To have roots as described, that means we have the following factors: From multiplicity 2 at x=1 has (x-1)^2 as its factor From multiplicity 1 at x=0 has x as a factor From multiplicity 1 at x = -4 has a factor of x+4 Putting these together we get that P(x) = A (x) (x+4) (x-1)^2 Multiply these out and find P(x) = A (x^2 + 4x) (x^2 - 2x + 1) A ( x^4 - 2x^3 + x^2 + 4x^3 - 8x^2 + 4x ) Combine like terms and find P(x) = A (x^4 + 2x^3 - 7x^2 + 4x) To find A, we use the point they gave us (5, 72) P(5) = A [ (5)^4 + 2(5)^3 - 7(5)^2 + 4(5) ] = 72 A [ 625 + 250 - 175 + 20 ] = 72 A [ 720 ] = 72 Divide both sides by 720 and find that A = 0.1 Final answer: P(x) = 0.1 ( x^4 + 2x^3 - 7x^2 + 4x) or P(x) = 0.1 x^4 + 0.2 x^3 - 0.7x^2 + 0.4x
Answer:
y = -1/2x
Step-by-step explanation:
Okay, so you probably heard of the slope-intercept form, y = mx + b. We have to use that formula to create a line that goes through (2,1), because thats the bisector.
Let's have our point start at the origin, (0,0). This you make our equation of y=mx+b <u>into</u> y = mx + 0. Since it's 0, let's just <em>drop</em> it out of our equation.
So now for slope. Rise/Run is what we're going to use to create our slope. Since we started at the origin, our slope is going to be negative. We can go down one over two from the origin to get to points (2,1) so why can't that be our slope? We're rising -1, and running 2, making our slope -1/2. In the equation, it would be y= -1/2x + 0, which can be simplified into y = -1/2x
It's a lot of writing and explaining, so I hope this helps! Try asking your teacher just to make sure it's correct.
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(a) The equation is given as Q=45e^1.03t
where e=2.718
Taking t=0 the equation will be :
This will give;
Q=45
