Answer:
Question 4 : 10 m
Question 5 : Square root 37
Explanation:
QUESTION 4: So for the this one here we need to make a drawing (unfortunately). Lets break down the question because having a math problem with a ton of words is confusing sometimes. So we have a pole that is 8m high, so we can draw that out. So we take some cable and go 6 m from the bottom of the pole. So now we want to know how long the cable is and if we go from the top of the pole to the bottom 6m away it looks like this. (Below I'll put what I have written) Since now it's a 90 degrees angle there is a specific formula we can use in situations like this. Where we know 2 sides and need 1 more. a^2 + b^2 = c^2 should look familiar if it doesn't its all good! :D a^2 + b^2 = c^2 is called 'Pythagorean's theorem' (we don't really need to know that part) but basically we use it whenever we need to figure out a side when we already know the other two. We know that the straight line is 8, and the horizontal line is 6. So we can use that formula to get the last number. just know that whenever we have the right triangle, we can use the a^2 + b^2 = c^2 to get all the sides for it. The a and b in the formula are always the straight lines. The c is always the slanted line (the red line I drew). We don't know what it is, so we'll just put c^2 into our equation but we can solve for it! So 8^2 would equal to 64. 6^2 would equal to 36. 64 + 36 here gets us 100. Here's another trick you might need to memorize. Whenever there is a number squared like c^2, we can take the square root of both sides to get rid of it. So c^2 just becomes c. It's a little weird but very useful to remember. But if you remember the a^2 + b^2 = c^2 and use that square root technique you can get an A+ every time. :D Now all we need to know is the square root of 100. It's a big one so using a calculator is fine, here its just 10. Therefore our answer is 10.
QUESTION 5: We'll start off by reading 'distance between points' is a big thing to note here. There is a formula that we can directly use here. (I'll write under the picture in black). So distance between points always uses this formula: (In black). Okay, so the formula in black has more letters in it (which sucks) but we can break it down. When we have numbers like this (3, 0) it means (x, y). So I wrote down what the x1, y1, x2, y2, are here. X1 is just the first number, y1 is the second, x2 is the third, and y2 is the fourth. I just plugged in all the numbers from above in the order we put (x2, x1, y2, y1). Basically we can just solve this now! As of right now we'll need to solve (-3 -3)^2 when we solve that we should get 36. Next we're gonna solve (-1 - 0)^2 and we should get the answer of 1. Now we need to solve 36 +1 and we should know that it equals 37. Therefore we'd get answer: square root 37.