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Just use the calculator to get

sqrt842 = 29.017

29.0172362571

Sin(x) = .2588     Given

ARCSin (x) = x = ARCSin(.2588)        using the calculator   = 14.9988 degrees  ( ~ 15 degrees)   

COMPLIMENTARY angle is the angle which added to 'x' will equal 90      so the COMPLIMENTARY Angle is 75 degrees

Using the calculator again    cos (75) = .2588   The same as the complimentary angle's SIN !!!

1/2*6=9

It looks like there are THREE  very similar qiestions related to potential energy and work posted this morning.  I'll show you how to do this one...you should be able to multiply hte others w/out much difficulty.  When an object has a CHANGE in potential energy and equivalent amount of work ahs to be done to change this potential energy.....so for THIS problem there is a CHANGE in potential energy as the man is raised from 2.3 to 7.6 meters:

Potential Energy (in joules) = U = mgh      m = mass in kg  g = gravitational constant 9.8 m/sec^2   h = change in height in meters

92.5 kg man     h = 7.6-2.3 = 5.3 meters        92.5 (9.8) (5.3) = potential enrgy change (work done) = 4804.45 j

integration of 1/(x^2 + 4x + 6) equals what

\(\frac{1}{(x^2 + 4x + 6)}\\ =\frac{1}{(x^2 + 4x + 4)+2}\\ =\frac{1}{(x+2)^2+2}\\ =\frac{1}{2}\frac{1}{\left(\frac{x+2}{\sqrt2}\right)^2+1}\\ \qquad let\\ \qquad y=\frac{x+2}{\sqrt2}\\ \qquad \frac{dy}{dx}=\frac{1}{\sqrt2}\\ \qquad \sqrt2dy=dx\\ =\frac{1}{2}\frac{1}{y^2+1}\\\)

\(\int\frac{1}{x^2 + 4x + 6}\;dx\\ =\int \frac{1}{2}\frac{1}{1+y^2}\;dx\\ =\int \frac{1}{2}\frac{1}{1+y^2}\;\sqrt2dy\\ =\int \frac{\sqrt2}{2}\frac{1}{1+y^2}\;dy\\ =\frac{\sqrt2}{2}tan^{-1}y\\ =\frac{\sqrt2}{2}tan^{-1}\left(\frac{x+2}{\sqrt2}\right)+c\\ \)

integration of 1/(x^2 + 4x + 6) equals what

As below:

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I am a bit rusty on questions like this but this is what I think

A paint manufacturer has a daily output X is normally distributed with an average of 450 000 L and a standard deviation of 45 000 L. The states conduit company made available an incentive for the production department. If the daily production is greater than the 90th percentile of the distribution, the department receives a premium. Determine the height of the production conduit in which the payment of premium.

I used this site

http://davidmlane.com/hyperstat/z_table.html

and put in that I wanted 90% below.....   it gave me a z score of 1.282

You may have needed to work this out from the body of a z score table

Now you have

z=1.282

mean=450,000L

SD= 45000L

now you just need to use the formula to get the x score

\(1.282=\frac{x-450000}{45000}\\ 1.282*45000=x-450000\\ 57690=x-450000\\ 57690+450000=x\\ x=507690\\\)

So I think the premium is paid if the production  is over  507 690 L

Here are answers to the first three.  Let's see if you can make use of these to do part (iv) yourself:

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\(\frac{(x-80)}{1,1}= 0,4198\)

\((x-80)=0,4198*1,1\)

\((x-80)=0.46178\)

\(x= 0.46178 +80\)

\(x=80.46178\)

1) 5-[(-3i+4)-2i]

  =5-[-3i+4-2i]

  =5-[-5i+4]

  =5+5i-4

  =1+5i

2) -i(-4+2i)(6-7i)+3

 =    -i    (-4+2i)(6-7i)    +3

=     -i   [ (-4)(6-7i)   +   2i(6-7i)        ]  +3

=     -i   [ (-24+28i)   +   (12i-14i^2)  ]  +3

=     -i   [ (-24+28i)   +   (12i-14*-1)  ]  +3

=     -i   [ (-24+28i)   +   (12i+14)      ]  +3

=     -i   [     -24+14+28i+12i      ]  +3

=     -i   [     -10+40i    ]                  +3

=        +10i-40i^2             +3

=         +10i-40*-1            +3

=         +10i  +  40           +3

=        +10i  +  43       

=        43   +10i 

I suspect that (3) and maybe (4) need brackets.   ://

X= the letter after W, but before Y

Hi MWizzard,  I think you still wanted me to do this problem.    :)

I did c first.

c)

    Volume of air = \(1333\frac{1}{3}cm^3\)

   and that is 2/3 of the total volume  so

   the total volume has to be  \(1333\frac{1}{3}\times \frac{3}{2} = 2000cm^3=2L\)

a)

    20*10*h=2000

    so

    h=10cm

b)

   volume of the water = \(2000-1333\frac{1}{3} = 666\frac{2}{3}ml \)

c)

   I already did 2L

d)

    If you pump air in it will still take up the same amount of space because the water will not compress, just the air pressure will become greater. So when you take out the 200ml of water the air will just expand to take up the space.

Air will take the space of

       \(1333\frac{1}{3}+200=1533\frac{1}{3}cm^3\)

Note: 1cm^3=1ml

Use Pythagoras theorem. The distance between the cars, 10km, is the hypotenuse of a right angled triangle, one leg of which is 6km and the other of which is, say, x km

x = sqrt(10^2 - 6^2) km. 

You can crunch the numbers.

100

52 Cards

Number of red cards = \(13 \times 2 \\ = 26\)

Number of jacks = 4

⁵²P₂ = 2652 ways to get two cards.

Number of ways to get 2 red cards:

²⁶P₂ = 650 ways to get two red cards

Number of ways to get 2 jacks:

⁴P₂ = 12 ways

As the Jack of Hearts and Jack of Diamonds are considered two red cards, subtract one way.

We get 650 + 12 - 1 = 661 ways.

P(2 red card or 2 jacks) = \(661 \over 2652\)

                                      = 0.24925 (correct to 5 significant figures)

                                      = 24.925%

8 = 2^3  so 1/8 = 1/2^3 → 2^(-3)  

x = -3

.

THANK YOU. But other problem are not solved.

As below:

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Thanks Chris :)

I think the function you are asking about is this one:

y = 10 sin [ (pi/9 +4pi) θ ] - 17

Melody's answer for the horizontal translation is correct.....

For the period.....we need to solve this for  "x"

[ pi/9 + 4pi]* x  = 2pi        .......divide through by pi

[ 1/9 + 4] * x  = 2

[ 37/9]x = 2     multiply both sides by 9/37

x = 18/37 rads  = about 27.87°

Here's the graph  [in degrees] :  https://www.desmos.com/calculator/unxizoured

How can you make 10 out of the numbers 1,5,6,8, and 12 using any or all operations?

 \(\begin{array}{rcll} \frac{8\cdot 12}{6} - 5 - 1 &=& 10\\\\ \frac{8\cdot 12}{1+5} - 6 &=& 10\\\\ \frac{5\cdot 6}{12-8-1} &=& 10\\\\ 8- \frac{12}{6} + 5 - 1&=& 10\\\\ 8+ \frac{(5-1)\cdot 6}{12} &=& 10\\\\ 6\cdot (\frac{12}{8}+1)-5&=& 10\\\\ 12-\frac{5+8-1}{6} &=& 10\\\\ \frac{6\cdot 12}{(5-1)} - 8 &=& 10 \end{array}\)