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ln(x) = −5

Since you already have the natural log of x=-5, then:

x = e^(-5) =0.006737947......etc.

the question is $215000 grows to$35000 in 16 years comp.monthly,find %/a

You have $215,000 grows to $35,000?????. I assume you mean $350,000?

If that is the case, then the annual rate of growth would be: 3.05% compounded monthly. The formula you would use for this is:

FV=PV [1 + R ]^N, where PV=Present value, FV=Future value, R=Interest rate per period, N=Number of periods.

In this case, you would solve for R using Logs.

Your question does not seem to make sense,unless what you are asking is how to convert -(5/9) radians into multiples of pi. (and then find the sine ratio of this )

I'll assume that's what you want:

there are pi radians in 180 degrees

so 1 radian = 180/pi     degrees

-(5/9) radians = -(5/9)  x (180/pi)  degrees which represents an angle in the clockwise direction with respect to the x - axis.

...and sin( -x)  = - sin(x).

Incidentally, you can't have the energy in Newtons (a measure of force).  I suspect you meant Joules (which is what I've assumed in my calculation above).

We  have:  E = (1/2)*m*v²

So:  m = 2*E/v²

Here:  m = 2*3528/98² kg  or m ≈ 0.37 kg

.

\(0.34r\)

\(\frac{34}{100}r\)

\(\frac{17}{50}r\)

(1/17)^0,5 х-1=9

(1/17)^(0.5х) - 1=9 If this is what you meant, then,

(1/17)^(0.5x) =10 take the Log of both sides,

0.5x =Log(10) / Log(1/17),

0.5x = -0.81271150 divide both sides by 0.5,

x=-1.625422

(1/17)^(0.5х-1)=9 If this is what you meant, then take the Log of both sides:

(0.5x - 1) =Log(9) / Log(1/17)

(0.5x - 1)=-0.77552387

0.5x =)=-0.77552387 + 1

0.5x =0.22447613 divide both sides by 0.5

x =0.44895226

(1/17)^(0.5)x-1=9

(1/17)^(1/2)x-1=9

sqrt(1/17)x-1=9

(sqrt(1)/sqrt(17))x-1=9

(sqrt(1)/sqrt(17))x=10

x=10/(sqrt(1)/sqrt(17))

x=10*(sqrt(17)/sqrt(1))

x=10*(sqrt(17)/1)

x=10*sqrt(17)

x=10sqrt(17)

2.

Picture the dots joined up to make a square of side 3cm.

The desired area is the area of this square + the area of 4*(3/4 of the area of a circle of radius 1cm) - 4*(the area of a semicircle of radius 1cm).

Area = (3² + 4*(3/4)*pi*1² - 4*(1/2*pi*1²)cm²

Area = 9 + pi ≈ 12.142 cm²

But using Max's reasoning we could also say that  infinity = 360n + 10 (say), where n is infinitely large integer (because, if you add a finite number to infinity you still get infinity),

and, since tan(360n + 10) = tan(10) when n is an integer, we would have tan(infinity) = tan(10) = 0.176

Repeat with any other number replacing the 10 above and you could get any number you like for tan(infinity)!!

tan(infinity) is undefined.

5. 

Area of sector OBC = pi (20)^2/ 6  = 200pi/3 cm^2

Area of equilateral triangle   (1/2) 20^2 sin60  = (1/2) 400* [√3/ 2] =  100√3 cm^2

Area between area of sector OBC and equilateral triangle = [ 200pi/3 -100√3] cm^2  →   (1)

And AC is the radius of the smaller circle  = (1/2)20cm  = 10cm

So....the shaded area = (1/2) area of the smaller circle  - (1)   =

[pi (10)^2/2  - (200pi/3 - 100√3) ] cm^2  = about 120.85 cm^2

3. Total area of sector  AOC =  pi(36)/ 3 =  12pi units^2

If the orange area = the blue area.....then, by symmetry......area BCEF   = the orange area 

And the area of the sector formed by OED = the blue area.....so......all these areas are equal and they divide the total area of sector AOC into 4 equal parts.......so area ODEF  (1/2) the area of sector AOC  = 6pi units^2

So....we have that OD is the radius of the the smaller circle

And we have:

1/3 area of the smaller circle  =  Area ODEF  = [ pi * OD^2] / 3

6pi = [ pi * OD^2] / 3      multiply both sides by 3

18  = OD^2

OD  = √18 units   =  3√2 units  = about 4.24 units

You cannot evaluate infinity, on any calculators.

