Answer:
65
Step-by-step explanation:
8x16=56, 3x6=18/2=9, 56+9=65
Answer:
a = -1/2
b = 2
Step-by-step explanation:
Step 1: Rewrite 1st equation
-b = -5 - 6a
b = 5 + 6a
Step 2: Substitution
4a - 3(5 + 6a) = -8
Step 3: Solve
4a - 15 - 18a = -8
-14a - 15 = -8
-14a = 7
a = -1/2
Step 4: Plug in <em>a</em> to find <em>b</em>
6(-1/2) - b = -5
-3 - b = -5
-b = -2
b = 2
Answer:
4 is a BCA def of rectangle
Comment
You can't get to quadrant 4 to quad 2 without 2 steps. The answers tell you that. The question is, did you use a reflection and a y or x translations or 2 reflections or 2 y or 2x translations.
Argument
You can take one point and see if it translate from beginning (purple triangle) to (yellow triangle) end. If two conditions will get you the right answer, then you have to try another point to break the tie.
We'll use Point C.
Choice A: If you reflect C over the y axis, you will go from (-5,1) to (5,1)
If you move C six units down, you will go from (5,1) to (5,-5) which is where C' is.
That is pretty much the answer.
I could confirm it with another point which is the way your should do it.
Try Point A
Choice A: Point A reflects across the y axis going from (-3,4) to (3,4)
Point A translates down by moving from (3,4) to (3,-2) to become A'
Answer reflection and translation in condition A
More Comment
I should do one more for you to show you that it is wrong.
You can try Choice B of the multiple Choice answers.
We will use Point C
If we translate C across the x axis it will go from (-5,1) to (-5,-1)
The we are to translate 1 unit up. We will go from (-5,0) from (-5,-1) That's nowheres near where C' is. Choice B is wrong.
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:
- 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\\\\](https://tex.z-dn.net/?f=M%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%5Cint%5Climits_z%20%7Br%2Ap%28r%2Ctheta%2Cz%29%7D%20%5C%2C%20dz.dr.dtheta%20%5C%5C%5C%5CM%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%5Cint%5Climits_z%20%7Br%2A%5B%201%20%2B%20%5Cfrac%7Bz%7D%7B81%7D%5D%20%7D%20%5C%2C%20dz.dr.dtheta%5C%5C%5C%5C)
- 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\\\\](https://tex.z-dn.net/?f=M%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%7Br%2A%5B%20z%20%2B%20%5Cfrac%7Bz%5E2%7D%7B162%7D%5D%20%7D%20%5C%2C%7C_0%5E8%5E1%5E-%5Er%5E2%20dr.dtheta%5C%5C%5C%5CM%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%7Br%2A%5B%2081-r%5E2%20%2B%20%5Cfrac%7B%2881-r%5E2%29%5E2%7D%7B162%7D%5D%20%7D%20%5C%2C%20dr.dtheta%5C%5C%5C%5CM%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%7Br%2A%5B%2081-r%5E2%20%2B%20%5Cfrac%7B6561%20-162r%20%2B%20r%5E2%7D%7B162%7D%5D%20%7D%20%5C%2C%20dr.dtheta%5C%5C%5C%5CM%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%7Br%2A%5B%2081-r%5E2%20%2B%2040.5%20-r%20%2B%5Cfrac%7Br%5E2%7D%7B162%7D%20%5D%20%7D%20%5C%2C%20dr.dtheta%5C%5C%5C%5CM%20%3D%20%5Cint%5Climits%5Cint%5Climits_r%7B%5B%20121.5r-r%5E2%20-%5Cfrac%7B161r%5E3%7D%7B162%7D%20%5D%20%7D%20%5C%2C%20dr.dtheta%5C%5C%5C%5C)
![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](https://tex.z-dn.net/?f=M%20%3D%202%2A%5Cint%5Climits_0%5E%5Cpi%20%7B%5B%20121.5r%5E2-r%5E3%20-%5Cfrac%7B161r%5E4%7D%7B162%7D%20%5D%20%7D%20%7C_0%5E6%20%5C%2C%20dtheta%5C%5C%5C%5CM%20%3D%202%2A%5Cint%5Climits_0%5E%5Cpi%20%7B%5B%20121.5%286%29%5E2-%286%29%5E3%20-%5Cfrac%7B161%286%29%5E4%7D%7B162%7D%20%5D%20%7D%20%20%5C%2C%20dtheta%5C%5C%5C%5CM%20%3D%202%2A%5Cint%5Climits_0%5E%5Cpi%20%7B%5B%204375-216%20-1288%5D%20%7D%20%20%5C%2C%20dtheta%5C%5C%5C%5CM%20%3D%202%2A%5Cint%5Climits_0%5E%5Cpi%20%7B%5B%202871%5D%20%7D%20%20%5C%2C%20dtheta%5C%5C%5C%5CM%20%3D%205742%5Cpi%20%20kg)
- The mass evaluated is M = 5742π
