Alan

I assume this is \(x=10^{x/6}-1\) and you want to solve for x.

There is one obvious solution, namely x = 0.  A graph shows there is another solution just beyond x = 4.

This solution needs to be found numerically (or graphically).  Rearrange the equation as \(x=6\log(x+1)\) and a simple iteration works:

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"Can someone find the solutions and the magnitudes of the following problems(This is from my complex numbers unit):

1. (x^4)-1=0

2. (x^3)+1=0

3.(x^3)-1=0

4.(x^6)-1=0

5.(x^6)+1=0"

This might help:

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"The proportion of observations from a standard Normal distribution that take values larger than -2.11 is, rounded to two decimal places, about what number? (Use a calculator.)"

0.98   (or 98.26%)

"is a²-4 prime"

Depends on the value of a.  

If a = 3, then a² - 4 = 5, which is prime.  

If a = 4 then a² - 4 = 12, which is not prime.

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"dn/dt = rn (1 - n/k)

solve for k if:

dn/dt = 127, r= 0.09, n = 2113"

Like so:

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Cut the triangle in two and rotate one part to make a new triangle as below (I've changed the notation somewhat):

Now we must have 2m < u + v   or   m < (u + v)/2  

or  AD < (AB + AC)/2

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When you integrated to find t you put the constant inside the log  term. If you'd simply added the constant to the right hand side you would have found that c₁ = 50ln(50g - 5k)/k and subsequently that k = 50g/65

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Assuming the pressure is in changed then V1/T1 = V2/T2 where V is volume and T is absolute temperature.

120/(273 + 33) = 200/(273 + t),  where t is initial temperature in C.  

I'll you to do the manipulations needed to find the actual value of t.

"Find the velocity of a falling body at t=5 seconds 

Air resistance is proportional to the velocity of the body.

weight of the body=50kg

Height = 100m

Initial velocity = 5m/sec

Limiting velocity = 65/sec"

I've assumed earth gravity above.  However, if you integrate again to find the height after 5 seconds you get a negative height, so perhaps this isn't on earth!  Also, air resistance is more normally taken to be proportional to velocity squared (though this means there is no nice closed form solution for velocity as a function of time - it has to be calculated numerically). 

Many thanks!!