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 x=acos(1 - h /R)  means that

cosx = ( 1 - h/R)

And using the identity

1 - cos^2x = sin^2x , we have

1 - [ 1 - 2h/R + h^2/R^2]  = sin^2x     simplify

[  2h/R - h^2/R^2]  = sin^2x       simplify and take the square root of each side [and assuming the sine is positive]

√[2hR/R^2 - h^2/R^2]  = sin x     

√ [ 2hR - h^2] / R  = sin x       multiply both sides by R

√ [ 2hR - h^2] /   = R sin x

lets pretend that letters and numbers are the same things. so we have got 1234567890 and lets call the letters just capital letters instead so all the numbers are 1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZ. the number plate is a bit like a combinatiobn lock (think about it) and the formula for the number of possible permutaions on a combination lock ( it should be could a permutation lock i don't know why it's called combonation lock ) is:

(amount of different numbers)^{(how many digits wide the lock is)}

so we replace amount of different numbers with 36 and how many digits wide the lock is with 5 to get 36⁵ = 60,466,176

so there you go.

f(x) is a monic polynomial such that f(0)=0 and f(1)=10. If f(x) has degree 2, what is f(x)? Express your answer in the form ax^2+bx+c, where a, b, and c are real numbers.

f(x) = 2.12x² + 7,844x - 0.0043

a = 2.12; b = 7.844; c = -0.0043

f(0) = -0,0043

f(1) = 9.9597

asinus :- )  !

As long as repeats are allowed, the number possible  is (26)(26)*10^3 = 676,000

"At least half" means that he gets 8 or more correct.

Probability of getting 8 correct

C(15,8)(1/2)^8(1/2)^7  = 6435/32768

Probability of getting 9 correct

C(15,9)(1/2)^9(1/2)^6 =   5005/32768

Probability of getting 10 correct

C(15,10)(1/2)^10(1/2)^5 = 3003/32768

Probability of getting 11 correct

C(15,11)(1/2)^11(1/2)^4  = 1365/32768

Probability of getting 12 correct

C(15,12)(1/2)^12(1/2)^3 = 455/32768

Probability of getting 13 correct 

C(15,13)(1/2)^13(1/2)^2 = 105/32768

Probability of getting 14 correct

C(15,14)(1/2)^14(1/2)^1 = 15/32768

Probability of getting 15 correct =

C(15,15)(1/2)^15(1/2)^0  = 1/32768

So....the total probability is  =   [6425 + 5005 + 3003 + 1365 + 455 + 105 + 15 + 1 ] / 32768   =

16374/32768  = 8187/16384

why is it wrong?

???

TROLOLOLOLOLOLOLOLOLOLOLOL

noooooooooooo that's wrong 

to work this out i need the values of p, r and t.

well, the probability of him getting the first question right is 1/2, and the probability of him getting the first and second questions correct is 1/2*1/2 and so on. since there are 15 different questions and 15 is an odd number, at least halve of 15 is [15/2]=8. so that means we have to multiply 1/2 by 1/2 eight times but doing this could be a bit tedious, so we do (1/2)⁸=1/(2⁸)=1/256

so the probability of him getting at least halve the questions correct is 1/256

9.95 times 10 to the 8th power / 4.2805

9.95*10^8/4.2805

= 232449480.2009111085153604 

= 2.324494802009111085153604 *   10^8

For a 2nd degree monic polynomial then a = 1, by definition.

If f(0) = 4 then that means c = 4

With f(1) = 10 we have 1 + b + 4 = 10 so b = 5

f(x) = x^2 + 5x + 4

.

Now that better, thanks!!! Oh and just for correcting you. Question 2 is worng! The answer is to compare the total cost of each plan. So for the DVDs total cost is $66 and for the different gifts is $76.99 so if you compare those two you see that she can afford the DVDs.

• What number do you compare to the total cost of each plan to decide whether it is affordable?

9.95 times 10 to the 8th power / 4.2805Hilfe bitte {nl}

9,95 mal 10 hoch 8 / 4,2805 = 232449480.201

Plan 1: 22*3 = 66, so she can afford plan 1.

Plan 2: 29.26+23.99+23.74 = 76.99, so she can not afford plan 2. 

Question 1: The associtative property of addition (when adding 3 numbers, it doesn't matter which numbers you add first: (a+b)+c = a+(b+c). 

Question 2: The maximum amount of money she can spend, which is $75. 

91s-21t=7(13s - 3t)

Keep the secret to yourself. Don't reveal it to anyone else!!!.

VALUE OF PIE? Apple pie, about $1. Pecan Pie, about $2. Pumpkin pie, about $0.50......etc.!!!!!?????.

If I understand what you are asking (I'm not entirely sure I do!) then when you divide by x to find the other roots, you are dividing by a non-zero value - because you are looking for values of x that are not zero.  The same is true when you divide by any of the other potential roots - although you seem to be dividing by zero (because x-x_a, say, gives a root at x_a) you are not, because now you are looking for values of x that are anything but x_a.

Not sure if that addresses your question!

log_2x+6(8) = 3  means  (2x+6)^3 = 8  so  (2x+6)^3 = 2^3   so  2x+6 = 2 so x = -2

.

What's the domain of this? f(x)= 2x + 1 / sqrt( x^2 + 5x + 8)

\(f(x)= 2x +\frac{1}{\sqrt{x^{2}+5x+8 } }\)

\(x^2+5x+8>0\)

The definition set is D = ℝ

Greeting asinus :- )  !

If the original numerator was 2 and 5 was added to both sides, then that means:

2+5=7 the new numerator. But, after adding 5 to both sides it changed the value of the fraction to 1/2. This means that if numerator was 7, then the denominator would have to be 14, or 7/14 =1/2. Therefore, the original denominator would have to be: 14 - 5 =9. So, the original fraction was:

2/9. So that: [2 + 5] / [9 + 5] =7/14 =1/2.