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3 years ago

9

Scientific notation of 0.00000008

1 answer:

RSB [31]3 years ago

6 0

8*10^-8 is the answer

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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

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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

Lori is picking up lunch for herself and her coworkers. Some of her coworkers ordered the salad which costs $7.50, and some of h

Step2247 [10]

Answer: 3 people ordered soup.

Step-by-step explanation:

Let x be the number of people ordered salad and y be the number of people ordered soup.

As per given,

x=2y (i)

7.50x+6.25y= 63.75 (ii)

Substitute value of c =2y in (ii) , we get

7.50(2y)+6.25y= 63.75

⇒ 15y+6.25y = 63.75

⇒21.25y = 63.75

⇒ y= 3 [divide both sides by 21.25]

Then, x= 2(3) =6

So 6 people ordered salad and 3 people ordered soup.

4 0

4 years ago

How to solve this equation 15(6-g)

NikAS [45]

<span>15<span>(<span>6−g</span>)</span></span><span>=<span><span>(15)</span><span>(<span>6+<span>−g</span></span>)</span></span></span><span>=<span><span><span>(15)</span><span>(6)</span></span>+<span><span>(15)</span><span>(<span>−g</span>)</span></span></span></span><span>=<span>90−<span>15g</span></span></span><span>=<span><span>−<span>15g</span></span>+<span>90</span></span></span>

7 0

3 years ago

I NEED THE ANSWER NOW

o-na [289]

1/8 is the answer to the question

6 0

3 years ago

Read 2 more answers

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into t

Svet_ta [14]

Answer:

$F_w=9408\ N$

Weight of the truck=9408 N

Step-by-step explanation:

Boat is experiencing the buoyant force as it is in the water and is sinking

According to the force balance in y direction. As both is floating, two forces balance each other:

$F_b-F_w=0$

where:

$F_b$ is the buoyant force

$F_w$ is the weight=mg

$F_b=F_w$ Eq (1)

Buoyant force is equal to the mass of water displaced * gravitational acceleration.

$F_b=m_{water\ displaced}*g\\F_b=\rho Vg\\$

Taking density of water to be 1000 Kg/m^3

$F_b=1000*(6*4*4*10^{-2})*9.8\\F_b=9408 N$

From Eq(1):

$F_w=9408\ N$

Weight of the truck=9408 N

6 0

4 years ago