For this case we have the following function:
By power properties we can rewrite the function as follows:
We have then:
Then rewriting the function we have:
Answer:
an equivalent function to is:
Can someone solve? i’ll mark brainliest!
1 answer:
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Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
= x²y cubic feet
1000 = x²y
y = -------(1)
Material used in the prism = Surface area of the rectangular prism
= 2(lb + bh + hl)
Here, h = height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
S = 2(x² + 2xy) - x²
S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² +
= x² +
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x -
2x - = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y =
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.
What is the Pythagorean Theorem?
The PyTheorem states that -- actually, why not just simplify things and make it a formula?
where a and b are legs of a triangle and c is the hypotenuse of a triangle.
It is only true applying to right triangles.
Now what are the legs of a triangle?
The sides that are NOT opposite the 90 degree angle!
Now, all you have to do is find the LENGTHS of the three triangles!
Rise over run, remember?
Let's take the triangle in the top right of the coordinate plane for example.
A=(1,1)
B=(4,4)
unnamed point=(4,1)
Rise, or length of unnamed point to B?
(4,1) to (4,4)
(x,y), remember!
So? 4-1=3!
Run, or length of unnamed point to A?
(1,1) to (4,1)
Remember (x,y)?
So, 4-1=3!
The triangle has legs of 3 and 3.
Square em and add!
9+9=18
That's for length of AB!!
Now do the same for the remaining lengths!
Hope this helps!
The PyTheorem states that -- actually, why not just simplify things and make it a formula?
where a and b are legs of a triangle and c is the hypotenuse of a triangle.
It is only true applying to right triangles.
Now what are the legs of a triangle?
The sides that are NOT opposite the 90 degree angle!
Now, all you have to do is find the LENGTHS of the three triangles!
Rise over run, remember?
Let's take the triangle in the top right of the coordinate plane for example.
A=(1,1)
B=(4,4)
unnamed point=(4,1)
Rise, or length of unnamed point to B?
(4,1) to (4,4)
(x,y), remember!
So? 4-1=3!
Run, or length of unnamed point to A?
(1,1) to (4,1)
Remember (x,y)?
So, 4-1=3!
The triangle has legs of 3 and 3.
Square em and add!
9+9=18
That's for length of AB!!
Now do the same for the remaining lengths!
Hope this helps!