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F = G x [M*m]/d^2

F =[6.67  x 10^-11] x [60 * 20] / 2^2

F =0.000000002001 = 2.001 x 10^-9 newtons.

sweet

right back at ya!!

What is the average rate of change over the interval [5pi/4, 7pi/4] with the function f(x) = cot x?

7pi/4 - 5pi/4 = 2pi/4 = pi/2

f(7pi/4)=cot(7pi/4) = -cot(pi/4) = -1

f(5pi/4)=cot(5pi/4) = +cot(pi/4) = +1

f(7pi/4) - f(5pi/4) = -1-1 = -2

Average rate of change = -2 divided by pi/2  = -4/pi

The z score is how many standard deviations a score is away from the mean. If it is lower than the mean then the z score will be negative. If if is bigger than the mean the z score will be poistive. 

Only if you consider a straight line to be a limiting form of a triangle!!

For a normal triangle the two shortest sides must sum to a length greater than the longest side.

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tan(60°) = (3 - 1)/(x - 2) → 2/(x - 2)

tan(60°) = sqrt(3)/2

So:  sqrt(3)/2 = 2/(x - 2)

x - 2 = 2*2/sqrt(3)

x = 2 + 4/sqrt(3) 

x = 2 + 4*sqrt(3)/3

x = (2*3 + 4*sqrt(3))/3  

x = (6 + 4*sqrt(3))/3

"You are working as an engineer for the New York City subway system. Your job is to evaluate the chains which will link the subway cars together. The chains that the city is thinking of using are rated at a maximum of 20,000 N (they will break if they experience a tension larger than this). Subway cars have two chains linking them to the next car (one on the left and right side of the car). Assuming each train has 4 cars, that each car has a mass of 5000 kg, and that the maximum acceleration of the trains is 3.0 m/sec2, are the chains safe to use? Your supervisor will want to know the tension in the chains for each of the three couplings, engineers are picky that way. [Hint: start by considering the forces on the last train car]."

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8n-(2n-3)=12

8n -2n + 3 = 12

6n + 3 = 12    subtract 3 from both sides

6n = 12 - 3

6n = 9              divide both sides by 6

n = 9/6

n= 1 1/2

.5d-3d+5=0

-2.5d + 5 = 0    subtract 5 from both sides

-2.5d = -5          divide both sides by -2.5

d = -5/-2.5

d = 2

-(w+5)=-14

-w - 5 = -14     add 5 to both sides

-w = -14 + 5

-w = -9             multiply both sides by -1

w = 9

2/3+n+6=3/4    subtract 6 2/3 from both sides

n = 3/4 - 6 2/3

n =3/4 - 20/3     GCD of 3 and 4 is 12

n =9/12 - 80/12

n = -71/12

n = - 5 11/12

a/20+4/15=9/15

Solve for a:
a/20 + 4/15 = 3/5

Put each term in a/20 + 4/15 over the common denominator 60: a/20 + 4/15 = (3 a)/60 + 16/60:
(3 a)/60 + 16/60 = 3/5

(3 a)/60 + 16/60 = (3 a + 16)/60:
(3 a + 16)/60 = 3/5

Multiply both sides of (3 a + 16)/60 = 3/5 by 60:
(60 (3 a + 16))/60 = (60×3)/5

(60×3)/5 = (60×3)/5:
(60 (3 a + 16))/60 = (60×3)/5

(60 (3 a + 16))/60 = 60/60×(3 a + 16) = 3 a + 16:
3 a + 16 = (60×3)/5
3 a + 16 = 12×3

12×3 = 36:
3 a + 16 = 36

Subtract 16 from both sides:
3 a + (16 - 16) = 36 - 16

16 - 16 = 0:
3 a = 36 - 16

36 - 16 = 20:
3 a = 20

Divide both sides of 3 a = 20 by 3:
(3 a)/3 = 20/3

3/3 = 1:
a = 20/3

Expand the following:
(2 x - 3)^2

(2 x - 3) (2 x - 3) = (2 x) (2 x) + (2 x) (-3) + (-3) (2 x) + (-3) (-3):
2 2 x x - 3 2 x - 3 2 x - 3 (-3)

2 x×2 x = 2×2 x^2:
2×2 x^2 - 3 2 x - 3 2 x - 3 (-3)

2×2 = 4:
4 x^2 - 3 2 x - 3 2 x - 3 (-3)

-3×2 = -6:
4 x^2 - 3 2 x + -6 x - 3 (-3)

-3×2 = -6:
4 x^2 + -6 x - 6 x - 3 (-3)

-3 (-3) = 9:
4 x^2 - 6 x - 6 x + 9

-6 x - 6 x = -12 x:
4x^2 - 12x + 9

Simplify the following:
sqrt(108) - sqrt(48)

sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):
sqrt(108) - 2^2 sqrt(3)

2^2 = 4:
sqrt(108) - 4 sqrt(3)

sqrt(108) = sqrt(2^2×3^3) = 2×3 sqrt(3):
2×3 sqrt(3) - 4 sqrt(3)

2×3 = 6:
6 sqrt(3) - 4 sqrt(3)

6 sqrt(3) - 4 sqrt(3) = 2 sqrt(3):
2 sqrt(3)

Circumference = Pi x Diameter

Diameter = 2Radii

Circuference =3.141592 x 2R

13 =3.141592 x 2R        divide both sides by Pi x 2

R = 13 /[2 x 3.141592]

R =2.069 feet- The Radius of the circle.

Let A be an odd number, B another odd number A = 2c + 1, B = 2d + 1 (where both c and d are integers) A - B = (2c + 1) - (2d + 1) = 2c-2d + (1-1) = 2(c+d) Since c and d are integers, c+d is an integer too, and A-B is even (since it can be expressed as 2*integer).

 

To get the reciprocal of any fraction, just flip them:

Reciprocal of  n/50 will be 50/ n

600 x 180 =108,000 cm^2- area of the wall
60 x 30 =1,800 cm^2- area of 1 tile
108,000 / 1,800 =60 tiles in total
60 x 3/5 =36 tiles will be  white.
60 - 36 =24 tiles will be blue and green
1/[1+3] x 24 =6 tiles will be green
3/[1+3] x 24 =18 tiles will be blue.

To find the distance of two numbers on the number line, simply subtract the 2 numbers.

PV =Present Value

FV =Future Value

R, or i = Rate of return or Interest

N = Number of periods.

It called “A Bird in Hand”

See, a bird in hand is worth two in the bush. 

So, future money is called “Two Birds in the Bush,” and present money is called, “A Bird in Hand.”

In order to calculate the surface area of a cylinder, you must know 2 measurements. They are the following:

1) The radius

2) The height

Once you know that, plug those values into the formula $A=2\pi r(h+r)$ where h is the height and r is the radius.

Likesqrt(2, 2)

-4 and 9

$\frac{11}{12}+\frac{7}{8}$

First, the denominators must be the same.

$2(\frac{11}{12})+3(\frac{7}{8})$

Simplify.

$\frac{22}{24}+\frac{21}{24}$

Combine.

$\frac{43}{24}$

You cannot simplify any further, so 43/24 is your final aswer.

$m^2-7m-60$

First, multiply a by c.

The base forula for an equation like this is ax²+bx+c.

So, a*b=1*-60=-60

Now, find two factors of 60 that add to -7 and multiply to -60.

In this case, it would be 5 and -12.

$(m+5)(m-12)$