MathProblemSolver101

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Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of f(x) + a(g(x))?

Since we are told that a is a constant, and since the coefficient does not matter so a doesn’t matter. We just need to find the degree of f(x), add it by the degree of g(x) [this is because for any a, b, c, d, a^b * c^d = ac ^ (b+d)] . The degree of f(x) is 4 and the degree of g(x) is 4. We found that the degree are both the same, and it is not multiply (which I thought before) so the largest degree is 4.

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Let m = number of men

Let w = work

Let d = days

We know that m * d = w

Since we are given that m men can finish a piece of work in 100 days, we have

m*100=w

Thus, 100m = w. (1)

We are also given that if there were 10 men less (m-10) it will take 10+100=110 days to finish it.

So we have (m-10)(110)=w,

110m-1100=w. (2)

Now, (1) = (2) because they both have w and so they’re equal.

Thus we have 110m-1100=100m

Subtracting both sides by 100m we have 10m - 1100 = 0.

Adding both sides by 1100 we have 10m = 1100

Dividing both sides by 10 we have m = 110.

Therefore there were 110 men originally.

18 * 18 = (20-2)^2 = 400 - 80 + 4 = 324

(c) 324

What is the degree of the polynomial  p(x)=5x^3−8x^2+4x?

A. 3

B. 2

C. 1
D. 0

DEGREE = highest exponent

 Highest exponent in poly: 3.

Degree = 3

ANSWER: (A) 3

if -5 is a root of the equation 0=x^2-ax-12 what is the other root

let b be the other root

By vieta’s we have -5+b=-(-a)/1 => -5+b=a (EQ 1)

We also have -5b=-12/1 => -5b = -12 (EQ 2)

EQ 2 => 5b = 12 => b = 12/5 (EQ 3)

(For fun let’s find a)

(EQ 3) & (EQ 1) = 12/5 - 5 = a => 12-25 / 5 = a

a = -13/5

—————

ANSWER: 12/5

Using Angle Bisector Theorem, we have 10.5 / y = 16.5 / x (EQ 1)

We also have that x+y=9.  (EQ 2)

cross multiplying EQ 1, we have 10.5x=16.5y

x2 to both sides: 21x=33y

dividing by 3: 7x=11y

x = 11/7 * y (EQ 3)

EQ 2 and EQ 3: 11y/7 + y = 9

11y/7 + 7y/7 = 9

(18y)/7 = 9

Divide both side by 9: 2y/7 = 1

Multiply both side by 7: 2y=7

Divide both side by 2: y=3.5 (EQ 4)

Substitute EQ 4 into EQ 2: 3.5+x=9

x=9-3.5

x=5.5

x=5.5, y=3.5

Long answer short: You need to be trustworthy, active, and have a good rep and answers. This is the bare minimum to have a small chance of qualifying.

Use Vieta's formulas.

sum of roots = -b/a

product of roots = c/a

then do some manipulation, don't be lazy

Why are you posting AoPS questions? I think I know which class you are in. ;) And also dude don't post AoPS questions AoPS is for learning not for posting on web2.0calc.