tertre

Solution:

So, we have $2+\frac{4}{1+\frac{4}{2+\frac{4}{1+\cdots}}}$, which at first looks rather scary. But we notice a pattern! Because the nested fractions descend forever, the fraction essentially contains itself! So let $a$  equal this fraction:

$a = 2+\frac{4}{1+\frac{4}{2+\frac{4}{1+\cdots}}}$

Thus,

$a = 2+\frac{4}{1+\frac{4}{a}}$

So now, we simply need to solve for a.

$a = 2+\frac{4}{1+\frac{4}{a}} = 2 + \frac{4}{\frac{4+a}{a}}= 2+\frac{4a}{4+a}=\frac{8+2a+4a}{4+a}=\frac{8+6a}{4+a}$


Getting rid of the fraction by multiplying y $4+a$, we get

$4a + a^2 = 8 + 6a \Longrightarrow a^2 - 2a - 8 = 0$



So now we factor...

$a^2 - 4a + 2a - 8 = 0$

$a(a-4)+2(a-4) = 0$

$(a+2)(a-4) = 0$  





So $a$ can be $-2$ or $4$. Since we know, by looking at the fraction, that $a$  must be positive, $a$, and the value of the fraction, must be $\boxed{4}$.

Tell me if you have any questions,

x^3=125

take cube root on both sides

So,  x=5

I think it's Ellipse. 

Here's a similar question: http://www.chegg.com/homework-help/submarine-traveling-90-mph-descending-angle-depression-many-chapter-5.2-problem-58e-solution-9781424089161-exc

Two right angles: 90+90=180

Angle opposite to the 90-degree angles is 150 degrees.

So, the answer is 180-150=$\boxed{30^\circ}$

This is just 5P2, or 5!/3!=5*4=20

Let's take a look at it more closely:

1st day: 1.5

Second day: 2

Third day:2.5

Adding everything up, we get 51 miles 

Smaller hint: Find the domain! 

We know that the formula to find the area of a parallelogram is b*h, so in the first figure, we know that the base is 20cm and the area of 320cm^2. So the height is, 320/20=16. Now, we find the relationship between 20 and 25

20cm=25cm

16cm=?

1cm=25/20

16cm=25/20*16=20

So, the area is 25*20=$\boxed{500}$