ok. so im resitting igcse maths next week (lol its my 3rd time - hopefully i get it this time xD). but im still rely struggling with algebra and other stuff. eg problems
3x = 9. solve for x. i no the answer but still dont get it
given r = 3, area = pie x r squared. how do i calculate area?
please help soon.
thanks alot
3x = 9. solve for x. i no the answer but still dont get it
given r = 3, area = pie x r squared. how do i calculate area?
please help soon.
thanks alot
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Okay, let me go through the thinking of solving 3X=9:
"3X = 9" says that the value of 3 times X and the value 9 are equal. Now, if two values are equal, and you do the same thing to each of them, they'll still be equal.
So if Jack and Joe have the same number of apples you can give them each two apples and they'll still have the same number. You can double the number of apples they both have, and they'll still be equal.
So your goal is to 'massage' "3X=9" into a form like "X=?" where ? is a number. So long as you use rules that keep the equality true, the answer will be correct.
The obvious answer here is to divide both sides by three. That obviously keeps the statement true. So let's try it:
3X = 9 -> 3X/3 = 9/3
3X is the same as (X)(3). And (X)(3)/3 is the same as X. And 9/3 is 3. So this becomes:
X=3
And that's the answer.
So, we have:
r = 3
a = Pi r^2
To calculate the area, just substitute. Since 'r' is equal to 3, you can replace and 3 with an 'r' and any 'r' with a 3 and anything that was true will still be true. So "Jack has six apples" can be replaced with "Jack has 2 times 3 apples" which can be replaced with "Jack has two times r apples". All the same thing.
So let's do it:
a = pi r^2 -> a = Pi (3)^2
3^2 is 9. So:
a = Pi 9
So the area is 9 times Pi.
Update: "a square has 4 sides of length 4cm. what is the total length around the square?"
The length around a square is just walking each of its four sides once, and they're all the same size. So 4+4+4+4.
"3X = 9" says that the value of 3 times X and the value 9 are equal. Now, if two values are equal, and you do the same thing to each of them, they'll still be equal.
So if Jack and Joe have the same number of apples you can give them each two apples and they'll still have the same number. You can double the number of apples they both have, and they'll still be equal.
So your goal is to 'massage' "3X=9" into a form like "X=?" where ? is a number. So long as you use rules that keep the equality true, the answer will be correct.
The obvious answer here is to divide both sides by three. That obviously keeps the statement true. So let's try it:
3X = 9 -> 3X/3 = 9/3
3X is the same as (X)(3). And (X)(3)/3 is the same as X. And 9/3 is 3. So this becomes:
X=3
And that's the answer.
So, we have:
r = 3
a = Pi r^2
To calculate the area, just substitute. Since 'r' is equal to 3, you can replace and 3 with an 'r' and any 'r' with a 3 and anything that was true will still be true. So "Jack has six apples" can be replaced with "Jack has 2 times 3 apples" which can be replaced with "Jack has two times r apples". All the same thing.
So let's do it:
a = pi r^2 -> a = Pi (3)^2
3^2 is 9. So:
a = Pi 9
So the area is 9 times Pi.
Update: "a square has 4 sides of length 4cm. what is the total length around the square?"
The length around a square is just walking each of its four sides once, and they're all the same size. So 4+4+4+4.