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V125BC [204]
3 years ago
8

Round 5,704 to the nearest hundred.

Mathematics
2 answers:
allsm [11]3 years ago
4 0

Answer:

5700

Step-by-step explanation:

labwork [276]3 years ago
4 0
Answer: 5,700

704 is closer to 700 than it is to 800
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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.

<h3>How to find the mass?</h3>

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

brainly.com/question/27846146

#SPJ4

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
1 year ago
At a sale this week, a suit is being sold for $244.20. This is 33% of the original price. What is the original price
Alecsey [184]

Answer:

$740

Step-by-step explanation:

244.20= x(.33)

244.2/.33= x(.33)/.33

740=x

4 0
3 years ago
Need help on #7 help if u know how to solve thanks!
mash [69]
7a) 302.5
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Explain how you use estimation to check the reasonableness of a solution to a practical problem.
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Estimation is just giving a general answer to the situation and can be specified on specifics depending on the numbers used and whichever question it's asking. But also remember that whenever you estimate your answer will be an approximate answers, not an exact.


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