F(x) = -4x^7 +x^3 -x^2 +5
a) It is a degree 7 polynomial, so will have 7 zeros (some may be repeated).
b) has 3 sign changes, so 1 or 3 positive real zeros. If odd powers have their signs reversed, the signs are changed to +--+, so there are 2 sign changes. There will be 0 or 2 negative real zeros.
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There is actually 1 positive real zero and 0 negative real zeros. This means there are 3 conjugate pairs of complex zeros.
The volume of a shape is the amount of space in it.
<em>The volume outside the cylinder, but inside the cube is 214.6 cubic inches</em>
The given parameter is:
---- length of the cube
So, the volume of the cube is:
![V_1 = l^3](https://tex.z-dn.net/?f=V_1%20%3D%20l%5E3)
![V_1 = 10^3](https://tex.z-dn.net/?f=V_1%20%3D%2010%5E3)
![V_1 = 1000](https://tex.z-dn.net/?f=V_1%20%3D%201000)
The volume of the cylinder is:
![V_2 = \pi r^2h](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20r%5E2h)
The diameter (d) of the cylinder equals the length of the cube.
This means that:
![d = l](https://tex.z-dn.net/?f=d%20%3D%20l)
![d = 10](https://tex.z-dn.net/?f=d%20%3D%2010)
Divide by 2 to calculate the radius of the cylinder
![r = \frac{10}{2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B10%7D%7B2%7D)
![r = 5](https://tex.z-dn.net/?f=r%20%3D%205)
Also, the height of the cube is::
![h =l](https://tex.z-dn.net/?f=h%20%3Dl)
![h =10](https://tex.z-dn.net/?f=h%20%3D10)
So, we have:
![V_2 = \pi r^2h](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20r%5E2h)
![V_2 = \pi \times 5^2 \times 10](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20%5Ctimes%205%5E2%20%5Ctimes%2010)
![V_2 = \pi \times 25 \times 10](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20%5Ctimes%2025%20%5Ctimes%2010)
![V_2 = \pi \times 250](https://tex.z-dn.net/?f=V_2%20%3D%20%5Cpi%20%5Ctimes%20250)
![V_2 = 785.4](https://tex.z-dn.net/?f=V_2%20%3D%20785.4)
So, the volume (V) outside the cylinder is:
![V = V_1 - V_2](https://tex.z-dn.net/?f=V%20%3D%20V_1%20-%20V_2)
![V = 1000 - 785.4](https://tex.z-dn.net/?f=V%20%3D%201000%20-%20785.4)
![V = 214.6](https://tex.z-dn.net/?f=V%20%3D%20214.6)
Hence, the volume outside the cylinder is 214.6 cubic inches
Read more about volumes at:
brainly.com/question/15861918
Given:
bake sale at least $300
price of each pie is $6.00
let the number of pies be represented by x.
Write the inequality:
6x <u>></u> 300
Solve the inequality:
6x <u>></u> 300
<u>÷6 ÷6</u>
x <u>></u> 50
Graph the inequality.
y = 6x
x is the number of pies sold; x at least 50 and gradually increases.
y is the total sales