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3 years ago

Melanie bought 4 gallons of slime and plans to sell

Mathematics

1 answer:

EastWind [94]3 years ago

4 0

Melanie has 16 small jar

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

Please HELP!!!!!!!!!

DaniilM [7]

Calculate the sum

5x - 10 + 7 = 65 - 20x + 32

Move terms

5x - 3 = 97 - 20x

Collect the like terms and calculate

5x + 20x = 97 +3

Divide both sides by 25

25x = 100

X= 4 ANSWER

I skipped some steps because it would be too long :/

Multiply parenthesis by 8

20x>8(4x - 5) -20

Calculate

20x>32x - 40 - 20

Move variable to the left

20x>32x-60

Collect like terms

20x - 32x > -60

Divide both sides by -12

-12x>-60

X<5 ANSWER

8 0

3 years ago

How to solve this <br>3 = (2x + 8)/3

seropon [69]

Answer:

x = 1/2

Step-by-step explanation:

First you want to get rid of the fraction, so you can multiply both sides of the equation by 3.

9 = 2x + 8

Then, subtract 8 from both sides to get x by itself.

1 = 2x

Finally, divide both sides by 2 so you only have one x

1/2 = x

This means that the answer is x = 1/2.

5 0

3 years ago

Read 2 more answers

An item that originally cost $12 is marked down 30%. What is the price of the item after the markdown? Show work please

Anettt [7]

First we have to determine 30% of 12.

(30×12)÷100=3.6 so 3.6 is 30% of 12.

12 - 3.6= 8.4

Your answer is 8.4

8 0

3 years ago

Rate this song

Alex17521 [72]

Answer:

100/100

Step-by-step explanation:

3 0

2 years ago