Answer:
Step-by-step explanation:
We are solving for 
in the equation:
First, isolate the variable term by subtracting 
from both sides of the equation:
Now, divide both sides of the equation by the coefficient of :
This solution for , as a decimal, would be non-terminating. If you divided 
into 
, you would get the non-terminating decimal of:
Therefore, our solution is:
-
We can check our solution by substituting 
for in the initial equation:
Substitute:
Simplify 
:
Add:
Since both sides of the equation are equal, our solution is correct!
Answer:
B = (x + 7)^2 + (y +3)^2 = 4
Step-by-step explanation:
If you've started pre-calculus, then you know that the derivative of h(t)
is zero where h(t) is maximum.
The derivative is h'(t) = -32 t + 96 .
At the maximum ... h'(t) = 0
32 t = 96 sec
t = 3 sec .
___________________________________________
If you haven't had any calculus yet, then you don't know how to
take a derivative, and you don't know what it's good for anyway.
In that case, the question GIVES you the maximum height.
Just write it in place of h(t), then solve the quadratic equation
and find out what 't' must be at that height.
150 ft = -16 t² + 96 t + 6
Subtract 150ft from each side: -16t² + 96t - 144 = 0 .
Before you attack that, you can divide each side by -16,
making it a lot easier to handle:
t² - 6t + 9 = 0
I'm sure you can run with that equation now and solve it.
The solution is the time after launch when the object reaches 150 ft.
It's 3 seconds.
(Funny how the two widely different methods lead to the same answer.)
The answer is from AL2006
Standard reduction of order procedure: suppose there is a second solution of the form
, which has derivatives
Substitute these terms into the ODE:
and replacing
, we have an ODE linear in
:
Divide both sides by
, giving
and noting that the left hand side is a derivative of a product, namely
![\dfrac{\mathrm d}{\mathrm dx}[wx]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bwx%5D%3D0)
we can then integrate both sides to obtain
Solve for
:
Now
where the second term is already accounted for by
, which means
, and the above is the general solution for the ODE.
That answer is 180. The formula is a=bh1/2
