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3 years ago

Reduce to simplest form 6/3+(- 1/6)

Mathematics

2 answers:

rusak2 [61]3 years ago

8 0

Answer: 11/6

Step-by-step explanation:

zavuch27 [327]3 years ago

5 0

Answer:

11/6

Step-by-step explanation:

6/3+(-1/6)

2+(-1/6)

2-1/6

12/6-1/6

11/6

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An augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of the system.

Angelina_Jolie [31]

Answer:

(x, y, z) = (-4, 2, 1)

Step-by-step explanation:

See the attachment for the output of a calculator that produces the reduced row-echelon form of the matrix.

The [x, y, z] result vector is the column on the right.

(x, y, z) = (-4, 2, 1)

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Numerous web sites are available for computing the row-reduced form of the matrix, or for solving the system of equations. Your graphing calculator will do it as well.

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3 years ago

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3 years ago

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Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.