Is 288/1155 in Lowest Terms

Solution:

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

Solve this problem by using elimination: 2x-3y=61 and 2x+y=-7

Solution:

1. 2x –  =y=61
2. 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

Need to get the answer to this problem by using elimination: =x-3y=61 and 2x+y=-7

Solution:

1. 2x –  =y=61
2. 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

How do you make a T chart for the problem y=2x^2+4x-5

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:

A 925 N crate is being pushed across a level floor by a force of 325 N at an angle of 25 degrees above the horizontal. The coefficient of kinetic friction is 0.25. Find the magnitude of the acceleration of the crate.

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.

The total area of a cylinder is 40. If height = 8, find the radius. (The formula for total area used in class is: Total area = 2πrh + 2πr²)

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:

r² + 8r – 20 = 0

(r+10)  (r-2) = 0

r = 2  or  -10

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

Factor the following expression: x^2-9

Solution:

First recognize that this is in the form of (x²-a²), which can always be factored as (x+a)(x-a). If you multiply these two terms, you get x²-ax+ax-a², which is equal to x²-a².

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

so  x²-9

=  x²-3²

= (x+3)(x-3)

Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest integer, then which equation could be used to solve the problem?

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.

A father is 3 times older than his son and the sum of their ages is 40 years. Find their present age?

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.

What is the difference between a scalar and vector Quantity?

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