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nirvana33 [79]
3 years ago
11

Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.

Mathematics
1 answer:
Shtirlitz [24]3 years ago
8 0

We could write such a number as

10^5a+10^4b+10^3c+10^2a+10b+c

=10^2(10^3+1)a+10(10^3+1)b+(10^3+1)c

=(10^3+1)(100a+10b+c)

10^3+1=1001=13\cdot77 so we're done.

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What natural disaster would pose the most serious threat to buildings were
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Answer:

The answer is "floods"

Step-by-step explanation:

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Sec squared 55 - tan squared 55
sergejj [24]

<u>Answer: </u>

sec squared 55 – tan squared 55  = 1

<u>Explanation:</u>

Given, sec square 55 – tan squared 55

We know that,

\sec \Theta=\frac{\text {hypotenuse}}{\text {base}}

And,

\tan \theta=\frac{\text { perpendicular }}{\text { base }}

where Ө is the angle

Substituting the values

\left(\frac{\text {hypotenuse}}{\text {base}}\right)^{2}-\left(\frac{\text { perpendicular }}{\text {base}}\right)^{2}

Solving,

\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}

According to Pythagoras theorem,

\text { (hypotenuse) }^{2}-\text { (perpendicular) }^{2}=(\text { base })^{2}

Putting this in the equation;

squared 55 - tan squared 55 =

\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}=\frac{(\text {base})^{2}}{(\text {base}) *(\text {base})}=1

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6 0
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