#1**+1 **

5. The next palindrome after 45954, is 46064, by calculating.

So, in 2 hours the car traveled 46064-45954=110 miles.

\(2h=110\)

\(\boxed{h=55}\)

.tertre May 19, 2018

#2**+2 **

3.

Once we commonize the denominator, we achieve:

\(\frac{1}{\tan{x}}+\frac{1}{\cot{x}}=\frac{\tan{x}+\cot{x}}{\tan{x}\cdot\cot{x}}\)

Since, the problem gives us the numerical value:

\(\tan{x}+\cot{x}=\frac{144}{25}\),

we just need to solve for:

\(\tan{x}\cdot\cot{x}\).

Since \(\tan{x}\) and \( \cot{x}\) are recipricals, \(\tan{x}\) is opposite over adjacent and \( \cot{x}\) is adjacent over opposite, their product is equal to 1.

So our final expression becomes:

\(\frac{\frac{144}{25}}{1}\) , you can simplify.

I hope this helped,

Gavin

GYanggg May 19, 2018

#3**+2 **

4.

y is only an integer when \(x\sqrt2\) is an integer.

If x is an integer, \(x\sqrt2\), is only an integer when x = 0.

Therefore, there is only one lattice points on the graph.

Here is the line:https://www.desmos.com/calculator/mmw7vprxhx

The one lattice point is: (0, -1)

\(y=0\cdot\sqrt2-1=-1\)

I hope this helped,

Gavin

GYanggg May 19, 2018