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3 years ago

Match the following terms with their definitions..

Mathematics

1 answer:

gavmur [86]3 years ago

6 0

Number 1 goes with wages number 2 goes with mean number 3 is demand number 4 is career and number 5 is profit

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Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = $\int_a^b \delta\left|r^{\prime}(t)\right| d t$

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

$\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}$

Further simplifying;

$\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}$

Now, use integration to find the mass of the wire;

$\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}$

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

5 0

2 years ago

2(x+4)=1/2(4x-4) answer and show work

taurus [48]

2(x+4) = 1/2(4x-4)

Multiply through by 2:-

4(x + 4) = 4x - 4

4x + 16 = 4x - 4

4x - 4x = -4 - 16

0 = -20

This is obviously wrong so there is NO Solution (answer).

8 0

4 years ago

And this (4+i)(4-i)<br> show work so i can understand pls ;-;

Irina18 [472]

(a+b)(a-b)=a^2-b^2

$\\ \tt\longmapsto (4+I)(4-i)$

$\\ \tt\longmapsto 4^2-i^2$

$\\ \tt\longmapsto 16+1$

$\\ \tt\longmapsto 17$

4 0

2 years ago

Read 2 more answers

Find the length of the missing side

shepuryov [24]

Answer:

A) $\sqrt{52}$

Step-by-step explanation:

$a^{2} +b^{2} =c^{2}$

$4^{2} +6^{2} =c^{2}$

16+36= $c^{2}$

$\sqrt{52} =\sqrt{c^{2}}$

$\sqrt{52} =c$

4 0

3 years ago

Using the quote, "Those of us on the margins wonder if our stories matter" what is the significance of the quoted text?

Andreyy89

The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

<h3>What is a quote?</h3>

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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7 0

2 years ago