\(f(x)=\frac{ln^2x}{2}=\frac{{(ln(x))}^2}{2}=\frac{2lnx}{2}=ln x\)

\(f(e) = ln (e) = 1\)

9 7/10 = 9.7

9.7 is nearer to 9.5 than 10.0

therefore 9 7/10 rounded to the nearest half is 9.5

Thx 

1.

a. Area of the rectangle  - area of smaller sector  =  the "large" white area in the rectangle  =

         [24 - 4pi] cm^2

b. Area of the large sector  - area of "large" white part of the rectangle = the total area of the shaded region =

  [ 9pi - ( 24 - 4pi)] cm^2  = [ 13pi - 24] cm^2   = about 16.841 cm^2  = about 16.8 cm^2

Let \(\alpha \) and \(\beta\) be the 2 roots of the equation ax²+bx+c

\(\alpha + \beta = -\frac{b}{a}\)

\(\alpha \beta = \frac{c}{a}\)

\(\frac{1}{2\alpha}+\frac{1}{2\beta}\)

=\(\frac{\alpha+\beta}{2\alpha\beta}\)

=\(\frac{-\frac{-8}{2}}{2(\frac{7}{2})}\)

=\(\frac{4}{7}\)

infinity is divisible by 360 (I hope because infinity over anything = infinity), tan(360) = 0, therefore tan(infinity) = 0

I assume you want either :

0.3444..... [4s repeating] 

Or 

0.343434.......[ 34 repeating ]

1st case

[  34  - 3] /  90   = 31/90   = 0.344444.........

2nd Case

[34 - 0] / 99  = 34/99  =  0.343434.......

d)  40 → 84

( [84 - 40] / 40 * 100) %      = ( 44/40 * 100)%  = (11/10 * 100)% =

(1100/10)% =  110 %

e)  4 → 13

( [ 13 - 4] / 4  *100) %   = (9/4 * 100)%  = (2.25 * 100) %  =  225%

535 * 47 = 25145...........magic

2*(2.7)^{-a^2}  =  1

(Same answer as guest, just a different style.)

Divide both sides by 2:

--->   (2.7)^{-a^2}  =  1/2

Find the log of both sides:

--->   log( (2.7)^{-a^2}  )  =  log( 0.5 )

Using the property of logs:

--->   -a² · log( 2.7 )  =  log( 0.5 ) 

Divide both sides by log ( 2.7 ):

--->   -a²  =  log( 0.5 ) / log ( 2.7 ) 

--->    -a²  =  -0.6978564745

--->     a²  =  0.6978564745

Either  a =  0.835378...   or  a  =  -0.835378...

hey

Solve for a over the real numbers:
2 2.7^(-a^2)=1

2 2.7^(-a^2)=(5/27)^(a^2) 2^(a^2+1):
(5/27)^(a^2) 2^(a^2+1)=1

Take the natural logarithm of both sides and use the identities log(a b)=log(a)+log(b) and log(a^b)=b log(a):
log(2) (a^2+1)-log(27/5) a^2=0

Expand and collect in terms of a:
(log(2)-log(27/5)) a^2+log(2)=0

Subtract log(2) from both sides:
(log(2)-log(27/5)) a^2=-log(2)

Divide both sides by log(2)-log(27/5):
a^2=-(log(2))/(log(2)-log(27/5))

Take the square root of both sides:
Answer: | 
 | a=sqrt((log(2))/(log(27/5)-log(2)))        or           a=-sqrt((log(2))/(log(27/5)-log(2)))=+-0.835378042837.........etc.