im stuck in this question,i tried everything but i failed... can u please help me.
find two numbers whose sum is 32 and whose product is a maximum.
please help me!!!
No one has answered this question yet.
Have you tried trial and error?
yes, at school
is it possible to do?
Of course it's possible.
1 * 32 = 32
2 * 31 = 62
3 * 29 = 78
Keep going till you find the answer.
thanks alot
You're welcome.
what is the vertex form of y-x^2+12x+2
Sure! I can help you with that. To find two numbers whose sum is 32 and whose product is a maximum, you can use the concept of maximizing the product of two numbers given their sum.
Let's denote the two numbers as x and y. We know that their sum is 32, so mathematically, we can write:
x + y = 32
To find the maximum product, we need to find the values of x and y that satisfy this equation while also maximizing their product, which is xy.
To solve this problem, we need to consider the relationship between x, y, and xy. We can rewrite the equation x + y = 32 as y = 32 - x. Then, we can express the product xy as x(32 - x) or 32x - x^2.
Now, to maximize the product, we need to find the maximum value of the quadratic equation 32x - x^2. One way to do this is by finding the vertex of the quadratic equation.
The x-coordinate of the vertex of a quadratic equation in the form ax^2 + bx + c can be found using the formula: x = -b / 2a.
In our case, the quadratic equation is -x^2 + 32x. Comparing this to the standard form ax^2 + bx + c, we have a = -1, b = 32, and c = 0. Plugging these values into the formula, we get:
x = -32 / (2 * -1)
x = -32 / -2
x = 16
So, x = 16 is the x-coordinate of the vertex. To find y, we can substitute this value into the equation y = 32 - x:
y = 32 - 16
y = 16
Therefore, the two numbers that have a sum of 32 and maximum product are 16 and 16.
To check if these numbers satisfy the conditions, let's verify. The sum of 16 and 16 is indeed 32. The product of 16 and 16 is 256, which is a maximum product given the sum of 32.
So, the answer to the question is: the two numbers whose sum is 32 and whose product is a maximum are 16 and 16.