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natali 33 [55]
2 years ago
10

What is the value of the rational expression 2x+1 when x = 5?

Mathematics
2 answers:
Nataly [62]2 years ago
6 0

Step-by-step explanation:

2x+1

x = 5

2(5)+1

=10+1=11

Stolb23 [73]2 years ago
6 0

Answer:

2(5)+1

10+1

11

Hope This Helps!!!

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Jon has 6 kites he and his friends will each fly one kite how many people in all will fly a kit
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Answer:

  6

Step-by-step explanation:

One person will fly a kite for each of the 6 kites Jon has.

6 people in all will fly a kite.

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3 years ago
Which equation represents a line that passes through (2,-1/2) and has a slope of 3 ?
Anna11 [10]

Answer:

C. y + \frac{1}{2} = 3(x - 2)

Step-by-step explanation:

Given

Point:  (2,\frac{-1}{2})

Slope: 3

Required

Equation of line

Let m represents the slope of the line;

m is calculated as thus

m = \frac{y - y_1}{x - x_1}

where (x_1,y_1) = (2,\frac{-1}{2})

So; x_1 = 2; y_1 = \frac{-1}{2}

m = 3

By substituting the right values in the formula above;

m = \frac{y - y_1}{x - x_1} becomes

3 = \frac{y - \frac{-1}{2}}{x - 2}

Multiply both sides by (x - 2)

3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)

3 *(x - 2) = (y - \frac{-1}{2})

3 *(x - 2) = (y + \frac{1}{2})

3(x - 2) = (y + \frac{1}{2})

3(x - 2) = y + \frac{1}{2}

Reorder

y + \frac{1}{2} = 3(x - 2)

Hence, the equation that represents the line is y + \frac{1}{2} = 3(x - 2)

4 0
3 years ago
HELP ME PLEASE! tell me if 11,12 are right and help w/ 13
Marysya12 [62]

Answer: I know 12 is right

Step-by-step explanation:

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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

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

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+<em>α</em><em>x,y+</em><em>β</em><em>y) </em>

Point A'(0+<em>(0.03)</em><em>(0),0+</em><em>(-0.01)</em><em>(0))</em>

Point A'(0<em>,0)</em>

Point B(x=1,y=0)

Point B'(x+<em>α</em><em>x,y+</em><em>β</em><em>y) </em>

Point B'(1+<em>(0.03)</em><em>(1),0+</em><em>(-0.01)</em><em>(0))</em>

Point <em>B</em>'(1.03<em>,0)</em>

Point C(x=1,y=1)

Point C'(x+<em>α</em><em>x,y+</em><em>β</em><em>y) </em>

Point C'(1+<em>(0.03)</em><em>(1),1+</em><em>(-0.01)</em><em>(1))</em>

Point <em>C</em>'(1.03<em>,0.99)</em>

Point D(x=0,y=1)

Point D'(x+<em>α</em><em>x,y+</em><em>β</em><em>y) </em>

Point D'(0+<em>(0.03)</em><em>(0),1+</em><em>(-0.01)</em><em>(1))</em>

Point <em>D</em>'(0<em>,0.99)</em>

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.

<em>Part b: Calculate the six strain components.</em>

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: <em>Find the volume change</em>

<em></em>\Delta V=(1.03 \times 0.99 \times 1)-(1 \times 1 \times 1)\\\Delta V=(1.0197)-(1)\\\Delta V=0.0197\\<em></em>

<em>Also the change in volume is 0.0197</em>

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.

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