What is if g(x,y,z) = x + y and S is the first octant portion of the plane 2x + 3y + z = 6 ?

Answers

Answer 1

Answer: The question asks for the value of $I=\int\int_Sx+y\textrm{ }dS$ where $S=\{(x,y,z)\mid2x+3z+y=6,x\ge0,y\ge0,z\ge0\}$ .

First let's look at what that surface looks like.

Letting $y=z=0$ yields $x=3$
Letting $x=z=0$ yields $y=2$
Letting $x=y=0$ yields $z=6$

Therefore $S$ is the area of the triangle defined by the three points $(3,0,0),(0,2,0),(0,0,6)$ .

We can thus reformulate the integral as $I=\int_(z=0)^6\int_(x=0)^(6-z)x+ydxdz$ .

By definition on the plane $y=\frac{6-2x-z}3$ thus $I=\int_(z=0)^6\int_(x=0)^(6-z)x+\frac{6-2x-z}3dxdz=\int_(z=0)^6\int_(x=0)^(6-z)2+\frac x3-\frac z3 dxdz$

$I=\int_(z=0)^6\left[2x+\frac{x^2}6-\frac{zx}3\right]_(x=0)^(6-z)dz=\int_(z=0)^62(6-z)+\frac{(6-z)^2}6-\frac{z(6-z)}3\right]dz$

$I=\int_(z=0)^6\frac{z^2}2-6z+18=\left[\frac{z^ 3}6-3z^2+18z\right]_(z=0)^6=36-108+108$

Hence $\boxed{I=\int\int_Sx+y\textrm{ }dS=36}$

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73/260 73 is what percent of 260. also 42/220 42 is what percent of 220. please help.

Answers

73 = x(260). Translate the word "is" as equals, and "of" as multiply. Divide both sides by 260 (as you already did): 73/260 = x

73/260 = 28%. (Move the decimal point two positions to the left).

42/220 = 19%.

Find dy/dx if y= (1+x)e^x^2

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$y=(1+x)e^(x^2)\ny'=(1+x)'\cdot e^(x^2)+(1+x)\cdot(e^(x^2))'\ny'=1\cdot e^(x^2)+(1+x)\cdot e^(x^2)\cdot (x^2)'\ny'=e^(x^2)+(1+x)e^(x^2)\cdot2x\ny'=e^(x^2)(1+(1+x)\cdot2x)\ny'=e^(x^2)(1+2x+2x^2)\ny'=e^(x^2)(2x^2+2x+1)\n$

You first need to know that:

$If\quad y=u\cdot v\n \n \frac { dy }{ dx } =u\frac { dv }{ dx } +v\frac { du }{ dx } \n \n$

Knowing that u is a function of x and that v is a function of x.

So:

$y=\left( 1+x \right) { e }^{ { x }^( 2 ) }=u\cdot v\n \n u=1+x,\n \n \therefore \quad \frac { du }{ dx } =1$

$\n \n v={ e }^{ { x }^( 2 ) }={ e }^( p )\n \n \therefore \quad \frac { dv }{ dp } ={ e }^( p )={ e }^{ { x }^( 2 ) }\n \n p={ x }^( 2 )\n \n \n \therefore \quad \frac { dp }{ dx } =2x$

$\n \n \therefore \quad \frac { dv }{ dp } \cdot \frac { dp }{ dx } =2x{ e }^{ { x }^( 2 ) }=\frac { dv }{ dx }$

And this means that:

$\frac { dy }{ dx } =\left( 1+x \right) \cdot 2x{ e }^{ { x }^( 2 ) }+{ e }^{ { x }^( 2 ) }\cdot 1\n \n =2x{ e }^{ { x }^( 2 ) }\left( 1+x \right) +{ e }^{ { x }^( 2 ) }$

$\n \n ={ e }^{ { x }^( 2 ) }\left( 2x\left( 1+x \right) +1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2x+2{ x }^( 2 )+1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2{ x }^( 2 )+2x+1 \right)$

Which graph displays a square root function?1)
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(1-4 are graphs and are answers)

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Hello,
last but not lease
Have a look to my graph.

answer 4

What is the answer to -16-90

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-16-90 = -16 + (-90) = -106

-106 is the right answer

A heptagon is a shape with how many sides?

Answers

A heptagon is a polygon with seven sides.

I believe a heptagon has 7 sides

What is the exact value of x in the exponential equation 2^8x − 3 = 7?x = log4/8log2
x = 1/8log2
x= 5/8
x =log5/8

Answers

Hello,

2^(8x)-3=7
==>2^(8x)=10
==>8x log (2)=log(10)
==>8x log(2)=1

==>x=1/(8*log(2))
With parenthesis on the denominator, the answer is B.