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sin 2theta = 2 sin cos

                 = 2 ( 3/5)(4/5) = 24/25

cos 2theta = cos^2 - sin^2

                  = (4/5 )^²  - (3/5)^2   =  16/25 - 9/25 =  7/25

SImilar for alpha....use double angle identities .....           tan(2alpha) =  2 tan / (1- tan²  ) .

Sum of boys /5   = 9.8               Sum of girls/15 = 10.2

S_b  = 5* 9.8 = 49                         Sg  = 153

(49 + 153)/  (5+15) = 10.1 years

Area = pi r^2

100 pi = pi r^2

100 = r^2

r = 10  units

There are 8x 8 = 64 possible rolls

ways to sum to 15:

78

87      two ways         2/64 = 1/32

Area = pi r^2

Circumference = pi d

   240       = pi d

d = 240/pi                    r = 120 / pi

Area = pi r^2 =   pi (120 /pi)^2 = 14400 / pi  ft² = 4583.66 ft ²

angle JIL encompasses the rest of the circle arc    360 - 228 = 132

  the angle inscribed on the circle encompasses 2 times as much arc    angle JIL = 66^o

Angle IJK and angle and angle ILK are supplementary (opposite angles inscrided quadrilateral = 180)

   180 - 131 = 49^o  = angle ILK

I think thats wrong.

From  fifth to 32 terms is  27 terms    or    27d

9 + 27d = -84

27d = -93

d = - 93/27

from   fifth  term  to  23rd     is 18 d

a₂₃  = 9 + 18 (-93/27) = -53

Evaluate the expression for x=-2. No decmial values in answer. 1/x/x^4. The answer is -1/32 but i dont know how to solve it i keep getting 8 please help and explain what i did wrong. This is using exponent rules! Thank you so much! :)   

    1                              x⁴  

———   divided by   ———  

    x                              1  

To divide by a fraction, invert the divisor and multiply.  

    1                                1     

———   multiplied by  ———  

    x                                x⁴     

    1                                1     

———   multiplied by  ———  

  –2                              (–2)⁴     

    1             1     

———  •  ———  

  –2            16  

Take it from there.

_.

Can anyone help Solveit ?

Set theory like this is quite alien to me.  I'm sorry I cannot help you Solveit.   

Hi Cal  :)

There are three turning points, so you have a fourth order polynomial.  It has roots at -5 and -1 (i..e. places where the function is zero.

Write the function as f(x) = -(x + 5)(x + 1)(x - a)(x - b)  where a and b are to be found (the initial negative sign is because the function goes to -infinity as x goes to +/- infinity)

When x = 0 we have f(0) = -25, so    -5*a*b = -25  ...(1)

There gradient of f is zero when x = -3, so differentiate f with respect to x and set the result equal to zero (with x = -3)

df/dx = -(4*x^3 + (18-3a-3b)*x^2 + (2ab-12a-12b+10)*x - 6ab - 5a -5b) 

so 4*(-3)^3 + (18 - 3a - 3b)*(-3)^2 + (2ab -12a -12b + 10)*(-3) -6ab - 5a -5b = 0   ...(2)

You now have two equations for the two unknowns a and b.

Can you take it from here?

I think you mean f(x)^16 rather than f(x)16.  This question has been asked and answered several times.  Search the Answers for the solution.

4 + 4 + 5.1 + 5.1 ≈ 18.2 

I figured this one out, no need to answer it anymore 

I don't know.  This looks hard.

1. The coefficient of a^9*b^11*c^4 is 1440.

2. The cofficient of u^2*v^9 is -432.

4 miles+1 mile= 5 miles

They are about 5 miles apart 

I thought it was window!!!

Hey there!

First you must find what the angles are. Angles $KJL$ and $MLN$ are equal, we can use this to find $x$,

$6x-2=5x+10$

$x=12^o$

Using this you now know what all angles are going to be:

$KLJ=70^o,MLN=70^o, NML=65^o, KJL=60$

Also using the knowledge that there is $180^o$ in a triangle you can find the last 2 angles:

$JKL=180-70-60=50^o$

$MNL=180-70-65=45^o$

Finally you can use this to find the true statements that you have provided.

Let me know how you go :)