Answer:
option (a) is correct.
2 + m - 1 + m is an equivalent expression to the given expression 3m+1-m
Step-by-step explanation:
Given expression 3m+1-m
We have to choose an equivalent expression from given options.
Equivalent expression are those expression that looks different but are same.
Like 4+2 = 6 and 3+ 3 = 6
Both have same value but looks differently.
Like terms are term having same variable with same degree.
Consider the given expression 3m+1-m
Simplify by adding like terms,
3m + 1 - m = (3-1) m + 1
Thus, (3-1) m + 1 = 2m + 1
Also 2m + 1 can be written as m + m + 2 - 1
Thus, option (a) is correct.
Answer: 
Step-by-step explanation:
Given
The area is bounded by 
and x-axis from [0,2]
The volume generated for 
when rotated about the x-axis in the interval [a,b] is
Insert the values
![\Rightarrow V=\int_0^2\pi x^4dx\\\\\Rightarrow V=\pi \int_0^2x^4dx\\\\\Rightarrow V=\pi \left[ \dfrac{x^5}{5}\right]_0^2\\\\\Rightarrow V=\dfrac{2^5\pi }{5}\\\\\Rightarrow V=\dfrac{32\pi }{5}\ \text{unit}^3](https://tex.z-dn.net/?f=%5CRightarrow%20V%3D%5Cint_0%5E2%5Cpi%20x%5E4dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cpi%20%5Cint_0%5E2x%5E4dx%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cpi%20%5Cleft%5B%20%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E2%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B2%5E5%5Cpi%20%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%20V%3D%5Cdfrac%7B32%5Cpi%20%7D%7B5%7D%5C%20%5Ctext%7Bunit%7D%5E3)
Answer: I'll solve A) since there is a lot of work to be shown.
Step-by-step explanation:
A)
(x−1)³+3x(x−4)+2=x³
Use binomial theorem to expand (x−1)³
x³- 3x² + 3x - 1 + 3x(x-4) + 2=x³
Use distributive property on 3x(x-4)
x³- 3x² + 3x - 1 + 3x²-12x + 2=x³
Add like terms
x³ −9x + 1 =x³
Subtract x³ from both sides.
x³ −9x +1 -x³ = 0
Add x³ and -x³
−9x+1=0
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
−9x=−1
Divide both sides by -9.
x=
1/9
Circumference is pi*diameter, so 94.2/ pi = 30, so the answer is C. 30 in
