All Answers 356020 Answers

Thankyou very much CPhill

[y^2-16] / [y^2+16 ]

The only thing that would make this undefined is when the denominator   = 0 .....however......no real number  for  y makes this so....thus.......this is defined for all  real values of y

Only God nows how long a person will live.

2x + 5y

 [(1,3), (1,8), (5,6), (10,3)]

(1,8) maximixes  the function  = 42

5N  - 3  =  3N - 5      simplify

2N  =   -2          divide by 2

N  = -1

sec ( -(168+ 2/15) )   ≈ -1.02184

D) zero......by the triangle inequality......the sum of any two sides must be greater than the remaining side to have a triangle.......but  3 + 1  = 4  ....so ......no triangle possible......

Depends, what is x? Like the previous answer, we cannot help you any further without knowing the value of x.

The shell method seems logical here.....we have

      4

2 pi ∫  (x + 1)[ 5 - (x + 4/x)]  dx  =

      1

      4

2 pi ∫   5x - x^2 - 4 + 5 - x - 4/x     dx

      1

       4

2 pi ∫   4x - x^2 + 1- 4/x     dx    =  [16137 / 1250]  pi units^3

      1

A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?

ln (x^2-1) - ln(x-1) = ln(6)      write as

ln [ (x^2 - 1) / (x - 1) ]  =  ln 6     we can forget the logs

(x^2 - 1) / (x - 1)  = 6     rearrange

x^2 - 1  =  6 (x - 1)  simplify

x^2 - 1  = 6x - 6

x^2 - 6x +  5  = 0     factor

(x - 1) ( x -5) = 0    set each factor to 0    and x  = 1  [reject because it makes one or more logs undefined]  or x  = 5  which is valid..

-1.07365953

21   

1,072,185,500,343,654,697,002,359,332,889,532,999,783,837,967,877,442,950,176,961,050 

Let's say you have a square. That square is split into 10 pieces. Five of those pieces are yellow. That means 5 out of ten are yellow. The slash (/) in a fraction means "out of". So the fraction that represents how many pieces are yellow, is 5/10. 

42. No questions asked. The answer is 42.

u are strange

3.14 as a fraction

That's as simplified as the equation gets. To go further, you would have to know the value of x.

9 plus 10 is 19.

If you need to complete more problems like this just punch them into the calculator on the home page!

Hope this helps!

15 x 20 = 300

sqrt(300) =17.32 Geometric mean.

Solve for x:
log(x^2 - 1) - log(x - 1) = log(6)

log(x^2 - 1) - log(x - 1) = log(1/(x - 1)) + log(x^2 - 1) = log((x^2 - 1)/(x - 1)):
log((x^2 - 1)/(x - 1)) = log(6)

Cancel logarithms by taking exp of both sides:
(x^2 - 1)/(x - 1) = 6

Multiply both sides by x - 1:
x^2 - 1 = 6 (x - 1)

Expand out terms of the right hand side:
x^2 - 1 = 6 x - 6

Subtract 6 x - 6 from both sides:
x^2 - 6 x + 5 = 0

The left hand side factors into a product with two terms:
(x - 5) (x - 1) = 0

Split into two equations:
x - 5 = 0 or x - 1 = 0

Add 5 to both sides:
x = 5 or x - 1 = 0

Add 1 to both sides:
x = 5 or x = 1

log(x^2 - 1) - log(x - 1) ⇒ log(1^2 - 1) - log(1 - 1) = (undefined)
log(6) ⇒ log(6) ≈ 1.79176:
So this solution is incorrect

log(x^2 - 1) - log(x - 1) ⇒ log(5^2 - 1) - log(5 - 1) = log(2) + log(3) ≈ 1.79176
log(6) ⇒ log(6) ≈ 1.79176:
So this solution is correct

The solution is:
Answer: |x = 5

y component of plane = 650   there is no x component w/out wind

y component of wind = 60 sin -45 = -42.42

x component of wind =60  cos-45=  42.42

Add components x's and y's

y = 650-42.42 =607.58

x=  42.42

Angle = arctan 607.58/42.42 = 86 degrees   (4 degrees off course to the east)

Airspeed over ground =  sqrt(607.58^2 + 42.42^2) = 609 km/hr