X^5 + ax^3 + bx^2 - 3 = (x^2 - 1)Q(x) - x - 2

find the value of a and b?

9514 1404 393

Step-by-step explanation:

Subtracting the remainder from the original polynomial gives a polynomial that has (x^2 -1) as a factor. Dividing, we find the quotient and remainder to be ...

  (x^5 +ax^3 +bx^2 +x -1)/(x^2 -1) = (x^3 +(1+a)x +b) remainder (2+a)x +(b -1)

Since we want the remainder to be zero, we require ...

  2+a = 0   ⇒   a = -2

  b -1 = 0   ⇒   b = 1

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The attachment shows the division as given in the problem statement (with the given remainder expression).

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

3x + 4y -25 =0 represents the amount of change sianna should recieve