Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- Solid lies between planes x = 0 and x = 4.
- The diagonals rum from curves y = sqrt(x) to y = -sqrt(x)
Find:
Determine the Volume bounded.
Solution:
- First we will find the projected area of the solid on the x = 0 plane.
A(x) = 0.5*(diagonal)^2
- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,
A(x) = 0.5*(sqrt(x) + sqrt(x) )^2
A(x) = 0.5*(4x) = 2x
- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluate limits 0 < x < 4:
V= 16 - 0 = 16 unit^3
2. 8x -28 = -140
8x -28 + 28 = -140 + 28
8x = -112
8x/8 = -112/8
x = -14
3. -9 + x/3 = -23
-9 + 9 + x/3 = -23 + 9
x/3 = -14
x/3/3 = -14/3
x = -14/3
4. x/-1.5 - 3.5 = -13.5
x/-1.5 - 3.5 + 3.5 = -13.5 + 3.5
x/1.5 = -10
x/-1.5/-1.5= -10/-1.5
x = 20/3
5.-6(x + 3) = -36
-6x - 18 = -36
-6x - 18 + 18 = -36 + 18
-6x = -18
-6x/-6 = -18/-6
x = 3
6. k + 3.7/9.8 = -0.22
k + 3.7/9.8/9.8 = -0.22/9.8
k + 3.7 = -2.156
k + 3.7 - 3.7 = -2.156 - 3.7
k = -5.856
7. 12(x - 6) = -108
12x - 72 = -108
12x - 72 + 72 = -108 + 72
12x = -36
12x/12 = -36/12
x = -3
8. -21.83x - -19.9 = -23.83
-21.83x + 19.9 = -23.83
-21.83x + 19.9 - 19.9 = -23.83 - 19.9
-21.83x = -43.73
-21.83x/-21.83 = -43.73/-21.83
x = 2
9. -10x - 68 + x = 40
-9x - 68 = 40
-9x -68 + 68 = 40 + 68
-9x = 108
-9x/-9 = 108/-9
x = -12
10. -34 - 3x - 2x = 71
-34 - 5x = 71
-34 + 34 - 5x = 71 + 34
-5x = 105
-5x/-5 = 105/-5
x = -21
11. 3x - 77 - 8x = 23
-5x - 77 = 23
-5x - 77 + 77 = 23 + 77
-5x = 100
-5x/-5 = 100/-5
x = -20
12. 3x - 5(2x - 12) = 123
3x - 10x + 60 = 123
-7x + 60 = 123
-7x + 60 - 60 = 123 - 60
-7x = 63
-7x/-7 = 63/-7
x = -9
13. -3x + 6(x + 6) = 15
-3x + 6x + 36 = 15
3x + 36 = 15
3x + 36 - 36 = 15 - 36
3x = -21
3x /3 = -21/3
x = -7
14. 5x + 2(4x - 9) = -174
5x + 8x - 18 = -174
13x - 18 = -174
13x - 18 + 18 = -174 + 18
13x = -156
13x/13 = -156/13
x = -12
15. -3x + 6(5x + 3) = -171
-3x + 30x + 18 = -171
27x + 18 = -171
27x + 18 - 18 = -171 - 18
27x = -189
27x/27 = -189/27
x = -7
Answer:
x + 6
Step-by-step explanation:
If you dont know the value of x you cant solve the problem fully
Answer:
a = -3/2
Step-by-step explanation:
3(6a+12)=9
Divide each side by 3
3/3(6a+12)=9/3
6a+12 = 3
Subtract 12 from each side
6a+12-12 = 3-12
6a = -9
Divide by 6
6a/6 = -9/6
a = -3/2
