as 10.

Hence 10√5 = √500

So we're using these rules:

√a·b = √a·√b

and of course

√a² = a (a>0)

8 0

3 years ago