1. A = πr^2 + 2πrh for h
2. x/4 - y/9 = 1
i just need them explain thoroughly!!!!
2. x/4 - y/9 = 1
i just need them explain thoroughly!!!!
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1. Solving means you have to get h on its own on one side of the equation, so everything else is on the other side.
There is only one term containing h, so first we get that term on its own.
That means getting rid of πr² from the right-hand side,
which we do by subtracting it from both sides:
A - πr² = πr² + 2πrh - πr²
i.e.
A - πr² = 2πrh
Now in the term containing h,
h is multiplied by 2πr
so to get h on its own we divide both sides by 2πr:
(A - πr²)/2πr = 2πrh/2πr
i.e.
(A - πr²)/2πr = h
h = (A - πr²)/2πr
[Is that detailed enough? too detailed?]
2. You don't say whether to solve this for x or y, but I'll assume it's y.
We could start by adding -x/4 to both sides, leaving -y/9 on its own,
but I prefer not to have a minus sign in front of the term we're solving for,
so let's add y/9 to both sides. But then, if we want y/9 on its own, let's get rid of the 1 on the right-hand side by adding -1 to both sides:
x/4 - y/9 + y/9 - 1 = 1 + y/9 - 1
x/4 - 1 = y/9
Now all we need to do to get y on its own is to multiply both sides by 9:
9x/4 - 9 = y
y = 9x/4 - 9
IF we had wanted to solve for x instead of y, we'd start by adding y/9 (but not -1) to both sides,
then after that multiply both sides by 4, giving
x = 4y/9 + 4
There is only one term containing h, so first we get that term on its own.
That means getting rid of πr² from the right-hand side,
which we do by subtracting it from both sides:
A - πr² = πr² + 2πrh - πr²
i.e.
A - πr² = 2πrh
Now in the term containing h,
h is multiplied by 2πr
so to get h on its own we divide both sides by 2πr:
(A - πr²)/2πr = 2πrh/2πr
i.e.
(A - πr²)/2πr = h
h = (A - πr²)/2πr
[Is that detailed enough? too detailed?]
2. You don't say whether to solve this for x or y, but I'll assume it's y.
We could start by adding -x/4 to both sides, leaving -y/9 on its own,
but I prefer not to have a minus sign in front of the term we're solving for,
so let's add y/9 to both sides. But then, if we want y/9 on its own, let's get rid of the 1 on the right-hand side by adding -1 to both sides:
x/4 - y/9 + y/9 - 1 = 1 + y/9 - 1
x/4 - 1 = y/9
Now all we need to do to get y on its own is to multiply both sides by 9:
9x/4 - 9 = y
y = 9x/4 - 9
IF we had wanted to solve for x instead of y, we'd start by adding y/9 (but not -1) to both sides,
then after that multiply both sides by 4, giving
x = 4y/9 + 4
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1. A = πr^2 + 2πrh ...
therefore A - πr^2= 2πrh [since πr^2 was added to the right hand side, we subtract it from A]
Example:
6=4+2
6 - 4= 2
h= (A - πr^2)/2πr [since h was multiplied by 2πr, we divide A - πr^2 by 2πr
Example:
6=3*2
so 3=6/2
2. This equation can't be solved in the true sense of working out values for x and y.
It's like saying that x+y= 100. There are many answers, eg if x=50, y=50. If x=10, y=90. If x=60,y=40.
Same thing for your equation, the most we can do is make x or y the subject.
x/4 - y/9 = 1
Multiply all sides by 36.
9x - 4y = 36
9x-36 = 4y
y= 9x/4 - 36/4
y=9x/4 - 9
Note: I have rewritten it to make y the subject, but this is not the same as 'solving' it.
therefore A - πr^2= 2πrh [since πr^2 was added to the right hand side, we subtract it from A]
Example:
6=4+2
6 - 4= 2
h= (A - πr^2)/2πr [since h was multiplied by 2πr, we divide A - πr^2 by 2πr
Example:
6=3*2
so 3=6/2
2. This equation can't be solved in the true sense of working out values for x and y.
It's like saying that x+y= 100. There are many answers, eg if x=50, y=50. If x=10, y=90. If x=60,y=40.
Same thing for your equation, the most we can do is make x or y the subject.
x/4 - y/9 = 1
Multiply all sides by 36.
9x - 4y = 36
9x-36 = 4y
y= 9x/4 - 36/4
y=9x/4 - 9
Note: I have rewritten it to make y the subject, but this is not the same as 'solving' it.