Maximize Q = xy^2, where x and y are positive numbers, such that x + y^2 = 4.
1 answer:
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Form an equation. Start by representing the number you want to find as X. Now add 1.
X + 1
Now we need to triple it. That basically means multiply X+1 by 3. You can write that as:
3 (X + 1)
Now we write out that the result is 17 more than the number we want to find. So set an equals sign up
3 (X + 1) =
And now write X + 17
3 (X + 1) = X + 17
Now we solve for X.
Firstly, let's get rid of the X on the right.
Remember, if we want to get rid of a number of variable on one side, we need to use opposites, and do the same to the other side of the equation.
In this case, we have a positive X on the right. To get rid of that, we subtract X from both sides. This will leave us with:
2x + 3 = 17
Now let's get rid of the +3 on the left. To do this, we subtract 3 from both sides of the equation.
2x = 17 - 3
2x = 14
Now we just need to get X by itself. The 2 in front of the X multiplies X by 2. Therefore, to get X on its own, we need to divide 2x by 2, which just gives us 2.
We also need to divide the other side by 2, because if we do something on one side, we need to do something on the other too. So divide 14 by 2, and we get 7.
X = 7
But before we celebrate, let's double check the answer. Add 1 to 7. This gives us 8. Triple 8. This is 24. This should be 17 more than 7. So go, 24 - 17. And whaddya know - it's 7!
X + 1
Now we need to triple it. That basically means multiply X+1 by 3. You can write that as:
3 (X + 1)
Now we write out that the result is 17 more than the number we want to find. So set an equals sign up
3 (X + 1) =
And now write X + 17
3 (X + 1) = X + 17
Now we solve for X.
Firstly, let's get rid of the X on the right.
Remember, if we want to get rid of a number of variable on one side, we need to use opposites, and do the same to the other side of the equation.
In this case, we have a positive X on the right. To get rid of that, we subtract X from both sides. This will leave us with:
2x + 3 = 17
Now let's get rid of the +3 on the left. To do this, we subtract 3 from both sides of the equation.
2x = 17 - 3
2x = 14
Now we just need to get X by itself. The 2 in front of the X multiplies X by 2. Therefore, to get X on its own, we need to divide 2x by 2, which just gives us 2.
We also need to divide the other side by 2, because if we do something on one side, we need to do something on the other too. So divide 14 by 2, and we get 7.
X = 7
But before we celebrate, let's double check the answer. Add 1 to 7. This gives us 8. Triple 8. This is 24. This should be 17 more than 7. So go, 24 - 17. And whaddya know - it's 7!
Answer:
Step-by-step explanation:
we have
step 1
Convert mixed number to an improper fraction
step 2
Adds the fractions
step 3
Convert to mixed number
Answer:
4.2
Step-by-step explanation: