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Romashka-Z-Leto [24]
2 years ago
12

Question 11 . 2 p Brent is considering buying a new circular track for his model train. He estimates that the model's circumfere

nce is about 3 times the measure of the circle's diameter. With this information, Brent could derive the value of OT O length O width area Previous Next > No new data to save. Last checked at 9:51am Submit​
Mathematics
1 answer:
neonofarm [45]2 years ago
4 0

Brent estimates that the model's circumference is about 3 times the measure of the circle's diameter, with this, he can estimate the area.

<h3>What is a circle? </h3>

A circle is the locus of a point, such that the distance from a fixed point (center) is always constant.

The circumference of a circle is given by:

Circumference = π * diameter

Brent estimates that the model's circumference is about 3 times the measure of the circle's diameter, with this, he can estimate the area.

Find out more on circle at: brainly.com/question/24375372

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Find the mass of the solid paraboloid Dequals=​{(r,thetaθ​,z): 0less than or equals≤zless than or equals≤8181minus−r2​, 0less th
Lubov Fominskaja [6]

Answer:

M = 5742π  

Step-by-step explanation:

Given:-

- Find the mass of a solid with the density ( ρ ):

                             ρ ( r, θ , z ) = 1 + z / 81

- The solid is bounded by the planes:

                             0 ≤ z ≤ 81 - r^2

                             0 ≤ r ≤ 9

Find:-

Find the mass of the solid paraboloid

Solution:-

- The mass (M) of any solid body is given by the following triple integral formulation:

                           M = \int \int \int {p ( r ,theta, z)} \, dV\\\\

- We can write the above expression in cylindrical coordinates:

                           M = \int\limits\int\limits_r\int\limits_z {r*p(r,theta,z)} \, dz.dr.dtheta \\\\M = \int\limits\int\limits_r\int\limits_z {r*[ 1 + \frac{z}{81}] } \, dz.dr.dtheta\\\\

- Perform integration:

                           M = \int\limits\int\limits_r{r*[ z + \frac{z^2}{162}] } \,|_0^8^1^-^r^2 dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{(81-r^2)^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{6561 -162r + r^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + 40.5 -r +\frac{r^2}{162} ] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{[ 121.5r-r^2 -\frac{161r^3}{162} ] } \, dr.dtheta\\\\

                           M = 2*\int\limits_0^\pi {[ 121.5r^2-r^3 -\frac{161r^4}{162} ] } |_0^6 \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 121.5(6)^2-(6)^3 -\frac{161(6)^4}{162} ] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 4375-216 -1288] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 2871] }  \, dtheta\\\\M = 5742\pi  kg              

- The mass evaluated is M = 5742π                      

8 0
3 years ago
3(c+4) what's da answer
lisov135 [29]

Answer:

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Step-by-step explanation:

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3 years ago
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LCM of 4, 6, 10, and 12
Amiraneli [1.4K]

Answer:

360 is the LCM of 4,6,10 and 12

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What is the product of (5× + 1)(5x - 1)?
padilas [110]

we are given

(5x + 1)(5x - 1)

we can distribute it

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25x^2-5x+5x-1

now, we can simplify it

25x^2-1...............Answer

6 0
3 years ago
What is 57,909,000 in scientific notation?
LenaWriter [7]
Hello,

Shall we begin?

<span>57,909,000
</span>
= 5.7909 * 10 ^7


Answers: 5.7909 * 10 ^7
5 0
3 years ago
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