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3 years ago

Does anyone know this

Mathematics

2 answers:

KonstantinChe [14]3 years ago

3 0

Answer:

I THINK IT'S THE 3th ONE

Step-by-step explanation:

Brilliant_brown [7]3 years ago

3 0

Answer:

$f^{-1}(x)=\sqrt[3]{x-3}+9$

Step-by-step explanation:

Let y = f(x)

y = (x - 9)³ + 3 - Now we need to solve for x

y - 3 = (x - 9)³

∛(y - 3) = x - 9

∛(y - 3) + 9 = x

Now we replace x with $f^{-1}$ and y with x:

$f^{-1}(x)=\sqrt[3]{x-3}+9$

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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0,5] into n equal subinterva

sergij07 [2.7K]

Given

we are given a function

$f(x)=x^2+5$

over the interval [0,5].

Required

we need to find formula for Riemann sum and calculate area under the curve over [0,5].

Explanation

If we divide interval [a,b] into n equal intervals, then each subinterval has width

$\Delta x=\frac{b-a}{n}$

and the endpoints are given by

$a+k.\Delta x,\text{ for }0\leq k\leq n$

For k=0 and k=n, we get

$\begin{gathered} x_0=a+0(\frac{b-a}{n})=a \\ x_n=a+n(\frac{b-a}{n})=b \end{gathered}$

Each rectangle has width and height as

$\Delta x\text{ and }f(x_k)\text{ respectively.}$

we sum the areas of all rectangles then take the limit n tends to infinity to get area under the curve:

$Area=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)$

Here

$f(x)=x^2+5\text{ over the interval \lbrack0,5\rbrack}$ $\Delta x=\frac{5-0}{n}=\frac{5}{n}$ $x_k=0+k.\Delta x=\frac{5k}{n}$ $f(x_k)=f(\frac{5k}{n})=(\frac{5k}{n})^2+5=\frac{25k^2}{n^2}+5$

Now Area=

$\begin{gathered} \lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{5}{n}(\frac{25k^2}{n^2}+5) \\ =\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{125k^2}{n^3}+\frac{25}{n} \\ =\lim_{n\to\infty}(\frac{125}{n^3}\sum_{k\mathop{=}1}^nk^2+\frac{25}{n}\sum_{k\mathop{=}1}^n1) \\ =\lim_{n\to\infty}(\frac{125}{n^3}.\frac{1}{6}n(n+1)(2n+1)+\frac{25}{n}n) \\ =\lim_{n\to\infty}(\frac{125(n+1)(2n+1)}{6n^2}+25) \\ =\lim_{n\to\infty}(\frac{125}{6}(1+\frac{1}{n})(2+\frac{1}{n})+25) \\ =\frac{125}{6}\times2+25=66.6 \end{gathered}$

So the required area is 66.6 sq units.

3 0

1 year ago

Taia wants to order custom yoga mats for her yoga studio that will be printed with her logo. She asks two local companies, We Pr

Mila [183]

Answer:

We print -> 21m + 25 ≤ 500
Print so good -> 18m + 44 ≤ 500

Maximum mats from We Print : the integer part of (500-25)/21 = 22

Maximum mats from Print So Good: the integer part of (500-45)/18 = 25

#Note
We take the integer part of the division because a mat cannot be in portions

Answered by GAUTHMATH

3 0

3 years ago

You have 6 large candy bars you want to split each one into thirds.how many candy bar pieces will you then have

Vilka [71]

Answer:

18 lol

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

if a truck uses 12 liters of petrol to travel 86 kilometers. how far will it travel on 42 liters of petrol

cricket20 [7]

Answer

The bus can travel 301 kilometers

Explanation

Set up a proportion

$\frac{12}{86} =\frac{42}{x}$

Solve

12x = 3612

x = 301

5 0

4 years ago

Determine the equation of the line passing through the points (-7,4) and (0,6)

Goryan [66]

A(-7,4) and B(0,6);
A(x₁,y₁) and B(x₂,y₂)
Equation form : y =mx+b

1st Calculate the slope m:

m=(y₂-y₁)/(x₂-x₁) = (6-4)/(0+7), m = 2/7
the equation becomes: y= 2/7.x +b

2nd Calculate b. to that end you plug any coordinates (either A or B) in the equation y=2/7.x + b:
Let's say I selected B(0,6)

6=2/7(0) +b and b =6

The final equation : y =(2/7).x + 6

6 0

3 years ago