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3 years ago

Question number 41 only . thank you

Mathematics

1 answer:

docker41 [41]3 years ago

7 0

Answer:

x^2 +y^2

Step-by-step explanation:

Dude this is Pythragorean Theorem =)).

You may have missed this part of your lesson. It's ok and also not ok at the same time beacause pythagorean theorem is a meme.

Ok I'll explain once =)).

Thousands of years ago, a mathematician named Pythagore found out that if we have 3 squares, with one square's area equals to the sum of two other squares, then when we put the sides of the squares together to form a triangle , it'll always be a right triangle ( a triangle with one of its angle is 90°). A square area is measured by the length of its side multipled by itself. So he came up with the statement : In a right triangle, the length of the hypotenuse( the side that does not connect to the right angle) is equalled to the sum of squared other sides.

EG.

In this triangle, the right angle is ^ACB. If length of BC is a, length of AB is c, length of BC is a

I We have a formula :

I \ a^2 + b^2 = c^2

I \

I b \ c

I \

I______\

C a B

So now you can use pythagorean theorem to show off =)).

HOPE YOU LEARN WITH JOY AND HIGH GRADES !!!

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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

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

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