Can you step by step solve 20x+12=4x-16
1 answer:
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Given:
The shape is square.
To find:
The surface area and volume of a square.
Explanation:
The length of each side of the square is "a" units.
The formula for the surface area of the square is,
The formula for the volume of the square is,
Using these formulas, we can find the surface area and the volume of the square that has side length "a" units.
For example:
Let the side length of 3cm for a square.
So, the dimensions are 3cm by 3cm by 3cm.
That is,
The Length is 3cm.
The breadth is 3cm.
The height is 3cm.
So,
The surface area of the square is,
Therefore, the surface area of the square is 54 square cm.
The volume of the square is,
Therefore, the volume of the square is 27 cubic cm.
Answer:
a = 2, b = -2
P is at a minimum
Step-by-step explanation:
For any polynomial function, the turning point is either a maximum or a minimum
It can be determined by taking the first derivative of the function and setting it equal to 0 and solving for x and y
In this case we are given the turning point as x=1, y = 3 and we have to calculate a and b in the equation y = ax² + (ab)x + 5
The first derivative of y, y' = 2ax + ab
If we set this equal to 0 we get 2ax + ab = 0 ==> 2ax = -ab ==> b = -2
So the equation is of the form y = ax² -2ax + 5 (subbing for b)
Since we know that at x = 1, y =3 substitute y and x values in the above equation and solve for a
y = 3 = a(1²) - 2a(1) + 5
a - 2a + 5 = 3
-a + 5 = 3
a = 2
So the equation is of the form y = 2x² -4x + 5
If we plot this we will find that P is a minimum point
However, we can always determine mathematically if P is a max or min by taking the second derivative of the original function and noting the sign. If it is positive, the point is a minimum, and if it is negative, the point is a maximum.
Taking derivatives,
y' = 4x - 4
y'' = (4x-4)' = 4
The sign is positive so P is a minimum
Graph attached for reference
