# QR's - Question of the Day

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#### Sugafoot79

##### Full Member
10+ Year Member
(A+B)'s share of property is \$20,000 & (B+C)'s share is \$30,000. If A has a share half of that of C, what is the total worth of the property?

#### ohohitsmagic08

##### Full Member
1. A+B=20,000
2. B+C=30,000
3. A=(1/2)C

Therefore, you can plug in the (1/2)C into A in the equation 1 to get:
4. (1/2)C+B=20,000
5. B+C=30,000

Now you have 2 unknowns and 2 equations so you can solve for B and C which can be used to solve for A

#### Sugafoot79

##### Full Member
10+ Year Member
Sweet you the best ohohitsmagic08. I got to that point of 2 equations and two unknowns, but I either got lazy or just a brain fart. This is great motivation. I'll post another one up just to keep it going

#### Sugafoot79

##### Full Member
10+ Year Member
Here is another...(I hate trig)

What is the maximum value for the expression 2sin(pi+x) + sin(x) +2?

#### Shinpe

##### Full Member
Here is another...(I hate trig)

What is the maximum value for the expression 2sin(pi+x) + sin(x) +2?

The largest value any sin or cos can have (as long as there's no irregularities inside the () argument) is 1.

So the max of this expression is 2*1+1+2 = 5

#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
Here is another...(I hate trig)

What is the maximum value for the expression 2sin(pi+x) + sin(x) +2?
Note that sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = -sin(x).

So you have -2sin(x) + sin(x) + 2..

So you really have 2 - sin(x). The way to maximize this is to make sin(x) as LOW as possible. This would be -1. So the maximum value is 3.

Use x = 3pi/2 and get a max value of 3.

Edit: Shinpe there's a pi in one of those parentheses.

#### Shinpe

##### Full Member
Note that sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = -sin(x).

So you have -2sin(x) + sin(x) + 2..

So you really have 2 - sin(x). The way to maximize this is to make sin(x) as LOW as possible. This would be -1. So the maximum value is 3.

Use x = 3pi/2 and get a max value of 3.

Edit: Shinpe there's a pi in one of those parentheses.

I guess I should have taken my own advice on looking inside the parenthesis more seriously lol

Thanks for correction

10+ Year Member
. nvm

#### Sugafoot79

##### Full Member
10+ Year Member
Note that sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = -sin(x).

So you have -2sin(x) + sin(x) + 2..

So you really have 2 - sin(x). The way to maximize this is to make sin(x) as LOW as possible. This would be -1. So the maximum value is 3.

Use x = 3pi/2 and get a max value of 3.

Edit: Shinpe there's a pi in one of those parentheses.

Couple of questions:
sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = -sin(x)

Also, how did you know to use -1?
Did you use the graph of y=sinx/y=cosx?

#### Sublimation

##### Full Member
10+ Year Member
5+ Year Member
Im sooooooo F *** ed for Trig lol. all i remember from highschool where the identities (and even these are iffy) and thats about it lol. You guys know any good trig sources, nothing over the top?

#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
Couple of questions:
sin(pi+x) = sin(pi)cos(x) + cos(pi)sin(x) = -sin(x)

Also, how did you know to use -1?
Did you use the graph of y=sinx/y=cosx?

sin(x+y) = sin(x)cos + sincos(x)

(sine of the first * cosine of the second) plus (sine of the second * cosine of the first)

For cos:

cos(x+y) = cos(x)cos - sin(x)sin

===

I chose -1 since I wanted the largest value for 2 - sin(x).

If you had 2-y and I said y lies between -1 and 1, what would you choose for y to make 2-y the largest? You would choose -1. So that's why I wanted sin(x) to be -1.

#### Sugafoot79

##### Full Member
10+ Year Member
OMG! I luv you!!! Thanks a bunch!!!

10+ Year Member
New Question:

Evaluate:

(t^2+2t+4)/(t+1)

Thanks again!!!

