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# Help with 3, 4, 5

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362
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Only 3, 4, 5, please show me how.

May 19, 2018

#1
+4299
+1

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

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

$$2h=110$$

$$\boxed{h=55}$$

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May 19, 2018
#2
+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
+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
+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