Answer:
a) We get ![\mathbf{A+B=x^2-2x+1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%2BB%3Dx%5E2-2x%2B1%7D)
So, Is the result of A+B is a polynomial:Yes
b) We get ![\mathbf{A-B=6x^3-7x^2+2x-1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA-B%3D6x%5E3-7x%5E2%2B2x-1%7D)
So, Is the result of A-B is a polynomial:Yes
c) We get ![\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}](https://tex.z-dn.net/?f=%5Cmathbf%7BA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2%7D)
So, Is the result of A.B is a polynomial:Yes
Step-by-step explanation:
We are giving the polynomial equations:
![A= 3x^2(x-1)\\B=-3x^3+4x^2-2x+1](https://tex.z-dn.net/?f=A%3D%203x%5E2%28x-1%29%5C%5CB%3D-3x%5E3%2B4x%5E2-2x%2B1)
We need to find
a) A+B
![A+B=3x^2(x-1)+(-3x^3+4x^2-2x+1)\\A+B=3x^3-3x^2-3x^3+4x^2-2x+1\\A+B=3x^3-3x^3-3x^2+4x^2-2x+1\\A+B=x^2-2x+1\\](https://tex.z-dn.net/?f=A%2BB%3D3x%5E2%28x-1%29%2B%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA%2BB%3D3x%5E3-3x%5E2-3x%5E3%2B4x%5E2-2x%2B1%5C%5CA%2BB%3D3x%5E3-3x%5E3-3x%5E2%2B4x%5E2-2x%2B1%5C%5CA%2BB%3Dx%5E2-2x%2B1%5C%5C)
So, we get ![\mathbf{A+B=x^2-2x+1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%2BB%3Dx%5E2-2x%2B1%7D)
So, Is the result of A+B is a polynomial:Yes
b) A-B
![A-B=3x^2(x-1)-(-3x^3+4x^2-2x+1)\\A-B=3x^3-3x^2+3x^3-4x^2+2x-1\\A-B=3x^3+3x^3-3x^2-4x^2+2x-1\\A-B=6x^3-7x^2+2x-1\\](https://tex.z-dn.net/?f=A-B%3D3x%5E2%28x-1%29-%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA-B%3D3x%5E3-3x%5E2%2B3x%5E3-4x%5E2%2B2x-1%5C%5CA-B%3D3x%5E3%2B3x%5E3-3x%5E2-4x%5E2%2B2x-1%5C%5CA-B%3D6x%5E3-7x%5E2%2B2x-1%5C%5C)
So, we get ![\mathbf{A-B=6x^3-7x^2+2x-1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA-B%3D6x%5E3-7x%5E2%2B2x-1%7D)
So, Is the result of A-B is a polynomial:Yes
c) A . B
![A.B=3x^3(-3x^3+4x^2-2x+1)-3x^2(-3x^3+4x^2-2x+1)\\A.B=9x^6+12x^5-6x^4+3x^3+9x^5-12x^4+6x^3-3x^2\\A.B=9x^6+12x^5+9x^5-6x^4-12x^4+3x^3+6x^3-3x^2\\A.B=9x^6+21x^5-18x^4+9x^3-3x^2](https://tex.z-dn.net/?f=A.B%3D3x%5E3%28-3x%5E3%2B4x%5E2-2x%2B1%29-3x%5E2%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA.B%3D9x%5E6%2B12x%5E5-6x%5E4%2B3x%5E3%2B9x%5E5-12x%5E4%2B6x%5E3-3x%5E2%5C%5CA.B%3D9x%5E6%2B12x%5E5%2B9x%5E5-6x%5E4-12x%5E4%2B3x%5E3%2B6x%5E3-3x%5E2%5C%5CA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2)
So, we get ![\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}](https://tex.z-dn.net/?f=%5Cmathbf%7BA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2%7D)
So, Is the result of A.B is a polynomial:Yes
Answer:
(20+75)/6 < (20+75)/2 < (20+75) × 3 < (20+75) × 4
Step-by-step explanation:
just solve each problem and compare the values.
Answer:
The given statement is correct for all positive integers.
Step-by-step explanation:
The given inequality is
for all positive integers
![\frac{1}{x}1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%3C1%5C%5C%5C%5C1%3Cx%28%5Cbecause%20x%3E0%29%5C%5C%5C%5C%5Ctherefore%20x%3E1)
Answer:
30 feet
Step-by-step explanation:
Let x be the length of the ladder. Then, x cos(60) = 15
If we divide both sides by cos(60), then x = 30 feet.