Tuesday, September 7th, 2010

### Solution:

- First, factorize the numerator using prime numbers: 288 = 2*12*12 = 2*3*4*3*4=2*2*2*2*2*3*
- Second, factorize the denominator: 1155 = 5*231=5*7*33 = 5*7*3*11
- Notice that the numerator and denominator have only one factor in common (3).
- Restate the ratio after removing the common factor
- New numerator = 2*2*2*2*2*3 = 96
- New denominator = 5*7*11 = 385
- Same ratio in lowest terms:

Saturday, July 24th, 2010

### Solution:

- 2x – =y=61
- 2x + y= -7

If you subtract the second equation from the first, you can eliminate x and you are left with **-4y = 68.**

So **y =3D -17**, and plugging this into the first equation we can figure out

y: 2x = (-51)=61,

so **x = 5**

Friday, July 23rd, 2010

### Solution:

- 2x – =y=61
- 2x + y= =7

If you subtract the second equation from the first, you can eliminate x and you are left with -4y = 68.

So y = 3D -17, and plugging this into the first equation we can figure out

y: 2x = (-51)=61,

so **x = 5**

Friday, July 23rd, 2010

### Solution:

First, you have to have a clear idea what y = 2x^2+4x-5 means. This is an equation that tells you that, for any value of x, you can find y by dividing by multiplying x by x, and then multiplying that by two, adding 2 times x and finally subtracting 5. Does that sound familiar?

Now, what is the table you have to make? You will list several values of x (which you will be using as x-coordinates in your graph), and for each one use the equation to find what y is. We’ll show the work:

For x = 1, **y** = 2*1*1 + 4*1 – 5 = 1

For x = 2, **y** = 2*2*2 + 4*2 – 5 = 11

For x = 3, **y** = 2*3*3 + 4*3 – 5 = 25

For x = 4, **y** = 2*4*4 + 4*4 – 5 = 43

For x = 5, **y** = 2*5*5 + 4*5 – 5 = 65

Do you see what we did there? We just replaced x in the equation by each value of x, and did the multiplication and addition.

Now your table will look like this:

x | y

–+—–

1 | 1

2 | 11

3 | 25

4 | 43

5 | 65

We’ve only shown the x,y values for 1 through 5, out there are an infinite number of x values that you could plug in, including negative numbers and fractions. You can use the resulting T chart to help you create a graph, which will look like this:

Friday, July 23rd, 2010

### Solution:

First, let’s define what a Newton (N) is: “The Newton (N) is defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s/s (one meter per second per second). Therefore, 1 N = 1 kg =D7 1 m/s/s.”

The force of friction opposing the 325 N force is .25 * 925 N (which is equal to 231.25 N). The force pulling the crate is 325 N * cos(25), i.e. 294.55 N. (This is the component of force acting parallel to the floor.)

Take the difference between these two and you will have the net force pulling the crate (which is 63.3 N). Using Newton’s equation F = ma, you will find the acceleration by dividing the net force by the mass of the crate (the mass is 925 =/(one standard gravity [9.80665 m/s/s], or 94.32 kg). The acceleration is therefore 63.3 N / 94.32 kg, which equals 0.671 m/s/s.

Friday, July 23rd, 2010

### Solution:

The total area is 40π=2πrh+2πr^2

=2πr*8 + 2πr²

=16πr + 2πr²

=16r + 2r²

If we rearrange the terms and divide the terms by 2 (in order to simplify the equation), we get:

r^{2} + 8r – 20 = 0

(r+10) (r-2) = 0

r = 2 or -10

Therefore, **r = 2** (assuming that -10 is not an option!).

Monday, July 19th, 2010

### Solution:

First recognize that this is in the form of (x^{2}-a^{2}), which can always be factored as (x+a)(x-a). If you multiply these two terms, you get x^{2}-ax+ax-a^{2}, which is equal to x^{2}-a^{2}.

So in this case, we can see that **a=3**,

so x^{2}-9

= x^{2}-3^{2}

= **(x+3)(x-3)**

Friday, July 16th, 2010

### Solution:

X is the smallest number

y=x+2

z=x+4

z+2x=25

x+4+2x=25

3x=21

X=7

Y=9

Z=11

The equation that we used to solve the problem is x+4+2x=25, which can be simplified to = x=21.

Friday, July 16th, 2010

### Solution:

**If we let the age of the father be “F”, and the age of the son be “S”, then we know the following:**

**1. F = 3 x S**

2. F+S=40

**Therefore, F=3x(40-F)…so 4F=120. **

**Therefore, F=30 and S=10.**

Friday, July 16th, 2010

Vector quantities have two characteristics: magnitude and a direction. Scalar quantities only have magnitude.