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avatar+211 

Only 3, 4, 5, please show me how. 

 May 19, 2018
 #1
avatar+4299 
+1

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

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

\(2h=110\)

\(\boxed{h=55}\)

smileysmiley

.
 May 19, 2018
 #2
avatar+988 
+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

 May 19, 2018
 #3
avatar+988 
+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

 May 19, 2018
 #4
avatar+988 
+2

The next palindrome after 45954 is 46064. 

 

Speed is distance divided by time. 

 

We already know the time, two hours, we just need to calculate the distance. 

 

46064 - 45954 = 110.

 

110 / 2 = 55

 

55 miles per hour, 

 

I hope this helped,

 

Gavin

 May 19, 2018

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