Can u answer this???????????????

What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)

8 0

3 years ago

How can completing the square aid in solving quadratic functions?

Elden [556K]

Completing the squares tells us exactly what square root we will need to calculate our answer.

Using the formula below you can find these answers:
$A(x-h)^2 + K = 0
(x-5)^ 2 = - K/A
$

Does this make sense?

4 0

3 years ago

What's the answer to: divide £48 in the ratio 7:5 (please show your working, much appreciated)

Brums [2.3K]

I can see you come from outside the USA. No insults intended!!
.
Anyways, we have to put one side of the ratio and match it to 48.
.
Or even better...
.
MAKE!!
A!!
PROPORTION!!
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So... Let's say 7 is proportional to 48... so 7/5 = 48/x, where x is the number equivalent to ratio of 5.
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Cross multiply!!
<span>.
</span>7x = 240.
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Divide 7 on both sides.
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x = 34 2/7.
.
Hope I helped!!

4 0

3 years ago

Hernan cuts a board that is 7/10 of a meter long After the cut the board is 3/10 of a meter long how long is the piece that he c

Darina [25.2K]

Given that original lenght of the board before cut $= \frac{7}{10}$ meter

Lenght of the board that is left after cutting from the original piece by Hernan $= \frac{3}{10}$ meter

Now we have to find the lenght of the piece which is cut.

To find that we just need to subtract smaller piece from larger piece

Required Length $= \frac{7}{10}-\frac{3}{10}$ meter

Required Length $= \frac{7-3}{10}$ meter

Required Length $= \frac{4}{10}$ meter

reduce the fraction

Required Length $= \frac{2}{5}$ meter

Hence final answer is $\frac{2}{5}$ meter.

7 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST

Alona [7]

Given:

One linear function represented by the table.

Another linear function represented by the graph.

To find:

The greater unit rate and greater y-intercept.

Solution:

Formula for slope (unit rate):

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the given table it is clear that the linear function passes through (0,5) and (5,15). The function intersect the y-axis at (0,15), so the y-intercept is 15.

$m_1=\dfrac{15-5}{5-0}$

$m_1=\dfrac{10}{5}$

$m_1=2$

So, the unit rate of first function is 2.

From the given graph it is clear that the linear function passes through (0,6) and (-4,0). The function intersect the y-axis at (0,6), so the y-intercept is 6.

$m_2=\dfrac{0-6}{-4-0}$