Answer:
x>=-1, B
Step-by-step explanation:
1. distribute 2 to get 7+x <= 2x+6+2
2. simplify to get 7+x <= 2x+8
3. subtract 7 on both sides to get x<=2x+1
4. subtract x on both sides to get 0 <= x+1
5. subtract 1 on both sides to get x >= -1
B fits this description
The line integral is the path of the function along a line having a continuous value.
The integral solved gives the value 111.
The given question is
![\int\limits^c {z}^2 \, dx+ {x}^2 \, dy+ {y} ^2\, dz](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ec%20%7Bz%7D%5E2%20%5C%2C%20dx%2B%20%7Bx%7D%5E2%20%5C%2C%20dy%2B%20%7By%7D%20%5E2%5C%2C%20dz)
where C is the line from (1, 0, 0) to (4, 1, 3)
Here
x→ 1⇒ 4
y→ 0⇒1
z→ 0⇒ 3
Let t be defined be the range 0≤ t ≤ 1
Then x= 4t+1 : dx= 4dt
y= t ": dy= dt
z= 3t : dz= 3dt
Putting the values
![\int\limits^1_0{9t^2} \, 4dt + \int\limits^1_0 {16t^2+1+8t} \, 3dt +\int\limits^1_0 {t^2} \,3dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E1_0%7B9t%5E2%7D%20%5C%2C%204dt%20%2B%20%5Cint%5Climits%5E1_0%20%7B16t%5E2%2B1%2B8t%7D%20%5C%2C%203dt%20%2B%5Cint%5Climits%5E1_0%20%7Bt%5E2%7D%20%5C%2C3dt)
= [36(1)²- 36(0)²]+ 3 [16(1)² +1+8(1)] - 3 [16(0)² +1+8(0)] + [3(1)²- 3(0)² ]
= 36 +75-3+3
= 111
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The slop of the line is Y=6x+7
ANSWER
![\frac{a + 3}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20%2B%203%7D%7B8%7D%20)
EXPLANATION
We want to simplify
![\frac{a + 3}{a} \div \frac{8}{a}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20%2B%203%7D%7Ba%7D%20%20%5Cdiv%20%20%5Cfrac%7B8%7D%7Ba%7D%20)
We multiply the first fraction by the reciprocal of the second fraction to obtain,
![\frac{a + 3}{a} \times \frac{a}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20%2B%203%7D%7Ba%7D%20%20%20%5Ctimes%20%20%5Cfrac%7Ba%7D%7B8%7D%20)
We cancel the common factors to get,
![\frac{a + 3}{1} \times \frac{1}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20%2B%203%7D%7B1%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B8%7D%20)
This gives us,
Answer:
Step-by-step explanation:
x^2 - 22x = 10
Next step is to complete the square on the left hand side of the equation and it would be balanced by adding the same number to the right side of the equation. It becomes
x^2 - 22x + (22/2)^2 = 10 + (22/2)^2
x^2 - 22x + (11)^2 = 10 + (11)^2
x^2 - 22x + (11)^2 = 10 + 121
x^2 - 22x + (11)^2 = 131
x^2 - 22x + 121^2 = 131
(x - 11)^2 = 131
Taking square root of both the left hand side and the right hand side of the equation, it becomes
x - 11 = ±√131
x - 11 = ±11.45
Adding 11 to the left hand side and the right hand side of the equation, it becomes
x - 11 + 11 = ±11.45 + 11
x = 11.45 + 11 or x = -11.45 + 11
x = 22.45 or x = - 0.45