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3 years ago

F(x)=x^2(x+3)^2 How do I find the roots of this equation?

Mathematics

1 answer:

Genrish500 [490]3 years ago

6 0

= x^2 ( x+3 ) (x+3)
= set equal to 0

X^2= 0
X=0

X+3=0
X=-3

Answer is -3 and 0

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What is the y-intercept of y= -3x

krek1111 [17]

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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

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

The number of Roberto’s baseball cards is ¾ the number of David’s cards If Roberto gives ½ of his cards to David, what will be t

inn [45]

Answer:

1/4, 0.25

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

8y cubed +3xy+2y squared - 4xy

Irina-Kira [14]

Answer:

8y^2 + 3xy + 2y^2 - 4xy

8y^2 + 2y^2 + 3xy - 4xy

10y^4 - 1xy

Step-by-step explanation:

8y^2 + 3xy + 2y^2 - 4xy

8y^2 + 2y^2 + 3xy - 4xy

10y^4 - 1xy

7 0

4 years ago

You would like to make a nutritious meal of eggs, edamame, and elbow macaroni. The meal should provide at least 40 g of carbohyd

Virty [35]

Answer:

Lets denote

1. eggs as x,

2. edamame as y

3. elbow macaroni as z

The problem then is

min TC=2x+5y+3z

subject to

$2x+12y+43z \geq40\\17x+12y+8z\geq20\\14x+6y+z\leq50\\x\geq0\\y\geq0\\z\geq0$

Step-by-step explanation:

First the objective is to minimize total cost subject to some nutritional requirements.

So the total cost function (TC) is the number of servings multiplied for the corresponding costs. Eggs cost 2, edamame 5, and macaroni 3

Next we have to meet the nutritional requirements, the first of the restrictions is the protein restriction. The problem requires that the meal contains at least 40g of carbohydrates (that is why the restriction is $\geq 40$ ). Then we add how much each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.

Same for protein, we need at least 20 grams of protein ( $\geq 20$ ). Eggs add 17g, edamame adds 12g, and macaroni adds 8g.

Finally we don't want more than 50 grams of fat ( $\leq50$ ). Eggs add 14g, edamame add 6g and macaroni 1g.

Finally, we add the non negativity restrictions-> we cannot buy negative quantities of these goods, but we allow for zero.

7 0

3 years ago