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3 years ago

How to solve? Inx - In 1/x = 2

Mathematics

1 answer:

zimovet [89]3 years ago

8 0

Answer:

Step-by-step explanation:

$\text{The domain:}\\\\D:x>0\\\\\ln x-\ln\dfrac{1}{x}=2\qquad\text{use}\ \log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\\\\ln\dfrac{x}{\frac{1}{x}}=2\\\\\ln x^2=2\qquad\text{use}\ \log_ab=c\iff a^c=b\ \text{and}\ \ln x=\log_ex\\\\x^2=e^2\iff x=e\in D$

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Simplify the following Questions. (IMPORTANT NOTE!!! #'s 2 AND 7 MUST BE IN SCIENTIFIC NOTATION!!!!!) 1.) (x)²(2xy³)^5 2.) (4x10

poizon [28]

Answer:

Step-by-step explanation:

Hint :

$(a*b)^{m}= a^{m}b^{m}\\\\\\(a^{m})^{n}=a^{mn}\\\\\\a^{m}*a^{n}=a^{m+n}\\$

$1)x^{2}(2xy^{3})^{5}=x^{2}*2^{5}*x^{5}*(y^{3})^{5}\\\\\\=x^{2}*2^{5}*x^{5}*y^{3*5}\\\\=x^{2}*2^{5}*x^{5}*y^{15}\\\\=2^{5}*x^{2+5}*y^{15}\\\\=2^{5}x^{7}y^{15}$

$2) (4x10^{8})^{2}=4^{2}*x^{2}*(10^{8})^{2}\\\\=16*x^{2}*10^{8*2}\\\\=1.6*10*x^{2}*10^{16}\\\\=1.6x^{2}*10^{16+1}\\\\=1.6x^{2}10^{17}$

$3)(-h^{4})^{5}=(-h)^{4*5}=-h^{20}\\\\\4)(3xy^{3})^{2}(xy)^{6}=3^{2}x^{2}(y^{3})^{2}x^{6}y^{6}\\\\=9x^{2}y^{3*2}x^{6}y^{6}\\\\\\=9x^{2}y^{6}x^{6}y^{6}\\\\=9x^{2+6}y^{6+6}\\\\=9x^{8}y{12}\\\\\\$

$5) (p^{9})^{-2}=p^{9*-2}=p^{-18}\\\\\\6)(5k^{2})^{3}=5^{3}(k^{2})^{3}=625k^{6}\\\\7)(7x10^{5})^{2}=7^{2}x^{2}(10^{5})^{2}\\\\=49x^{2}10^{5*2}\\\\=4.9*10^{1}x^{2}10^{10}\\\\=4.9x^{2}10^{10+1}\\\\=4.9x^{2}10^{11}$

$8)x^{3}(-x^{3}y)^{2}=x^{3}*(-x^3})^{2}y^{2}\\\\\\=x^{3}*(-1)^{2}*x^{2*3}y^{2}\\\\=x^{3}*1*x^{6}y^{2}=x^{3+6}y^{2}\\\\=x^{9}y^{2}\\\\\\9)w^{5}(w^{2})^{-4}=w^{5}w^{2*-4}\\\\=w^{5}w^{-8}\\\\=w^{5-8}=w^{-3}\\\\=\frac{1}{w^{3}}\\\\\\10) (2x^{5})^{4}=2^{4}x^{5*4}\\\\=2^{4}x^{20}\\\\=16x^{20}$

5 0

3 years ago

This table represents a function plot points to represent the function as a graph. X -4 y 9

Lelechka [254]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have the ordered pairs

(-4,9),(-1,3),(0,1),(2,-3)

Using a graphing tool

Plot the given ordered pairs in the coordinate plane

Remember that

In a ordered pair (x,y), the first coordinate is the location of the point in the x-axis and the second coordinate is the location of the point in the y-axis

see the attached figure

The graph represent a line

<em>Find the equation of the line</em>

Find the slope

take two points

$(0,1),(2,-3)\\m=(-3-1)/(2-0)=-2$

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-2\\b=1$

substitute

$y=-2x+1$

4 0

3 years ago

2 points Jason's friend George jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as

vitfil [10]

we need to substitute t=5

$h(5)=16(5^2)+16(5)+480$ $h(5)=16(25^{})+16(5)+480$ $h(5)=400+80+480=960$

The George's height after 5 seconds was 960

3 0

1 year ago

Pair of pants<br> List Price $24.95<br> Rate of Discount 20%<br> DISCOUNT =

Sergeu [11.5K]

So when we solve this problem I am assuming you mean the price of the pants after the discount like I said I am assuming but the final price after the discount is applied is 19.96 like I said I repeat this I am assuming you are talking about the total price after the discount is applied have a nice day :D oh and here is the work for it

X/24.95 20/100 So we take 24.95 and multiply it by 20 then divide by 100 and get 4.99 then we subtract that to the list prices 24.95 which will be 19.96 have a nice day :D

7 0

3 years ago

Experimental vs. Theoretical Probability:

liubo4ka [24]

Hello Nitagomez,

To start the numbers 1 through 6 are on a number cube.
Half of them are even, 2, 4, and 6.

So it makes sense that when you roll the cube 60 times, you should have 30 even numbers. The theoretical probability is 30.

A predication of 20 is 10 less than the expected value of 30.
10 out of 30 is 33%.

The predication is off by 33%, I would argue that it is not a very good prediction.

I hope this helps, Good luck!
MrEquation

6 0

3 years ago