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vova2212 [387]
3 years ago
15

Evaluate each absolute value expression below | 2 | + | 4 | | − 3 | + | 5 | | − 7 | + | − 1 | − | 6 |

Mathematics
1 answer:
Bingel [31]3 years ago
4 0

Answer:

  44

Step-by-step explanation:

The absolute value symbols turn any negative inside of them to a positive, so your expression is ...

  2 + 4·3 +5·7 +1 -6

  = 2 +12 +35 +1 -6

  = 44

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Give a real world example for when you would
Lelechka [254]

Answer:

Let's say that someone was building a yard.

(I tired to make this all connected.)

For Part 1) He wants to put his fence around the yard. If it's a rectangle measuring 45 * 32 ft, he would have to find the perimeter of the rectangle so he could install the correct amount of fences. The perimeter is the measurement 'around' a shape.

For area (part 2), if he wanted to know how much he was able to put stuff inside, he would have to find the area of the rectangle. The area is the space occupied by a 2D shape.

Part 3: The person then wants to paint a box as a decoration. He has a small 3 * 3 *3 box. The person needs to find how much paint he needs to cover the box appropriately, or the surface area of the box. Surface area is the total measurement of the surface in a 3D figure.

Part 4: He then wants to put something in the box. He does not know how much can he fit in it, so he would have to find the volume of the box. The volume of a 3D figure is the measurement of how much it can 'fill' the shape.

Hope this helps.  

8 0
3 years ago
500 grams of tomatoes cost £1.76 how much will 1.75kg cost??
ValentinkaMS [17]
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3 0
3 years ago
What is the recursive rule for the sequence?
adoni [48]
An= -2 (an+1), a1 = 5
5 0
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)

4 0
3 years ago
How do I find the slope of the line?
charle [14.2K]

Answer:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Step-by-step explanation:

yeah

5 0
2 years ago
Read 2 more answers
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