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2 years ago

sues to gallons of gas on a 300-mile trip Jen's car used 5 gallons of gas on 140 road trip whose car got more miles per gallon

Mathematics

1 answer:

ehidna [41]2 years ago

8 0

Sue has more miles per gallon.

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) Set up a double integral for calculating the flux of F=3xi+yj+zk through the part of the surface z=−5x−2y+2 above the triangle

Fynjy0 [20]

The surface (call it $S$ ) is a triangle with vertices at the points

$x=0,y=0\implies z=2\implies(0,0,2)$

$x=0,y=2\implies z=-2\implies(0,2,-2)$

$x=2,y=0\implies z=-8\implies(2,0,-8)$

Parameterize $S$ by

$\vec s(u,v)=(1-v)(2,0,-8)+v\bigg((1-u)(0,2,-2)+u(0,0,2)\bigg)=(2-2v,2v-2uv,-8+6v+4uv)$

with $0\le u\le1$ and $0\le v\le1$ . Take the normal vector to $S$ to be

$\vec s_v\times\vec s_u=(20v,8v,4v)$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^1\int_0^1\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^1\int_0^1(6-6v,2v-2uv,-8+6v+4uv)\cdot(20v,8v,4v)\,\mathrm du\,\mathrm dv$

$=\displaystyle8\int_0^1\int_0^1(11v-10v^2)\,\mathrm du\,\mathrm dv=\boxed{\frac{52}3}$

8 0

3 years ago

What is the value of the expression?

mr Goodwill [35]

Answer: B.792

Step-by-step explanation:

5 0

1 year ago

The equation y=x^3 + 3 is symmetric with respect to which of he following?

lianna [129]

$y = x^{3} +3$

Subtract 3 from both sides,

$y-3=x^{3}$

Let x = X and y - 3 = Y

Then,

$Y = X^{3}$

So, we have shifted the origin to a point (0, 3).

This is an odd function and the graph of an odd function is symmetrical about the origin.

That is, symmetrical about X = 0, Y = 0

Symmetrical about x = 0,, y - 3 = 0

Symmetrical about x = 0, y = 3.

Hence, the graph is symmetrical about the point (0, 3).

3 0

2 years ago

Statement Reason

andrew11 [14]

Answer:vhv

Step-by-step explanation:hhgjhghjgjg

7 0

2 years ago

A student buys a guitar that is on sale for 15% off the regular price of $200. He also must pay an 8% sales tax. What is his tot

EastWind [94]

Answer:

option c

Step-by-step explanation:

a guitar 15% off means that the cost is now 85%

$100percent---200dollars\\85percent---x\:dollars\\\\x=\frac{200*85}{100}\\\\x=2*85\\\\x=170$

now the 8% of 170 is

$100\:percent---170\:dollars\\\\8\:percent---x\:dollars$

$x=\frac{8*170}{100}\\\\x=\frac{8*17}{10}\\\\x=13.6$

so the total cost is

170+13.6

183.6

6 0

2 years ago