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LuckyWell [14K]
3 years ago
11

Find the equation of the line with a slope of -3, passing through the point (2,5).

Mathematics
1 answer:
Alexxx [7]3 years ago
8 0
Y = -3(2) + 11
y = -6 + 11
y = 5

Answer is a) y = -3x + 11 , when x is 2 y is 5
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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
The owner of a bookstore ordered 75 copies of a book and paid $1,350. The owner of another bookstore also ordered the same book
kherson [118]

Answer:

$18

Step-by-step explanation:

I did the following expressions:

1,350 / 75 = 18

1,080 / 60 = 18

4 0
2 years ago
In a right triangle, if a = 8in and c = 14in, what is b? Round to three decimal places.
Arte-miy333 [17]

Answer:

11.49

Step-by-step explanation:

If A=8

And C=14 then

4 0
3 years ago
a school has 2 computer labs.Each lab has 30 computers. A total of 6 computers in the school are not working. which experission
jasenka [17]

Answer:

30(2)-6

Step-by-step explanation:

30 computers in 2 labs minus the 6 broken computers.

3 0
3 years ago
Read 2 more answers
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The answer is f(x) will eventually exceed g(x) because f(x) is an exponential function.
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