1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mars1129 [50]
3 years ago
14

Plz help me solve this

Mathematics
1 answer:
Sidana [21]3 years ago
4 0
The answer is C, lmk if i helped
You might be interested in
Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) f
Sholpan [36]

Answer:

<u>Mass</u>

\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)

<u>Center of mass</u>

<em>Coordinate x</em>

\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

<em>Coordinate y</em>

\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

<em>Coordinate z</em>

\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)  

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass  m would be the curve integral along the path W

m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt

The density D(x,y,z) is given by

D(x,y,z)=x^2+y^2+z^2=t^2+16cos^2(t)+16sin^2(t)=t^2+16

on the other hand

||W'(t)||=\sqrt{1^2+(-4sin(t))^2+(4cos(t))^2}=\sqrt{1+16}=\sqrt{17}

and we have

m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt=\\\\\sqrt{17}\displaystyle\int_{0}^{2\pi}(t^2+16)dt=\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)

The center of mass is the point (\bar x,\bar y,\bar z)

where

\bar x=\displaystyle\frac{1}{m}\displaystyle\int_{W}xD(x,y,z)\\\\\bar y=\displaystyle\frac{1}{m}\displaystyle\int_{W}yD(x,y,z)\\\\\bar z=\displaystyle\frac{1}{m}\displaystyle\int_{W}zD(x,y,z)

We have

\displaystyle\int_{W}xD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}t(t^2+16)dt=\\\\=\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)

so

\bar x=\displaystyle\frac{\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

\displaystyle\int_{W}yD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}4cos(t)(t^2+16)dt=\\\\=16\sqrt{17}\pi

\bar y=\displaystyle\frac{16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

\displaystyle\int_{W}zD(x,y,z)=4\sqrt{17}\displaystyle\int_{0}^{2\pi}sin(t)(t^2+16)dt=\\\\=-16\sqrt{17}\pi

\bar z=\displaystyle\frac{-16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

3 0
2 years ago
What is the median of 5, 7, 2, 4, 3 (remember to place the numbers in order first.)
Inessa05 [86]

Answer:

4

Step-by-step explanation:

The numbers in order would be

2, 3, 4, 5, 7

The number in the middle is always the median

Therefore, 4 is the median

5 0
3 years ago
11. What is true of a kite (select all that apply)​
astra-53 [7]

Answer:

Step-by-step explanation:

Diagonals are perpendicular

no parallel sides

1 parallel of congruent angles

only these

3 0
3 years ago
Scientific notation 3.000052
notka56 [123]
There is really nothing to change here but it could be written as
3.000052x10 with no power
3 0
3 years ago
About how many times heavier is the blue whale than the rhinoceros
makkiz [27]

Answer:

1 x 10^2

Step-by-step explanation:

(2 x 10^5) / (2 x 10^3) = 1 x 10^2

5 0
3 years ago
Other questions:
  • Can someone pls help me fast
    8·2 answers
  • The sun produces 3.9 ⋅ 10 to the 33th power ergs of radiant energy per second. How many ergs of radiant energy does the sun prod
    6·1 answer
  • Is 9/31 an irrational number
    9·2 answers
  • He ages of mark and adam add up to 28 years total. mark is 20 years older than adam. how many years old is adam
    15·1 answer
  • What is the range of g(x) = - 2x + 3, if the domain is {-2, - 1,0, 1, 2}?
    9·1 answer
  • The perimeter of a Parallelogram is 72 meters.
    10·1 answer
  • What is 2 2/3, 2 6/15, 2 3/5, and 2 4/9 in Least To greatest form?
    7·1 answer
  • Which function represents a line with a rate change of 4 and an initial value of -4?
    11·1 answer
  • How do I solve this problem correctly?
    7·1 answer
  • ⚠️Answer needed quickly⚠️<br> *Brainliest to right answer*
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!