All categories

3 years ago

Isaak is writing an explicit formula to represent the sequence.

2 answers:

7 0

In a geometric progression:
a, b, c, d...
The common ratio can be obtained using:
b/a = c/b = d/c
b/a = 112 / 64 = 1.75
c/b = 196 / 112 = 1.75
d/c = 343 / 196 = 1.75
The common ratio = 1.75

mihalych1998 [28]3 years ago

3 0

The answer is 1.75 on e2020

You might be interested in

PLZZZZ HELP The Lakeview city council is considering two different plans to help reduce the amount of pollution in the city. Pla

sdas [7]

1. The two equations follow the slope-intercept form which y=mx + b. They have the same y-intercept which is equal to 900.

2. Suppose x= 10
Plan Alpha: y=-7x+900=-7(10)+900=830
Plan Foxtrot: y = -17x+900 = -17(10)+900=730

Between the 2 plans, the lower value is 730. Plan Foxtrot is better for reduction of pollution.

3. The city council should choose Plan Foxtrot because the reduction of pollution is much greater. Their goal would be reached faster if they go with faster reduction of pollution.

5 0

3 years ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

Write an expression for the sequence of operations described below. triple v, then subtract 7 from the result Do not simplify an

oee [108]

Given:

The sequence is defined as "triple v, then subtract 7 from the result".

To find:

The expression for the given sequence.

Solution:

Triple v means 3 times of v, i.e., 3v.

So, the result is 3v.

Then subtract 7 from the result. So, the expression for the sequence is

$3v-7$

Therefore, the required expression is $3v-7$ .

6 0

3 years ago

Solve using the box method

Lena [83]

$\huge\text{Hey there!}$

$\large\text{Just SIMPLIFY the given EQUATION or find the DIFFERENCE}\\\large\text{OF the SQUARES... Here is the formula: }\mathsf{\bf a^2 - b^2 =(a+b)(a-b)}$

$\large\text{Equation: }\mathsf{\dfrac{(4x^2-9)}{(2x + 3)}}$

$\large\text{Rewrite }\mathsf{ 4x^9 - 9}\large\text{ in the formation of }\mathsf{a^2 - b^2}\large\text{ whereas}\mathsf{a = 2x \ \&\ b = 3.}$

$\large\text{Equation: }\mathsf{\dfrac{(2x)^2-3^2}{2x + 3}}$

$\large\text{This is where you try to do the DIFFERENCE OF its SQUARES}$

$\mathsf{\dfrac{(2x + 3)(2x - 3)}{2x + 3}}$

$\large\text{CANCEL out: }\mathsf{(2x + 3)\ - (2x +3)}\large\text{ because it gives you 0}$

$\large\text{This leaves us with }\mathsf{\bf 2x - 3}\large\text{ as your POSSIBLE ANSWER}$

$\boxed{\boxed{\large\text{Answer: \huge \bf 2x - 3}}}\huge\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

$\large\text{Note: There is/are many ways to solve for equations like this.... this was just}\\\large\text{the quickest and easiest way to understand it!}$

3 0

3 years ago

Find the volume of the pyramid to the nearest cubic unit. Use a calculator.

Lady bird [3.3K]

Answer:

Step-by-step explanation:

V=lwh/3

im guessing its a square pyramid?

14(12)/3

=56

6 0

3 years ago