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3 years ago

6. Based on this situation, give the real world meaning of the slope. Be specific.

Mathematics

1 answer:

Marat540 [252]3 years ago

7 0

Answer:

Getting paid $15 an hour in your job

Step-by-step explanation:

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If the perimeter of a square is 18.48 cm, how long is one side of the square?

Andrew [12]

One side is 4.62 cm long

6 0

3 years ago

Strain-displacement relationship) Consider a unit cube of a solid occupying the region 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1 After loa

Anastasy [175]

Answer:

please see answers are as in the explanation.

Step-by-step explanation:

As from the data of complete question,

$0\leq x\leq 1\\0\leq y\leq 1\\0\leq z\leq 1\\u= \alpha x\\v=\beta y\\w=0$

The question also has 3 parts given as

Part a: Sketch the deformed shape for α=0.03, β=-0.01 .

Solution

As w is 0 so the deflection is only in the x and y plane and thus can be sketched in xy plane.

the new points are calculated as follows

Point A(x=0,y=0)

Point A'(x+αx,y+βy)

Point A'(0+(0.03)(0),0+(-0.01)(0))

Point A'(0,0)

Point B(x=1,y=0)

Point B'(x+αx,y+βy)

Point B'(1+(0.03)(1),0+(-0.01)(0))

Point B'(1.03,0)

Point C(x=1,y=1)

Point C'(x+αx,y+βy)

Point C'(1+(0.03)(1),1+(-0.01)(1))

Point C'(1.03,0.99)

Point D(x=0,y=1)

Point D'(x+αx,y+βy)

Point D'(0+(0.03)(0),1+(-0.01)(1))

Point D'(0,0.99)

So the new points are A'(0,0), B'(1.03,0), C'(1.03,0.99) and D'(0,0.99)

The plot is attached with the solution.

Part b: Calculate the six strain components.

Solution

Normal Strain Components

$\epsilon_{xx}=\frac{\partial u}{\partial x}=\frac{\partial (\alpha x)}{\partial x}=\alpha =0.03\\\epsilon_{yy}=\frac{\partial v}{\partial y}=\frac{\partial ( \beta y)}{\partial y}=\beta =-0.01\\\epsilon_{zz}=\frac{\partial w}{\partial z}=\frac{\partial (0)}{\partial z}=0\\$

Shear Strain Components

$\gamma_{xy}=\gamma_{yx}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}=0\\\gamma_{xz}=\gamma_{zx}=\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x}=0\\\gamma_{yz}=\gamma_{zy}=\frac{\partial w}{\partial y}+\frac{\partial v}{\partial z}=0$

Part c: Find the volume change

$\Delta V=(1.03 \times 0.99 \times 1)-(1 \times 1 \times 1)\\\Delta V=(1.0197)-(1)\\\Delta V=0.0197\\$

Also the change in volume is 0.0197

For the unit cube, the change in terms of strains is given as

$\Delta V={V_0}[(1+\epsilon_{xx})]\times[(1+\epsilon_{yy})]\times [(1+\epsilon_{zz})]-[1 \times 1 \times 1]\\\Delta V={V_0}[1+\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}+\epsilon_{xx}\epsilon_{yy}+\epsilon_{xx}\epsilon_{zz}+\epsilon_{yy}\epsilon_{zz}+\epsilon_{xx}\epsilon_{yy}\epsilon_{zz}-1]\\\Delta V={V_0}[\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\$

As the strain values are small second and higher order values are ignored so

$\Delta V\approx {V_0}[\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\ \Delta V\approx [\epsilon_{xx}+\epsilon_{yy}+\epsilon_{zz}]\\$

As the initial volume of cube is unitary so this result can be proved.

5 0

3 years ago

Which combination of three side lengths will NOT form a triangle?

SpyIntel [72]

Answer:

The combination 9 mm, 6mm, 5mm will not form a triangle.

9 +6 = 15 > 5

6+5= 11 < 9

9+5 =14 > 6

Explanation :

because the side length of triangle does not obey triangle inequality theorem.

The triangle inequality theorem:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

4 0

3 years ago

Write the expression in simplest form: 5n - 6 + n - 1

nata0808 [166]

To write this equation in simplest form, we simply need to combine all like terms. The like terms in this particular expression are the terms with an n-variable and the terms with no variable. So we can combine them to simplify our expression.

5n - 6 + n - 1

First step, we can reorder our terms so that like terms are near each other

5n + n - 6 - 1

Now we can combine easily

(5n + n) - (6 - 1)

6n - 5

And that is your simplified expression.

5n - 6 + n - 1 in simplest form is 6n - 5.
Hope that helped! =)

4 0

3 years ago

Emily decided to take up Weightlifting she thought it would be

melisa1 [442]

Answer:

Common Ratio = 2

Step-by-step explanation:

Emily started with 12 lb at start.

She will double each day

So,

2nd day she will take up weight = 12 * 2 = 24

3rd day she will take up weight = 24 * 2 = 48

and so on

This is a geometric sequence, which is a sequence where each term is found by multiplying the previous term by a constant which is known as the common ratio.

Here, we are multiplying by "2" to get the next term, so we an say the common ratio is "2".

Answer: Common Ratio = 2

8 0

3 years ago