Answer:
the radius of the base is equal to ![x=2\sqrt[3]{\frac{105}{\pi } }](https://tex.z-dn.net/?f=x%3D2%5Csqrt%5B3%5D%7B%5Cfrac%7B105%7D%7B%5Cpi%20%7D%20%7D)
And the height is equal to:
![y=\frac{840}{\pi(2\sqrt[3]{\frac{105}{\pi}})^{2} }](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B840%7D%7B%5Cpi%282%5Csqrt%5B3%5D%7B%5Cfrac%7B105%7D%7B%5Cpi%7D%7D%29%5E%7B2%7D%20%7D)
Step-by-step explanation:
We write the volume function
where x is the radius of the base and y is the height of the cylinder
The surface of a cylinder is given by
on the interval from 0 to infinity
We now determine the critical values by differentiating and making the equation equal to 0
This equation have 2 complex solutions and one real solution
For x=0 and infinity the equation goes to infinity also so the radius of the base is equal to
And the height is equal to:
![y=\frac{840}{\pi (2\sqrt[3]{\frac{105}{\pi } })^{2} }](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B840%7D%7B%5Cpi%20%282%5Csqrt%5B3%5D%7B%5Cfrac%7B105%7D%7B%5Cpi%20%7D%20%7D%29%5E%7B2%7D%20%7D)
Answer:
142
Step-by-step explanation:
This is a Total Surface Area problem.
The box has 6 faces (sides): front, back, left, right, top, bottom. They are all rectangles. Area of a rectangle is length × width.
You find the area of each face and add them all up.
see image.
TSA = 15+15+21+21+35+35
= 30+42+70
= 142 sq inches
Erica needs 142 pieces of paper to decorate her box.
1 sq yrd = 9 sq. ft
so 30 sq. yards times 9 = 270 square feet
-"270 square feet"-
The factors are therefore; (4x – 3), (x + 3) and (x – 1)
<h3>What is a polynomial?</h3>
A polynomial is is a function that contains an algebraic term which is raised to a particular power.
- If it is raised to power 1 it is linear
- If it is raised to power 2 it is quadratic
- If its is raised to power 3 it is cubic
- If it i raised to power 3 it is quartic
Now we have;
4x³ + 5x² – 18x + 9
Thus we can write;
4x³ – 3x² + 8x² – 6x – 12x + 9
Using the factors;
x²(4x – 3) + 2x(4x² – 3) – 3(4x – 3)
Therefore;
(4x – 3)(x² + 2x– 3)
(4x – 3)(x² + 3x – x – 3)
(4x – 3)(x + 3)(x – 1)
The factors are therefore; (4x – 3), (x + 3) and (x – 1)
Learn more about polynomials:brainly.com/question/21334281
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