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Definite Integral Problem - Having trouble

$68.38

what do you want to know?

Thank You!!!

2^(x + 3)  = 5^(3x - 1)  take the log of both sides

log 2^(x + 3)  = log 5^(3x - 1)    and we can write

(x + 3) log 2  = (3x - 1) log 5     simplify

x log 2 + 3 log 2  =  3x log 5 - log 5     rearrange as

x log 2 - 3x log 5   =  - 3 log 2 - log 5     multiply through by -1

3x log 5 - x log 2  =  3log 2 + log 5   factor the left side

x (3 log 5 - log 2)  = 3log 2 + log 5      divide both sides by (3 log 5 - log 2 )

x  =  [ 3log 2 + log 5 ] / [ 3 log 5- log 2 ]  ≈   .892

Convert to improper fractions then multiply straight across.

\(9\frac14\times3\frac12=\frac{37}{4}\times\frac{7}{2}=\frac{37\times7}{4\times2}=\frac{259}{8}\)

and...   \(\frac{259}{8}=32.375\)

110% sure ??? How can you be more than 100% sure?

Lol, I'm just messin 

x^2-4x/x^2-16 divided by x^2+2x-24/x^2-2x-24

Inverting the second fraction, we can write this as

[ x^2 - 4x ] / [x ^2 - 16 ]  * [ x^2 - 2x - 24 ]  / [ x^2 + 2x - 24 ]    simplify

[ x (x - 4) ] / [ (x + 4) (x - 4) ]  * [ (x - 6) ( x + 4)] / [ (x +6) ( x - 4) ]  

[ x / (x + 4) ]  *  [ (x - 6) ( x + 4) / ( x + 6) ( x - 4) ]

[ x (x - 6)] / [ (x + 6) ( x - 4) ]

[ x^2 - 6x ]  / [ x^2 + 2x - 24 ]

thanks a bunch! :)

We have the volume of a hemisphere and the volume of a cylinder

The hemisphere has a radius of   10m / 2   = 5m

And its volume  =  (2/3) * pi (radius)^3  =  (2/3) * pi  (5)^3   =  (250/3) pi m^3

The cylinder has a radius of 5 and a height  of  25m

Its volume is   pi (radius)^2 (height)  =  pi (5)^2 ( 25)  =  625 pi m^3

So..... the total volume is

pi ( 250/3 + 625) m^3      =    (2125 / 3) pi  m^3

The scale factor for the two parallelograms is just the square root of the ratio of the areas =

sqrt (40/10)  =  sqrt (4)  = 2

So....this means that each side of the larger parallelogram is 2 times that of the smaller

So......the perimeter of the larger parallelogram is also 2  times that of the smaller  =  2 * 22  = 44 cm

(x , y)

(4,12)

(5,36)

(6,108)

Note that we can write this as an exponential function  in the form :  y = a(b)^x

So we have :

12  =  a(b)^4     →   a  =  12 / (b^4)      (1)

36 = a(b)^5       (2)

Sub  (1)  into (2)

36 = (12 / b^4) b^5    simplify

3 =  b

Subbing this into (1), we have that   a =  12 / 3^4  =  12/81  =  4/27

So  the function is

y  = (4/27) (3)^x

volume of cone = (1/3) * (π * radius²) * (height)

surface area of a cone \(= (π *\text{radius}*\text{slant height})+ (π * \text{radius}^2) \)

Or...if you are not given slant height:

surface area of a cone \(=\pi*\text{radius}(\sqrt{ \text{height}^2+\text{radius}^2}+\text{radius}) \)

FV = PV x e^(0.1*3)

FV = 70 x  1.3498588.....

FV =$94.49

thanks alot what i needed

Thank you

Hi Helperid,

I only just saw your question to me.

I actually have no idea what the question asker is asking .....

Area_circle   =  pi * (radius)^2   or   pi * (diameter / 2 )^2

(-3)^2   = 9

1.

I think this is the equation for the circle:

x² + y² − 12x + 6y − 19 = 0

Add 19 to both sides and rearrange the terms.

x² − 12x + y² + 6y = 19

Add (12/2)² = 36  and  (6/2)² = 9 to both sides.

x² - 12x + 36 + y² + 6y + 9 = 19 + 36 + 9

Factor the left side.

(x - 6)(x - 6) + (y + 3)(y + 3) = 64

(x - 6)² + (y + 3)² = 64

Now that the equation is in this format, we can see that the center of the circle is located at (6, -3)

2.

This is the equation of a circle:

x² + (y + 3)² = 36

Darren can hear Tom as long as Tom stays within the radius of that circle.

The radius of that circle = \(\sqrt{36}\) = 6 miles

Thanks, helperid   !!!

3.52 rads  x   180° / pi rads   ≈  201.7° 

Doesn't really help a lot does it..

If you go back in time a bit you might find the other post. Maybe there was a better (more complete) answer but I do not recall one.

Here is an answer that I posted a day or two ago.

I will admit that I have not looked at it seriously myself yet.  There may have been other answers, I am not sure about that :)