I NEED HELP THANK YOUUUY

Solve the following questions<br>

Simora [160]

Start with

$\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1}$

Observe that this implies that the domain is

$2x+1,\ 2x-1\neq 0 \implies x \neq \pm\dfrac{1}{2}$

The least common denominator is

$\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1} = \dfrac{(2x-1)^2-(2x+1)^2}{(2x+1)(2x-1)}=\dfrac{-8x}{4x^2-1}$

In the right hand side, we have

$-2\dfrac{2}{3}=-\left(2+\dfrac{2}[3}\right)=-\left(\dfrac{6}{3}+\dfrac{2}{3}\right)=-\dfrac{8}{3}$

So, the equation becomes

$-\dfrac{8x}{4x^2-1}=-\dfrac{8}{3} \iff \dfrac{x}{4x^2-1}=\dfrac{1}{3}$

Multiply both sides by 3:

$\dfrac{3x}{4x^2-1}=1 \iff 3x=4x^2-1 \iff 4x^2-3x-1=0$

This equation has solutions

$x=-\dfrac{1}{4},\quad x=1$

Which are compliant with the domain of the equation

7 0

4 years ago

cylinder has radius 2.5 cm and lateral area 20π cm2.20π cm2. 20 pi . cm squared , . What is the surface area of the cylinder in

uysha [10]

$\bf \textit{lateral area of a cylinder}\\\\
LA=2\pi rh\qquad 
\begin{cases}
r=radius\\
h=height\\ -----\\
LA=20\pi \\
r=2.5
\end{cases}\implies 20\pi =2\pi \cdot 2.5h
\\\\\\
\cfrac{20\pi }{2\cdot 2.5\pi }=h\implies \boxed{4=h}\\\\
-------------------------------\\\\
\textit{total surface area of a cylinder}\\\\
SA=2\pi r(h+r)\implies SA=2\pi \cdot 2.5(4+2.5)$

7 0

4 years ago

In a dice game if you roll a 2, 4, or 6 you get the value of the die. If you roll as 1, 3, or 5 you lose $5. What is the expecte

Vlad [161]

Answer: -$0.5

Step-by-step explanation:

event Probability

+ $2 1/6

+ $4 1/6

+ $6 1/6

- $5 3/6

E(X) = (2*1/6)+(4*1/6)+(6*1/6)+(-5*3/6) = -$0.5

5 0

2 years ago

Anyone know this.......

RideAnS [48]

Answer:

a) The basic rate of pay is 6 sterling pounds per hour.

b) The higher rate of pay is 10 sterling pounds per hour.

Step-by-step explanation:

Both segments of the curve are first order polynomials, which means that each have constant slopes.

a) The basic rate of pay is the value of the slope ( $r$ ), in sterling pounds per hour, of the line for the first 20 hours worked, that is:

$r = \frac{\Delta y}{\Delta x}$ (1)

Where:

$\Delta x$ - Change in hours worked, in hours.

$\Delta y$ - Change in pay, in sterling pounds.

If we know that $\Delta x = 20\,h$ and $\Delta y = \pounds\, 120$ , then the basic rate is:

$r = \frac{\Delta y}{\Delta x}$

$r = \frac{\pounds\,120}{20\,h}$

$r = 6\,\frac{\pounds}{h}$

The basic rate of pay is 6 sterling pounds per hour.

b) By using (1), we calculate the higher rate of pay below. If we know that $\Delta x = 10\,h$ and $\Delta y = \pounds \,100$ , then the higher rate is:

$r = \frac{\Delta y}{\Delta x}$

$r = \frac{\pounds\,100}{10\,h}$

$r = 10\,\frac{\pounds}{h}$

The higher rate of pay is 10 sterling pounds per hour.

7 0

3 years ago

What are the domain and range of f(x) = 1/6x +2

Rashid [163]

Hello from MrBillDoesMath!

Answer:

My interpretation of f(x) is f(x) = (1/6x) + 2

Domain = {Real Numbers} - {0}

Range = {Real Numbers}

Discussion:

Domain of f = all x where f(x) is defined. For f(x) the only singularity occurs at x = 0 so the domain is the set of all real numbers except for 0. For x>0, x values close to 0 cause y to grow large while large x causes y to approach 0. A similar argument for x <0 shows that the range of f is all real numbers.

Thank you,

MrB

7 0

3 years ago