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mamaluj [8]
3 years ago
14

Multiply. Express your answer in lowest terms. 3/8 x 2/7 = ?/?

Mathematics
2 answers:
Murljashka [212]3 years ago
6 0
Simple, multiply.

3/8*2/7

You can cross cancel the 2 and the 8, making them into a 1 and 4.

Making it,

3/4*1/7

Multiply,

3/28. This can't be simplified further; thus, 3/28 is your answer.
andrew11 [14]3 years ago
5 0
The answer is 6/56 or because 3*2=6 and 8*7=56
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Graph the relation shown in the table. Is the relation a function? Why or why not?
patriot [66]

Answer:

The chosen topic is not meant for use with this type of problem. Try the examples below.

x + 6 y = 5

6 x + 2 y = 8

x − y + 4 = 8

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Step-by-step explanation:

Find the equation with a point and y-intercept.

y = ( y/ x  −  y )  x  +  x y

The chosen topic is not meant for use with this type of problem. Try the examples below.

( 0 , 9 )  ,  ( 8 , 6 )

( 0 , 9 )  ,  ( 5 , 4 )  ,  ( 1 , 4 )

( 1 , 2 )  ,  ( 3 , 4 )

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3 years ago
Tania creates a chain letter and sends it to
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Step-by-step explanation:

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3 years ago
Find the critical points of the function f(x, y) = 8y2x − 8yx2 + 9xy. Determine whether they are local minima, local maxima, or
NARA [144]

Answer:

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

Step-by-step explanation:

The function is:

f(x,y) = 8\cdot y^{2}\cdot x -8\cdot y\cdot x^{2} + 9\cdot x \cdot y

The partial derivatives of the function are included below:

\frac{\partial f}{\partial x} = 8\cdot y^{2}-16\cdot y\cdot x+9\cdot y

\frac{\partial f}{\partial x} = y \cdot (8\cdot y -16\cdot x + 9)

\frac{\partial f}{\partial y} = 16\cdot y \cdot x - 8 \cdot x^{2} + 9\cdot x

\frac{\partial f}{\partial y} = x \cdot (16\cdot y - 8\cdot x + 9)

Local minima, local maxima and saddle points are determined by equalizing  both partial derivatives to zero.

y \cdot (8\cdot y -16\cdot x + 9) = 0

x \cdot (16\cdot y - 8\cdot x + 9) = 0

It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:

\left \{ {{-16\cdot x + 8\cdot y=-9} \atop {-8\cdot x + 16\cdot y=-9}} \right.

The solution of the system is (3/8, -3/8).

Let assume that y = 0, the nonlinear system is reduced to a sole expression:

x\cdot (-8\cdot x + 9) = 0

Another solution is (9/8,0).

Now, let consider that x = 0, the nonlinear system is now reduced to this:

y\cdot (8\cdot y+9) = 0

Another solution is (0, -9/8).

The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:

H = \frac{\partial^{2} f}{\partial x^{2}} \cdot \frac{\partial^{2} f}{\partial y^{2}} - \frac{\partial^{2} f}{\partial x \partial y}

The second derivatives of the function are:

\frac{\partial^{2} f}{\partial x^{2}} = 0

\frac{\partial^{2} f}{\partial y^{2}} = 0

\frac{\partial^{2} f}{\partial x \partial y} = 16\cdot y -16\cdot x + 9

Then, the expression is simplified to this and each point is tested:

H = -16\cdot y +16\cdot x -9

S1: (0,0)

H = -9 (Saddle Point)

S2: (3/8,-3/8)

H = 3 (Local maximum or minimum)

S3: (9/8, 0)

H = 9 (Local maximum or minimum)

S4: (0, - 9/8)

H = 9 (Local maximum or minimum)

Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:

S2: (3/8,-3/8)

f(\frac{3}{8} ,-\frac{3}{8} ) = - \frac{27}{64} (Local minimum)

S3: (9/8, 0)

f(\frac{9}{8},0) = 0 (Local maximum)

S4: (0, - 9/8)

f(0,-\frac{9}{8} ) = 0 (Local maximum)

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

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3 years ago
There are 6 swimmers in a race. In how many ways can they finish in first and second place?
hodyreva [135]

Answer:

step 1. 6x2=12 first place way

step 2. 12×2=24

step 3. 24+6=30 second place way

6 0
2 years ago
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