#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
New Question:

Evaluate:

(t^2+2t+4)/(t+1)

Thanks again!!!
It doesn't divide evenly since the numerator doesn't factor into (t+1) * something. You need to do long division...

t+1 into t^2 + 2t + 4

Always put them in decreasing exponential order (highest power first, constant term last) and make sure you fill in the gaps if there's an exponent missing!! If you had t^2 + 1 you'd need to write it as t^2 + 0t + 1.

t goes into t^2, t times. So write a 't' at the top.

Multiply through by t: t * (t+1) = t^2 + t. Subtract from t^2 + 2t + 4.

Get t + 4.

Repeat. t goes into t, 1 time. So you have a +1 up top now. So you have t + 1.

Multiply through by 1: 1 * (t+1) = t+1. Subtract.

Okay I had to go to dinner at that point. Here's the rest:

Subtract the t+1 and get 3 left over. Since t can't go into 3, you're done. You have 3 as a remainder. Proper notation is:

or

t + 1 + [3/(t+1)]

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#### Sugafoot79

##### Full Member
10+ Year Member
Man Street, ur the best. It's been awhile since I've done long division with polynomials. Thanks again.

P.S. Be on the look out. I'll be posting more QR's questions. Thanks again.

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#### Sugafoot79

##### Full Member
10+ Year Member
Here is another:

A mother is twice as old as her son. 12 years ago, the ratio of the mother and son age was 5:2. What was the mother's age 2 years ago?

I hate working with word problems and ratios.

#### Longhorns

##### New Member
10+ Year Member
M = mother
S = son

M=2S

12 years ago...
(M-12)/(S-12) = 5/2
Then you get 2M-24 = 5S-60
Substitute M=2S
Then; 4S-24 = 5S-60
-S = -36 or S=36
M = 2(36) = 72
2 Years ago she was 70

To double check (M-12) = 60 and (S-12) = 24, and 60/24 = 5/2

#### Sugafoot79

##### Full Member
10+ Year Member
Nicely done!

Here is another of which I can't figure out:

If z=x-3, then the value of z+1/z is?

#### jay47

##### Think Positively!
10+ Year Member
5+ Year Member
Man Street, ur the best. It's been awhile since I've done long division with polynomials. Thanks again.

P.S. Be on the look out. I'll be posting more QR's questions. Thanks again.

I haven't seen a math question go unanswered by him in two years....he is good.

#### Sugafoot79

##### Full Member
10+ Year Member
I haven't seen a math question go unanswered by him in two years....he is good.

I know street is awesome!

#### Sugafoot79

##### Full Member
10+ Year Member
Here is how CDM explains it:

z+(1/z) = (x-3) + 1/(x-) = ((x-3)^2 +1)/(x-3) = (10-6x+x^2)/(x-3)

I don't understand how they got (x-3)^2 (see red highlight above)...

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#### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
I haven't seen a math question go unanswered by him in two years....he is good.
Look harder... I've missed a few

Some other good math people around.

#### UCB05

##### Full Member
Question asks for z+(1/z), not (z+1)/z

z + 1/z = (x-3) + 1/(x-3)

multiply the first term by (x-3)/(x-3) to set the same denominator so you can add them together:
(x-3)(x-3)/(x-3) + 1/(x-3)

etc until you get the answer.

#### Sugafoot79

##### Full Member
10+ Year Member
OMG!!! I'm a ****ing idiot!!! Thanks!

#### suhshi

##### Full Member
10+ Year Member
If N is any positive integer, how many consecutive integers following N are needed to insure that at least one of the integers is divisible by another positive integer m?

Im confused

#### jay47

##### Think Positively!
10+ Year Member
5+ Year Member
Here's another for everyone to practice that integrate biology and probability (and don't look at Streetwolf's....err... anyone else's answer, before trying to do it on your own):

Hemophilia, an X linked recessive disorder, causes decreased blood clotting in those with the condition. A mother whose father had hemophilia has children with a normal man.

This couple's son then marries another lady whose father had hemophilia. What is the probability that they will have a daughter with hemophilia?