1. The problem statement, all variables and given/known data a) given, a + 5 and 2a-1, one is 40% greater than the other one, solve for a. b) given, 5x[tex]^{4}[/tex] + 4x[tex]^{3}[/tex] + 3x[tex]^{2}[/tex] + Px + Q. When divided by x[tex]^{2}[/tex] - 1, you get a remainder of 0, solve for p and q. c) given csc(6b + [tex]\frac{pi}{8}[/tex]) = sec(2b - [tex]\frac{pi}{8}[/tex]), solve for b. 2. Relevant equations 3. The attempt at a solution please help, i can't get started on these three at all... edit: c) i know that cscx = 1/sinx and secx = 1/cosx, i then cross multiplied to get [tex]cos(2b-pi/8) = sin(6b+pi/8)...
well then you get a+5 = 0.8a - 0.4 + 2a -1 a+5 = 2.8a - 1.4 1.8a - 6.4 = 0 1.8a = 6.4 a = 3.55555556 or 2a - 1 = .4a + 2 + a + 5 2a - 1 = 1.4a + 7 0.6a - 8 = 0 0.6a = 8 a = 13.3333333 therefore a can be 13.333 or 3.555 ?
do you use the original equation? so a = 5, b = 4, and c = 3? but that doesn't work... cause then you get:[tex]5x^4 + 4x^3 + (3 - 5)x^2 - 4x - 3[/tex]
You realize by yourself there's something wrong. Ok. You should come alone to the solution. The next step would be giving you the solution.
I don't see what I could possibly do to get the answer I know that c - a = 3, that's all... but c itself is 3
oh, well i based it on the original... a = 5, b = 4, c = 3... well, then if that's the case, [tex]ax^4 + bx^3 + (c - a)x^2 - bx - c[/tex] [tex]=5x^4 + 4x^3 + (c - 5)x^2 - 4x - c[/tex] therefore [tex] c = 8 [/tex]? and therefore: [tex]P = -4[/tex] [tex]Q = -8[/tex] is that what you meant? Thanks for your help! Means a lot!
Not quite.... You solve for the cases where one term is 40% of the other, not 40% greater then the other, as the question asked! In other words, suppose you have a number (let's say 20) and you want to find the value that is 40% greater. 0.4 * 20 = 8 which is clearly not 40% greater. In fact, it is less! What would you do to determine the value that is 40% greater than 20?
Yes, but that simplifies... 0.4 * 20 + 20 = (0.4 + 1) * 20 = 1.4 * 20 Therefore, a number that is 40% larger than x is 1.4 * x
well at first glance (and i do mean i only "glanced" at it for a split second), i thought the same thing...here are the equations he set up: look closer at the right-hand side of the first equation. 0.4(2a-1) + 2a-1 = 1.4(2a-1), and the original equation becomes a+5 = 1.4(2a-1), which certainly implies that a+5 is 40% larger than 2a-1. likewise, we can see that the left-hand side of the 2nd equation, 0.4(a+5) + (a+5), equals 1.4(a+5). and so equation 2 becomes 1.4(a+5) = 2a-1, which certainly implies that 2a-1 is 40% greater than a+5. your calculations are correct - you just chose to represent the quantity on one side ofthe equation as 0.4x + x instead of 1.4x.
Hi I Like Pi!! (since you like them so much, have a pi: π ) Yes, and now use cosθ = sin(π/2 - θ) to get that in the form sinA = sinB.