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3 years ago

Find the value of x.

Mathematics

1 answer:

vredina [299]3 years ago

8 0

Answer:

Step-by-step explanation:

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The estimated value of the integral from 0 to 2 of x cubed dx , using the trapezoidal rule with 4 trapezoids is

bulgar [2K]

The integral is approximated by the sum,

$\displaystyle\int_0^2f(x)\,\mathrm dx\approx\sum_{n=0}^4\frac12\times\frac{f(x_n)+f(x_{n+1})}2=\frac14\sum_{n=0}^3(f(x_n)+f(x_{n+1}))$

where $f(x)=x^3$ and $x_n=\dfrac12n$ , giving you

$\displaystyle\frac14\sum_{n=0}^3\bigg(\left(\frac n2\right)^3+\left(\frac{n+1}2\right)^3\bigg)$
$\displaystyle\frac1{32}\sum_{n=0}^3(n^3+(n+1)^3)$
$\displaystyle\frac1{32}\sum_{n=0}^3(2n^3+3n^2+3n+1)$

Faulhaber's formulas make short work of computing the sum. You have

$\displaystyle\sum_{n=0}^k1=k+1$
$\displaystyle\sum_{n=0}^kn=\frac{k(k+1)}2$
$\displaystyle\sum_{n=0}^kn^2=\frac{k(k+1)(2k+1)}6$
$\displaystyle\sum_{n=0}^kn^3=\frac{k^2(k+1)^2}4$

which gives

$\displaystyle\frac1{16}\sum_{n=0}^3n^3+\frac3{32}\sum_{n=0}^3n^2+\frac3{32}\sum_{n=0}^3n+\frac1{32}\sum_{n=0}^31$
$\displaystyle\frac{36}{16}+\frac{42}{32}+\frac{18}{32}+\frac4{32}$
$\implies\displaystyle\int_0^2x^3\,\mathrm dx\approx\frac{17}4=4.25$

4 0

3 years ago

How do you find what number you need to get a certain average?

likoan [24]

1.you add up all of the numbers you have
2.subtract the number you get from the average
3.if you know how many numbers there is then you know how many numbers you need to get
4.divide the number you got from the problem you made from step 1 & 2
5.what numbers you get from that are the numbers you needed to find

6 0

3 years ago

!!!!!20points help asap!!!!

dangina [55]

Answer: Step-by-step explanation:

x=39°

alternate exterior angles of parallel lines

8 0

2 years ago

8. Use ratios to convert the following:

SpyIntel [72]

1) 60 feet = 20 yards

2) 50 pound = 22679.6 grams

Step-by-step explanation:

1) Convert 60 feet to yards:

The conversion rule is:

<u>1 feet = 1/3 yards</u>

Applying to rule to convert 60 feet to yards:

1 feet = 1/3 yards

60 feet = 60/3 = 20 yards

So, 60 feet = 20 yards

2) Convert 50 pounds to grams.

The conversion rule is:

1 pound= 453.592 grams

Applying to rule to convert 50 pounds to grams

1 pound= 453.592 grams

50 pound = 50*453.592 grams

= 22679.6 grams

So, 50 pound = 22679.6 grams

Keywords: Conversion of units

Learn more about Conversion of units at:

#learnwithBrainly

4 0

3 years ago

the area of the shaded portion of the diagram below is equal to half the total area. find the area of the unshaded part.

BabaBlast [244]

Answer:

27 cm^2

Step-by-step explanation:

Suppose the line divided the triangle into two equal triangles

The side lengths for unshaded area is 6 9 10

To find the area of a triangle all we do is multiply height with base and that divided by two

9×6÷2 = 27 cm^2

4 0

2 years ago