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Morgarella [4.7K]
3 years ago
15

A company designs its packing so that it is a cylinder with a diameter of 4 inches and a height of 7 inches

Mathematics
1 answer:
jenyasd209 [6]3 years ago
6 0

Answer:

28

Step-by-step explanation:due to the lack of information I'm gonna have to include that the total amount of space would be 28

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PLZ HELP!!! Use limits to evaluate the integral.
Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

where 1\le i\le n. Each interval has length \Delta x_i=\frac{2-0}n=\frac2n.

At these sampling points, the function takes on values of

f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}

We approximate the integral with the Riemann sum:

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4

so that the sum reduces to

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

Just to check:

\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28

4 0
3 years ago
What do you subtract from -3 td get positive 4?*
kogti [31]

Answer:

7

Step-by-step explanation:

3 0
3 years ago
A) Write 2 expressions for the area of the shaded region.
Trava [24]

Answer:

(a)9×3=37' 97 and 8 are factors of 37

3 0
2 years ago
Please tell me what is (7+3x)4
Savatey [412]

Answer:

28+12x

Step-by-step explanation:

Multiply 7 with 4

Multiply 3x with 4

5 0
2 years ago
Read 2 more answers
I'm trying to rearange this equation so that t is the subject and i need help
gregori [183]
Work backwards.

s=ut+(at^2)/2

Subtract ut.

s-ut=(at^2)/2

Multiply by 2.

2(s-ut)=at^2

Divide by a.

2(s-ut)/a=t^2

Find the square root:

\sqrt{2(s-ut)/a}=t
6 0
3 years ago
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