All Answers 356050 Answers

step 1 distribute the 8 into 2x-14

16x-112 +13 = 4x-27

step 2 combine like terms

16x-99 = 4x-27

 step3 subtract 4x from both sides

12x -99 = -27

step 4 add 99 to both sides

12x = 72

step 5 divide both sides by 12

x = 6

Here is an oold answer.

think about which terms could be included

x^4, x^3, x^2  will all tead to terms the power of x bigger than 1

so the only bit that could be relevant is (x+1)^4

the general term in the expansion is   \(\binom{4}{n}x^n\)   where x can be 0,1,2,3,or 4

so the term you want is  \(\binom{4}{1}x^1=4x\)

so the coefficint of x is 4

None.    Zero.    Nada.    Nix.  

g(x)=x+sinx

f(x)=x^4

There is a start

3 batches    *     7/12   cup/batch   = 21/12 =   1  3/4 cups              ( note that the number of pancakes per batch is irrelevant)

5 min = 1/12 hr      in five minutes your friend will have a  3 m/hr * 1/12 hr = 1/4 mile head start

    You are walking two miles per hour faster and will take    1/4 m / 2 m/hr = 1/8 hr to catch her = 7.5 mins

         7.5 + 5 = 12.5 mins

Find slope , m, between the points    (y1-y2) / (x1-x2) =  -1

y = -x + b    sub in one point to find b = 10

y = -x + 10       when the line crosses the x axis    y = 0

0 = - x + 10       shows   x = 10

For clarity, I re-labelled the points   alpha and beta in the diagram below

   Now if you look at point R    you can see that it is just point  b   minus the amount of point  a    ......   right?

      similarly    point   b    PLUS the maount of point  a     would land you at  S

        b   is approximately 145 degrees      2 * 145 = 290 degrees ....which would be point  U

              look at point  a     go the same amount in the clockwise direction from the x-axis to get to   -a  ...... this would be point  T

The shaded sector is  60 degrees out of the ENTIRE circle's 360 degrees

Find the area of the ENTIRE circle by using   Area = pi r²

     then multiply by   60 / 360   to get the answer in ft²

8.5/0.5 = 17

17 * 25 = ___

It has been a while since I did these kind of calculations, but here is my stab at it :

140 MPa  = 140 x 106  N/m²

15 m - 1.6 m free board  = 13.4 m high

Volume of the cylinder of molasses = pi r² h  = pi (12)²  * 13.4  = 1929.6 pi  m³

    mass of this volume        1929.6 pi m³  ( 1.5)(1000 kg/m³)   = 2 894 400 pi kg

Find stress using    F_s = ma     using mass above   =  28 394 064 pi  N

Now find the thickness ( if 100% weld efficiency)

   F = stress * area             where stress is  28 394 064 pi N     area = pi d t = pi 24 t  =  75.39822 t

   140 x 10^6 N/m²  =  28 394 064 pi  N  * 75.398223 t  m²

       solve for t = .0208155 m       

Now factor in the 80% efficiency of the welds     .0208155 m / .8 = .02601 m   =   ~~ 3 cm     ( I think !    ~ EP  )

Hello ElectricPavlov, 

Thank you very much for the response, I greatly appreciate your help. Can you please explain your thought process for solving this question? It would really help me in future problems such as this. 

128.67m

2/3  of  3/4   =  2/3 * 3/4 =   6/12  = 1/2 of a large pizza

Guess I should have noted that the equation is 'balanced' ..... for the solution posted above to be true.

r = b - a

s = a + b

u = 2 b

t = - a

2KI+Pb(NO3)2⟶ 1 PbI2+2KNO3             One mole of lead iodide is produced from 2 moles of KI

1 item for 1 penny

1 item for 2 pennies

1 item for 3 pennies

1 item for 5 cents

1 item for 6 cents

1 item for 7 cents

1 item for 8 cents

1 item for 10 cents

1 item for 11 cents

1 item for 12 cents

1 item for 13 cents

1 item for 25 cents 

1 item for 26 cents 

1 item for 27 cents

1 item for 28 cents

1 item for 30 cents

1 item for 31 cents

1 item for 32 cents

1 item for 33 cents

1 item for 35 cents

1 item for 36 cents

1 item for 37 cents

1 item for 38 cents.

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Total  23 different items for exact change.

Have you drawn the picture?

If you have then you will see that there are 2 pairs of similar triangles.

You can solve the ratios simultaneously to get your answer.  This  part is actually very easy.

If you want to interact with me then you are encouraged to do so.

y=g(x)

y'=g'(x)

g'(4)=-3

The tangent of g(x) is  y=-3x-11       and   when   x=4    y=-1      so   (4,-1) is on the tangent point.

When x=4

g(4)=-1

[g(4)]^3 = (-1)^3 = -1

\(\frac{d}{dx}[g(x)]^3=3[g(x)]^2*g'(x)\\ \frac{d}{dx}[g(4)]^3=3[g(4)]^2*g'(4)\\ \frac{d}{dx}[g(4)]^3=3[-1]^2*-3\\ \frac{d}{dx}[g(4)]^3=3*1*-3\\ \frac{d}{dx}[g(4)]^3=-9\\ \)

so the gradient of the tangent of [g(x)]^3 at x=4 is -9

I did do a sample graph to check it worked at least for that example.  It did  

Draw XY.

This creates right triangle(WXY).

By the Pythagorean theorem, WY  =  4·sqrt(2).

Since triangle(WXY) is an isosceles right triangle, angle(XYW) = 45^o.

This makes angle(ZYW) = 90^o.

Use the Pythagorean Theorem:  WZ²  =  WY² + YZ².

--->     9²  =  [ 4·sqrt(2) ]² + a²

Finish this to get the answer ...