geno3141

To change a decimal into a percent, multiply by 100.

therefore,  .25  as a percent is  .25 x 100  =  25%.

10 is also a decimal, because  10  =  10.00

So, multiply  10 x 100  =  1000%

Since you have variables on both sides (there are x's on both sides), subtract the smaller number of x's from both sides:

Since 3x is smaller than 4x, subtract 3x from both sides:

3x - 3x + 1  =  4x - 3x - 2

              1  =  x - 2

Now, add 2 to both sides:

       1 + 2  =  x - 2 + 2

             3  =  x

the formula for potential energy is:  P.E.  =  m·g·h

The values for g (acceleration due to gravity) and h (height) will be the same for both boulders.

The only difference will be in their masses.

If the the boulder with the P.E. of 8,800 J has twice the mass as the other boulder, then it must have twice the P.E. of the other boulder.  The P.E. of the smaller boulder is 4,400 J.

Use the calculator to find (2nd) atan( 0.195121 ), which will be your answer.

Because the problem isn't stated clearly, I'm going to assume that it was tossed from the ground, that the time is in seconds, and that the distance is in feet.

If you graphed this equation, you would get a parabola. Also, if you graphed it, you would get the vertex, which helps answer some of the questions.

We need to know the vertex; the  x-value  of the vertex is found by using the expression:  -b/(2a).

Since the formula is:  y  =  -16t² + 50t,     a = -16   and  b = 50

The  x-value  at the vertex is:  -50/(2·-16)  =  -50/-32  =  1.5625.

1.5625 seconds is the time that it takes to get from ground level to the highest point; it will take another 1.5625 seconds to fall back to the ground. This results in a total launch times of 2(1.5625) or 3.125 seconds.

At 1.5625 seconds, the object will be at its maximum height; put in this value into the equation:

     y  =  -16(1.4625)² + 50(1.5625)  =  39.0625 feet  <---  maximum height

To find its height at 2 seconds:  y  =  -16(2)² + 50(2)  =  36 feet

Since it hits the ground at  3.125  seconds, at  5.3 seconds,  it's laying on the ground (?).

K.E.  =  (1/2)·m·v²

K.E.  =  (1/2)·(0.06kg)·(50 m/s)²

K.E.  =  75 j    (assuming the the mass was in kg)

To solve an extended inequality:  what you do to one part, you must do to all three parts.

You want to get the 'x' all by itself in the center part.

-3  ≤  x - 3 < 2

Add 3:

-3 + 3  ≤  x - 3 + 3 < 2 + 3

       0  ≤  x  < 5

If this is the problem:  -1 / (x + 1)  =  -3 / (x + 7)

Cross-multiply:            -1 · (x + 7)  =  -3 · (x + 1)

Simplify:                             -x - 7  =  -3x - 3

Add  3x  to both sides:         2x - 7  =  -3

Add  7  to both sides:                2x  =  4

Divide by 2:                                x  =  2

CPhill's answer is, in the words of one of my instructors, elegant.

That won't be said for mine; more like a brute force attempt:

To make the typing easier,

let  A  =  (9 + 4√5)^(1/3)          --->          A³  =  9 + 4√5

let  B  =  (9 - 4√5)^(1/3)           --->          B³  =  9 - 4√5

Let  X  =  A + B             So, now:  X  = (9 + 4√5)^(1/3) + (9 - 4√5)^(1/3)    (the problem)

Also:   A·B  =  [ (9 + 4√5)^(1/3) ] · [ (9 - 4√5)^(1/3) ]

                 =  [ (9 + 4√5) · (9 - 4√5) ] ^(1/3)

                 =  [ 81 - 16 · 5 ] ^(1/3)

                 =  [ 1 ] ^(1/3)

                 =  1

Since  A·B  =  1,

     A²·B  =  A(AB)  =  A(1)  =  A  =  (9 + 4√5)^(1/3) 

     A·B²  =  (AB)B  =  (1)B  =  B  =  (9 - 4√5)^(1/3) 

Sinc  X  =  A + B,

        X³  =  (A + B)³  =  A³ + 3A²·B + 3A·B² + B³

        X³  =  (9 + 4√5) + [ 3(9 + 4√5)^(1/3) ] + [ 3(9 - 4√5)^(1/3) ] + ( 9 - 4√5 )

Rearranging:

        X³  =  18 + 3[ (9 + 4√5)^(1/3) + (9 - 4√5)^(1/3) ]

        X³  =  18 + 3[ A + B ]

But, since A + B  =  X

       X³  =  18 + X

       X³ - X - 18  =  0

Factoring:

      (X - 3)(X² + 3X + 6)  = 0

So:  X = 3  or X = [-3 ± i√(15) ] / 2

Since the answer is a pure real number, the answer is  3!

If this is the problem:  (5.2 x 10^7) / (2 x 10^-4)

then the answer is 2.6 x 10^11.

5.2 ÷ 2  =  2.6

10^7 ÷ 10^-4  =  10^(7 - -4)  =  10^(7 + 4)  =  10^11  (when you divide two numbers with the same base, subtract their exponents)