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2 years ago

What is the radical form of the expression? (5x3y4)37 ↡

Mathematics

1 answer:

hram777 [196]2 years ago

4 0

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Step-by-step explanation:

Given expression is:

$(\sqrt{5x^3y^4})^{\frac{3}{7}$

In order to convert an exponent into radical form, the power should be in the form of 1/x where x is any number

so,

in case of 3/7, it will be broken down

$(\sqrt{5x^3y^4})^{3*\frac{1}{7}}$

The 1/7 will be converted into base of radical while 3 will be he exponent

$\sqrt[7]{(5x^3y^4)^3}$

Multiplying exponents

$=\sqrt[7]{5^3x^{3*3}y^{4*3}}\\=\sqrt[7]{125x^9y^{12}}$

Hence,

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Keywords: Radicals, Exponents

Learn more about exponents at:

#LearnwithBrainly

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The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor?

PtichkaEL [24]

Answer:

$\left(y-8\right)$

Step-by-step explanation:

$y^2-10y+16$

$=\left(y^2-2y\right)+\left(-8y+16\right)$

$y^2-2y$

$=yy-2y$

$=y\left(y-2\right)$

$-8y+16$

$=-8y+8\cdot \:2$

$=-8\left(y-2\right)$

$=y\left(y-2\right)-8\left(y-2\right)$

$=\left(y-2\right)\left(y-8\right)$

The other factor is:

$\left(y-8\right)$

5 0

2 years ago

Read 2 more answers

(a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩r→1(t)=⟨x(t),y(t),z(t)⟩ for the shadow of the circular cylinder x2

motikmotik

Answer: (a) r1(t) = <2cost , 0 , 2sint>

(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>

Step-by-step explanation:

x2+z2=4

Now, in the xz plane, we know that y = 0...

So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..

This can be easily parameterized as

x = 2cos(t)

z = 2sin(t)

So, the required parameterization is :

r1(t) = <2cost , 0 , 2sint>

Cylinder : x^2 + z^2 = 4

Plane : 5x+8y+6z=1

Easily enough, the x^2 + z^2 = 4 can again be parameterized as

x = 2cost , z = 2sint

With this, we can find y using plane equation...

5x+8y+6z=1

5(2cost) + 8y + 6(2sint) = 1

8y = 1 - 12sint - 10cost

y = (1 - 12sint - 10cost)/8

So, the parameterization is :

<2cost , (1 - 12sint - 10cost)/8 , 2sint>

6 0

2 years ago

Amelia and Elliott are collecting empty soda cans for recycling. Amelia has 13 less than 5 times the cans that Elliott has. Toge

xeze [42]

Answer:

D.) Elliott has 212 cans, Amelia has 45 cans

Step-by-step explanation:

257 = x + (5x - 12)

257 = 6x - 13

+13 +13

270 = 6x

/6 /6

45 = x (the amount of Amelia's cans)

257 - 45 = 212 (the amount of Elliott's cans)

please rate and thank : )

6 0

2 years ago

If the screws that are 4/8 of an inch are laid end to end touching each other how far would the row extend?

Irina18 [472]

Idk because you did not say yes you did how many sides there were

8 0

2 years ago

Read 2 more answers

What is the true solution to the equation below?

jarptica [38.1K]

Answer:

Step-by-step explanation:

some rules of logarithmic function

$ln(a) - ln(b)=ln(\frac{a}{b})$

$e^{ln(a)}=a$

$ln(a)^{n}=nln(a)$ vice-versa $nln(a)=ln(a)^{n}$

If ㏑(a) = ㏑(b), then a = b

∴ $2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)$

Use the 2nd rule to simplify it

$e^{ln(2x)}=2x\\e^{ln(10x)}=10x\\$

2㏑(2x) - ㏑(10x) = ㏑(30)

Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

$ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})\\\\ln(\frac{4x^{2}}{10x})=ln(30)\\\\ \frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x\\\\ ln(\frac{2}{5}x)=ln(30)$

Use the 4th rule

$\frac{2}{5} x = 30$

Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

3 0

2 years ago