1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
padilas [110]
3 years ago
13

Someone explain what happened from line 1 to line 2

Mathematics
1 answer:
ser-zykov [4K]3 years ago
7 0
Expand the 1st line ==> xlog2+3log2 = xlog6 - log6

Transpose : xlog2 - xlog6 = -log6 - 3log2

MULTIPLY BOTH SIDE BY (-1)==> -xlog2+xlog6 = log6 +3log2
FACTORIZE: x(log6-log2) = log6+3log2
Got it??
You might be interested in
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
Write and solve and equation to find how many movies they have time to show.
GalinKa [24]

Answer:

Equation 0.5 + 1.75(x) = 4

x = 2movies

Step-by-step explanation:

Given that,

movie night will last for 4 hours

each movie take 1.75 hours

time for eating popcorn 0.5 hours

To find,

number of movies which can be watched

<h2>Equation</h2><h2>0.5 + 1.75(x) = 4</h2><h2>Solve for x</h2><h3>1.75(x) = 4 - 0.5</h3><h3>1.75(x) = 3.5</h3><h3>x = 3.5/1.75</h3><h3>x = 2  </h3>

So, total number of movies which could be watched in 4hr = 2

<h3 /><h3 /><h3 /><h3 /><h3 /><h3 /><h3 />

7 0
3 years ago
PLS ANWSER ASAP IN TI<br> ED!!
NikAS [45]

Answer:

Option (2)

Step-by-step explanation:

x = 1 is represented by a solid point on a number line.

x > 1 is represented by an arrow starting from x = 1 towards infinity

If we mix both the properties, x ≥ will be represented by an arrow starting from a solid point at x = 1 and moving towards the values greater than one.

From the options given,

Arrow mentioned in Option (2) will be the correct representation of the inequality.

7 0
2 years ago
Points C, D, and G lie on plane X. Points E and F lie on plane Y.Which statements are true? Select three options.
Slav-nsk [51]

Answer:

2nd , 3rd, & 4th

Step-by-step explanation:

4 0
3 years ago
How do I solve this?
lubasha [3.4K]
Here is your answer to the question

8 0
3 years ago
Other questions:
  • maria saves $25.00 a month and her sister Luisa saves $37.50 a month. How many months will it take for Luisa to save exactly $10
    13·1 answer
  • The stock of Company A lost $5.31 throughout the day and ended at a value of $112.69. By what percentage did the stock decline?
    6·1 answer
  • Which equation has no solution?
    7·1 answer
  • I need help fast !!
    13·1 answer
  • I NEED HELP PLS AND THX &lt;3
    5·2 answers
  • Ten subtracted from a number if the difference is 30 what was the orginal number​
    11·1 answer
  • 15,23,31,39, find the 60th term
    6·1 answer
  • Which decimal is one hundredth greater than 375.754?
    7·2 answers
  • The recursive formula for an arithmetic sequence is:
    11·1 answer
  • -0.056 + 0.27 = ?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!