Answer:
"The sum of two rational numbers is rational."
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.
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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Step-by-step explanation:
I guess you just slove the exponent can I see the actual question
Answer:go0gle
gle come in clutch
Step-by-step explanation:
Next, let's solve 3x+2y = 10 for the variable y. Move the 3x to the right hand side by subtracting 3x from both sides, like this: 3x - 3x = 0. The answer is 2y. The answer is 10-3x.