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3 years ago

Find the simplified product:

Mathematics

2 answers:

ivann1987 [24]3 years ago

8 0

I think we can do this by converting the radicals to exponents

the given expression = 2^1/3 * x^5/3 * 4 x^3
= 4* 2^1/3 * x^14/3

the third option = 4 x^4 * 2^1/3 * x^2/3
= 4*2^1/3 * x^14/3

so its the third option

Sunny_sXe [5.5K]3 years ago

4 0

Use:
$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{a\cdot b}\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^n}=a$

$\sqrt[3]{2x^5}\cdot\sqrt[3]{64x^9}=\sqrt[3]{2x^5}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^9}\\\\=\sqrt{2x^5}\cdot4\cdot\sqrt[3]{x^9}=4\sqrt[3]{2x^5\cdot x^9}\\\\=4\sqrt[3]{2x^{5+9}}=4\sqrt[3]{2x^{14}}=4\sqrt[3]{2x^{2+12}}=4\sqrt[3]{2x^2x^{12}}\\\\=4\sqrt[3]{2x^2x^{4\cdot3}}=4\sqrt[3]{2x^2(x^4)^3}=4\sqrt[3]{2x^2}\cdot\sqrt[3]{(x^4)^3}\\\\=4\sqrt[3]{2x^2}\cdot x^4=\boxed{4x^4\sqrt[3]{2x^2}}$

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Describe the steps to dividing imaginary numbers and complex numbers with two terms in the denominator?

zlopas [31]

Answer:

Let be a rational complex number of the form $z = \frac{a + i\,b}{c + i\,d}$ , we proceed to show the procedure of resolution by algebraic means:

1) $\frac{a + i\,b}{c + i\,d}$ Given.

2) $\frac{a + i\,b}{c + i\,d} \cdot 1$ Modulative property.

3) $\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)$ Existence of additive inverse/Definition of division.

4) $\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}$ $\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}$

5) $\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}$ Distributive and commutative properties.

6) $\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}$ Distributive property.

7) $\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}$ Definition of power/Associative and commutative properties/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction.

8) $\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}$ Definition of imaginary number/ $x\cdot (-y) = -x\cdot y$ /Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Step-by-step explanation:

Let be a rational complex number of the form $z = \frac{a + i\,b}{c + i\,d}$ , we proceed to show the procedure of resolution by algebraic means:

1) $\frac{a + i\,b}{c + i\,d}$ Given.

2) $\frac{a + i\,b}{c + i\,d} \cdot 1$ Modulative property.

3) $\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)$ Existence of additive inverse/Definition of division.

4) $\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}$ $\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}$

5) $\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}$ Distributive and commutative properties.

6) $\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}$ Distributive property.

3 0

3 years ago

Please someone help?!!<br><br> WILL MARK BRAINLIEST^^^^

garik1379 [7]

The answer for that question is about 3 I think is this mathswatch

8 0

3 years ago

Read 2 more answers

HELP ASAP PLEASE

Stels [109]

Solution (1) using angles of sectors:

Area of A = pi r^2 x 90/360 = 4.9

Area of B = pi r^2 x 270/360 = 14.2

Check: Area of A/B = 4.9/14.72 = 1/3 (as given)

Solution (2) using given info:

Area of B + Area of A = area of circle

Area of B + 1/3 Area of B = 3.14 * (2.5)^2 = 19.625

4/3 Area of B = 19.625

Area of B = 3/4 * 19.625

Area of B = 14.72

Area of A = 1/3 * 14.72 = 4.9

There is more solutions to this problem , like polar coordinate integration , and so on. for more just request.

8 0

3 years ago

The table shows the input and output of a function Table(input:3,4,6,11. Output:5,7,11,21) (a) Explain what makes this set of da

Maslowich

Answer:

(a) The data set is a function, since for each input value {3,4,6,11} there is a single output value {5,7,11,21}

(B) A function is a mathematical relationship that associates one or more inputs with a single output value. So that the data set is not a function, there should be - for one or more values of the input - more than one output.

for example, if for the input value {3} there were two outputs {5, -5} then, the data set would not be a function.

The frelation $y ^ 2 = x$ is not a function because:

When x = 1, y = +1 and y = -1.

The slope is:

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

$m =\frac{7-5}{4-3}$

m = 2

$b = y_1-mx_1$

b = 5 - 2*3

b = -1

Then, the function is:

y = 2x-1

You can substitute any of the points shown in the equation and check that equality is satisfied, for example:

(11 , 21)

y = 2 (11) -1

y = 22-1

y = 21. The equation is satisfied. The same goes for the rest of the values.

4 0

3 years ago

Janie receives R150 pocket money per month. In the new year his mother increase his pocket money in the ratio 6:5. Calculate Jan

dimaraw [331]

Answer:

Janies' monthly pocket money is $180.

Step-by-step explanation:

Janies' adjusted monthly pocket money:

Initial pocket money = $150

Ratio of new pocket money = 6:5

Let his new pocket money be represented by x,

x:$150 = 6:5

$150 x 6 = x (5)

$900 = 5x

x = $\frac{900}{5}$

x = $180

Therefore, Janies' monthly pocket money is $180.

6 0

3 years ago