Multiplication Questions

[MathStudent1999]

2. When John Smith started he was paid $10,000 dollars a year. Each year, he recieved a 5% raise. Ignoring taxes how much had he made during his working life after working fro 40 years? Round your answer to the nearest dollar.

This question is a problem that involves geometric sequences. The Forumula for the sum of a geomectric sequence is {a[1-(r^n)]}/(1-r) "a" would be 10,000. "r" would be 21/20, and n would be 40. Simplyfing everything would give me. (10000*{-[(21/20)^40]})/[-(1/20)]. Now I'm stuck. I can't simplyfy this further so I can't finish the problem.

28. Defin a#b to be a squared plus twice b. For example 2#1 = 6. if a#b is equakl to b#a, what is the value of a+b?

I first got the equation which was a^2 + 2b = b^2 +2a. The a^2 - b^2 + 2b - 2a = 0. Nothing comes up nomatter what I do.

Can somone give me some hints, tips, and nudges to the right direction?

 

[srmichael]

2. When John Smith started he was paid $10,000 dollars a year. Each year, he recieved a 5% raise. Ignoring taxes how much had he made during his working life after working fro 40 years? Round your answer to the nearest dollar.

This question is a problem that involves geometric sequences. The Forumula for the sum of a geomectric sequence is {a[1-(r^n)]}/(1-r) "a" would be 10,000. "r" would be 21/20, and n would be 40. Simplyfing everything would give me. (10000*{-[(21/20)^40]})/[-(1/20)]. Now I'm stuck. I can't simplyfy this further so I can't finish the problem.

28. Defin a#b to be a squared plus twice b. For example 2#1 = 6. if a#b is equakl to b#a, what is the value of a+b?

I first got the equation which was a^2 + 2b = b^2 +2a. The a^2 - b^2 + 2b - 2a = 0. Nothing comes up nomatter what I do.

Can somone give me some hints, tips, and nudges to the right direction?

For the first one, just make r = 1.05. No need to make it an improper fraction like 21/20. I'm not sure where the 1 went in your numerator, but the sum would be {10000[1-(1.05)^40]}/(1-1.05) which is approximately = to [10000(-6.03999)]/(-.05) = -60,399.9/-.05 = 1,207,998

28) Complete the square for both "a" and "b" and see if you see if you can take it from there.

 

[soroban]

Hello, MathStudent1999!

28. Define a # b to be a² + 2b.
For example: 2 # 1 .= .2² + 2(1) .= .6.

If a # b = b # a, what is the value of a + b ?

I first got the equation: .a² + 2b .= .b² + 2a

Then: .a² - b² + 2b - 2a .= .0

Nothing comes up no matter what I do.

We have: .a² - b² - 2a + 2b .= .0

Factor: .(a - b)(a + b) - 2(a - b) .= .0

Factor: .(a - b)(a + b - 2) .= .0


We have:

. . a - b .= .0 . . → . . a .= .b

. . a + b - 2 .= .0 . . → . . a + b .= .2

 

[MathStudent1999]

Hello, MathStudent1999!


We have: .a² - b² - 2a + 2b .= .0

Factor: .(a - b)(a + b) - 2(a - b) .= .0

Factor: .(a - b)(a + b - 2) .= .0


We have:

. . a - b .= .0 . . → . . a .= .b

. . a + b - 2 .= .0 . . → . . a + b .= .2

Thanks, I didn't think of factoring like that!