Irrational numbers are real numbers that can not be made by dividing 2 integers, like π , √2, √3, ...
And whole numbers are rational. For example: 5 can be written as 5 / 1.
Answer:
No irrational numbers are whole numbers.
True.
Answer:
y = 4x - 4 is one equation.
Step-by-step explanation:
You haven't given a list but we can create one equation:
If a system of equations have one solution they are consistent and independent.
Finding an equation to pair with y = 3x - 2 to create this :-
Let x = 2 then y = 3(2) - 2 = 4.
So our equation will also have this solution.
One equation could be:
y = 4x - 4.
Answer:
Slope=4 y-intercept=(0,-21) or -21
Step-by-step explanation:
To find<u> slope</u>
m=-13-(-17)/2-1
m=4/1
m=4
To find <u>y-intercept</u>
y-(-17)=4(x-1)
y+17=4(x-1)
y+17=4x-4
Subtract both sides by 17
y=4x-21
y-intercept=-21
Answer:
Step-by-step explanation:
A 90° portion of your volume is shown below.
Let's use the shell method and decompose the solid of revolution into cylindrical shells.
The volume of each cylindrical shell is
dV = 2πrh dx
where
r = ln16 - x
h = eˣ
So
dV = 2π(ln16 - x)eˣdx
Let's integrate the two terms separately.
![\begin{array}{rcl}A &=& 2\pi \ln16 \int_{0}^{\ln16}e^{x}dx\\\\&=& 2\pi\ln16[e^{x}]_{0}^{\ln16}\\\\&=& 2\pi\ln16(16 - 1)\\&= &\mathbf{30\pi\ln1}\\\\B &=&2\pi\int_{0}^{\ln16}xe^{x}dx\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DA%20%26%3D%26%202%5Cpi%20%5Cln16%20%5Cint_%7B0%7D%5E%7B%5Cln16%7De%5E%7Bx%7Ddx%5C%5C%5C%5C%26%3D%26%202%5Cpi%5Cln16%5Be%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D%5C%5C%5C%5C%26%3D%26%202%5Cpi%5Cln16%2816%20-%201%29%5C%5C%26%3D%20%26%5Cmathbf%7B30%5Cpi%5Cln1%7D%5C%5C%5C%5CB%20%26%3D%262%5Cpi%5Cint_%7B0%7D%5E%7B%5Cln16%7Dxe%5E%7Bx%7Ddx%5C%5C%5Cend%7Barray%7D)
Use the integration by parts formula
![\begin{array}{rcl}uv - \int v du &=&\\B &=& 2\pi[xe^{x}]_{0}^{\ln16} - 2\pi \int_{0}^{\ln16} e^{x}dx\\\\&=&2\pi[xe^{x}]_{0}^{\ln16}-2\pi [e^{x}]_{0 }^{\ln16}\\\\&= &2\pi(16\ln16- 0) -2\pi(16 - 1)\\&=& \mathbf{32\pi \ln16 -30\pi}\\A - B &= &30\pi\ln16 - 32\pi \ln16 +30\pi\\&=& 30\pi - 2\pi \ln16\\&=&\mathbf{2\pi(15 - \ln16)}\end{array}\\\text{The volume of the solid is $\large \boxed{\mathbf{2\pi(15 - \ln16)}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Duv%20-%20%5Cint%20v%20du%20%26%3D%26%5C%5CB%20%26%3D%26%202%5Cpi%5Bxe%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D%20-%202%5Cpi%20%5Cint_%7B0%7D%5E%7B%5Cln16%7D%20e%5E%7Bx%7Ddx%5C%5C%5C%5C%26%3D%262%5Cpi%5Bxe%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D-2%5Cpi%20%5Be%5E%7Bx%7D%5D_%7B0%20%7D%5E%7B%5Cln16%7D%5C%5C%5C%5C%26%3D%20%262%5Cpi%2816%5Cln16-%200%29%20-2%5Cpi%2816%20-%201%29%5C%5C%26%3D%26%20%5Cmathbf%7B32%5Cpi%20%5Cln16%20-30%5Cpi%7D%5C%5CA%20-%20B%20%26%3D%20%2630%5Cpi%5Cln16%20-%2032%5Cpi%20%5Cln16%20%2B30%5Cpi%5C%5C%26%3D%26%2030%5Cpi%20-%202%5Cpi%20%5Cln16%5C%5C%26%3D%26%5Cmathbf%7B2%5Cpi%2815%20-%20%5Cln16%29%7D%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20volume%20of%20the%20solid%20is%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B2%5Cpi%2815%20-%20%5Cln16%29%7D%7D%24%7D)
