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Now your friend has found proof and is about to start writing it up_ Warn them about 2 common mistakes they might make in writing proof and how to avoid them....

Question

Now your friend has found proof and is about to start writing it up_ Warn them about 2 common mistakes they might make in writing proof and how to avoid them.

Now your friend has found proof and is about to start writing it up_ Warn them about 2 common mistakes they might make in writing proof and how to avoid them.



Answers

LOGICAL REASONING Your friend does not understand how the product of $a$ and $(b+c)$ is given by both $a b+a c$ and $b a+c a$ Use the properties of multiplication to write a convincing argument to show your friend that both statements are correct.

We have to know what vertical angles need in order to answer this question. A vertical able is an opposite pair of angles that are formed by two opposite raise or two opposite sides of the line. So this would be an example of a pair of vertical angles. These raise Thies air straight raise that are going in the exact opposite direction of these race. So if we look at this picture angle one angle four are the angles in question. These are the to raise that create angle one. But these are not opposite raise. They're not going in the opposite direction of those from angle one. These two raised you not form two straight lines. So therefore, these air, not vertical angles. So your friend is correct. These are not congruent because they're not vertical angles.

Okay, So if we get a air message when we try to plug this into our calculator, what might be happening is we might be considering our native assign to be inside of our power of 3/2 because we could be right. This as a radical, that is, it's the square roots of native nine to part of three if we include our negative inside of our, um, power of do or two. But this is actually not the case. He actually have native nine to depart of today over to, and this year is equal to square roots of nine to the power of three. So that's equal to negative 3 to 53 which is equal to negative 27.

Different. Probably joint, you compute man escort line. But instead they put minus my people. Just got road doesn't means that doesn't result in the skull of the minus, and I just give it a result in the imaginary number. So that's where that calculated shows the error.

Matter. Alien off 100 kilogram weight stepped on Earth. No, What would happen is off 2 100 kilograms off. Normal matter can combine with this antimatter on become pure energy because matter and antimatter, for example, like an electron and a positron when they meet each other, they're simply unholy, unplayed themselves into energy on the amount of energy released will obviously be easy, called M C Square, where M is the total mass that was lost. So when 200 kilograms off masses lost, the amount off energy released will be 200 kg times C squared, which is three into 10 party meter per second squid. No, this will be 200 times nine times 10 par 16 Jules, which can be read in us 18 times in part 18. Jules. So that's a moat to into 10. Part 19. Jules, no. How much is this? Obviously the one thing that is wrong in the question is the fact that the whole world would not explore in tow pure radiant energy. Only 100 grams off the world would exploring the pure radiant energy Not all off the not all of our it will explode. But at the same time. This is a tremendous amount of energy. The first nuclear bomb dropped in on here. Oshima produced about 63 Terra Jules Affinity, which is 63 times 10 part 12 Jules. So this alien would be equivalent toe it owned. You can simply divided That's 20 part, 20 times 10 plastic 18 divided by 63 times 10 part well, so that's about 300,000 such bombs. So that alien would cause an explosion that is equivalent to 300,000 off little by bombs that were dropped on Hiroshima. So obviously it would be a catastrophe. But not all off earth would simply vanishing on become a pure, radiant cloak off in it.


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