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poizon [28]
3 years ago
6

Evaluate the line integral, where C is the given curve. C (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to

(2, 4, 1) and from (2, 4, 1) to (2, 6, 4)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Parameterize the first line segment C_1 by

\vec r(t)=(1,0,1)(1-t)+(2,4,1)t=(1+t,4t,1)

and the second line segment C_2 by

\vec s(t)=(2,4,1)(1-t)+(2,6,4)t=(2,4+2t,1+3t)

both with 0\le t\le1. Then

\displaystyle\int_{C_1}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz

\displaystyle=\int_0^1\bigg((1+5t)\cdot1+2(1+t)\cdot4+(1-t)4t\cdot0\bigg)\,\mathrm dt

=\displaystyle\int_0^1(9+13t)\,\mathrm dt=\frac{31}2

and

\displaystyle\int_{C_2}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz

\displaystyle=\int_0^1\bigg((2+(4+2t)(1+3t))\cdot0+2(2)\cdot2+2(4+2t)(1+3t)\cdot3\bigg)\,\mathrm dt

\displaystyle=\int_0^1(32+84t+36t^2)\,\mathrm dt=86

Then

\displaystyle\int_C(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz=\frac{31}2+86=\boxed{\frac{203}2}

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Please help me answer this :) and explain how you got your answer ! ( will give brainslt )
Bess [88]

Answer: y = - 0.4 x - 4.5

Step-by-step explanation:

Equation y=mx+b

m is the slope

x is *ANY* x coordinate

y is *ANY* y coordinate

b is y intercept or WHERE the point is on the Y AXIS

Lets look at the given:

Slope (m) is -2/5

Passes through point 15, -9/2

As you can see, the point goes through the Y axis at (-9/2)

Our equation is y = - 0.4 x - 4.5

5 0
2 years ago
3y2+y3−5)+(4y2−4y+2y3+8)
jeka57 [31]

Answer: 3y3+7y2+−4y+3

Step-by-step explanation:

3y2+y3+−5+4y2+−4y+2y3+8

Combine Like Terms:

=3y2+y3+−5+4y2+−4y+2y3+8

=(y3+2y3)+(3y2+4y2)+(−4y)+(−5+8)

=3y3+7y2+−4y+3

5 0
3 years ago
Can you show me how you can get this answer step by step
tiny-mole [99]

Answer:

Plug in the values for x

Step-by-step explanation:

plug in x values into the equation

for example, plug -2 into the equation.  y= -2(-2).  y=4

So on and so forth

4 0
3 years ago
if an ice cream factory makes 350 quart of ice cream in 2 hours?how many quarts could be made in 12 hours? what was the rate in
UkoKoshka [18]
2,100 quarts could be made in 12 hours. The rate for that day was 175 quarts every hour. We get this by dividing 350 by 2.
8 0
3 years ago
¿cuál es el vértice de una parábola que corta los ejes en los puntos (-1,0) , (5,0), (0,-10) ?​
kvasek [131]

Answer:

vertex: (2,-18)

Step-by-step explanation:

y = ax² + bx + c

(-1,0) : a - b + c = 0       ...(1)

(5,0) : 25a +5b +c = 0  ...(2)

(0,-10): 0a + 0b + c = -10        c=-10

(1) x5: 5a - 5b + 5c = 0  ...(3)

(2)+(3): 30a + 6c = 0          30a = -6c = 60        a = 2

(1): 2 - b -10 = 0     b = -8

Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18

equation: y = a(x-h)²+k     (h,k): vertex

vertex: (2,-18)

3 0
3 years ago
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