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2 years ago

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In , is a right angle. find the remaining sides and angles. round your answers to the nearest tenth . show your work. a = 3, c =

1 9

1 answer:

ki77a [65]2 years ago

5 0

The answer is either 18.76 or 18.77

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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

2 years ago

Someone help with this math question please!!

Reptile [31]

In rectangle : US=RT
2SO=US
6x+4=14x-12
X=16/8
6(16/8)+4=your answer

6 0

2 years ago

I'LL GIVE BRAINLIEST:

vitfil [10]

Answer:

its C

Step-by-step explanation:

7 0

2 years ago

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What is the surface area

ArbitrLikvidat [17]

Answer:

184 m²

Step-by-step explanation:

Surface Area = 2(10*2) + 2(10*6) + 2(2*6)

Surface Area = 2(20 + 60 + 12)

Surface Area = 2(92)

Surface Area = 184 m²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

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2 years ago

How much money will there be in an account at the end of 10 years if $4000 is deposited at 6% compounded quarterly

Elena L [17]

Answer:

$7,256.07

Step-by-step explanation:

A = p(1+r/n)^nt

A = 4000(1+.06/4)^(10*4)

7 0

2 years ago