Ask question

Ask question

All categories

3 years ago

12

Simplify: x^1/3( x^1/2 + 2x^2)

2 answers:

Firlakuza [10]3 years ago

7 0

Answer:

Step-by-step explanation:

x^1/3( x^1/2 + 2x^2)

x^(1/2 + 1/3) + 2x^(2 + 1/3)

x^(5/6) + 2x^(7/3)

earnstyle [38]3 years ago

3 0

Answer:

Step-by-step explanation:

x^1/3( x^1/2 + 2x^2)

x^(1/2 + 1/3) + 2x^(2 + 1/3)

x^(5/6) + 2x^(7/3)

You might be interested in

3^x= 3*2^x solve this equation

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$

(Both answers are equivalent)

8 0

3 years ago

What are the steps to writing an equation from a graph? Give at least three steps.

zhannawk [14.2K]

Answer:

1. Calculate the slope from 2 points.

2. Substitute either point into the equation.

3.Solve for b, which is the y-intercept of the line.

4. Substitute b, -1, into the equation from step 2.

Step-by-step explanation:

I gave you one extra than what you expected, if thats ok.

Hope this helps : )

6 0

3 years ago

In a class of 40 students, 5 like neither Nokia nor

STatiana [176]

Answer:

<em><u>The number of students that like only Nokia </u></em>

<h2>= 30</h2>

Step-by-step explanation:

consider N the number of students who like Nokia → N=?

T the number of students who like Techno → T=35

Statement 1: In a class of 40 students, 5 like neither Nokia nor Techno

we can translate it like this: 35 student like Nokia or Techno

we can note it like this : T∪N= 35

Statement 2: 30 like Techno and Nokia

we can note it : T∩N = 30

using a rule concerning the number of element of a set :

T∪N = N + T - T∩N

then

35 = N + 35 - 30

⇒ N - 30 = 0

⇒ N = 30

7 0

3 years ago

Sammy had $3000 and lost $150 per day gambling.<br> iso-

bagirrra123 [75]

Answer:

sammy would run out of money in 20 days if that 's the answer your looking for

Step-by-step explanation:

i don't exactly understand the question but i hope this helps :)

3 0

2 years ago

Read 2 more answers

If a scalene triangle has its measures 4 m, 11 m and 8 m, find the largest angle.

soldier1979 [14.2K]

Answer:

129.8 approximately

Step-by-step explanation:

So this sounds like a problem for the Law of Cosines. The largest angle is always opposite the largest side in a triangle.

So 11 is the largest side so the angle opposite to it is what we are trying to find. Let's call that angle, X.

My math is case sensitive.

X is the angle opposite to the side x.

Law of cosines formula is:

$x^2=a^2+b^2-2ab \cos(X)$

So we are looking for X.

We know x=11, a=4, and b=8 (it didn't matter if you called b=4 and a=8).

$11^2=4^2+8^2-2(4)(8)\cos(X)$

$121=16+64-64\cos(X)$

$121=80-64\cos(X)$

Subtract 80 on both sides:

$121-80=-64\cos(X)$

$41=-64\cos(X)$

Divide both sides by -64:

$\frac{41}{-64}=\cos(X)$

Now do the inverse of cosine of both sides or just arccos( )

[these are same thing]

$\arccos(\frac{-41}{64})=X$

Time for the calculator:

X=129.8 approximately

3 0

3 years ago