2 years ago

Write an expression that is equivalent to 30(x + y + 1)

Mathematics

1 answer:

Lerok [7]2 years ago

4 0

Answer:

30x + 30y +30

Step-by-step explanation:

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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

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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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3 years ago

Solve the following 1-step equation for x

shtirl [24]

X/0.5 = 24
X/0.5(0.5) = 24(0.5)
X = 12

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3 years ago

What is the approximate volume of a half sphere with a diameter of 8 cm?

Anestetic [448]

Answer:

134.04

Step-by-step explanation:

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2 years ago

Given that у=6 cm and θ=15 °, work out x rounded to 1 decimal place.

Lubov Fominskaja [6]

Sin(15)=6/x
x=6/sin(15)
x=23.2°

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2 years ago

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You will have to go step by step

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2 years ago