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3 years ago

Solve the system of equations y=9x+13 y=2x+48

1 answer:

7 0

Both are equal y. So you can set them equal to each other

9x+13=2x+48

Subtract 2x from both sides

7x+13=48
Subtract 13 from both sides

7x= 35

X=5

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Y (y-4) – (y-2) (y-3)=10

marshall27 [118]

Answer:

y =16

I have solved it . It's in the picture above. Hope it helps

8 0

3 years ago

I.5y=2x-5 II.5y=4+3x III.5y-3x=-1

Ratling [72]

Answer:

Step-by-step explanation:

the vale of x differs in each situation are we talking AB value

6 0

2 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

2 years ago

Use the Distance Formula to find the distance between D(2, 0) and E(8, 6).

Mazyrski [523]

Answer:

The answer is

<h2> $6 \sqrt{2} \: \: \: or \: \: \: 8.50 \: \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question

The points are D(2, 0) and E(8, 6

The distance between them is

$|DE| = \sqrt{ ({2 - 8})^{2} + ({0 - 6})^{2} } \\ = \sqrt{( { - 6})^{2} + ( { - 6})^{2} } \\ = \sqrt{36 + 36} \\ = \sqrt{72} \: \: \: \: \: \: \: \: \: \: \\ = 6 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \\ = 8.4852813$

We have the final answer as

$6 \sqrt{2} \: \: \: or \: \: \: 8.50 \: \: \: \: units$

Hope this helps you

5 0

3 years ago

A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after

morpeh [17]

Answer:

=0.1587 or 15.87%

So option A is correct answer so 15.87% of the invoices were paid within 15 days of receipt.

Step-by-step explanation:

In order to find the percent of the invoices paid within 5 days of receipt we have to find the value of Z first.

$Z=\frac{X-u}{S}$

where:

X is the random varable which in our case is 15 days

u is the mean or average value which is 20 days

S is the standard deviation which is 5 days

$Z=\frac{15-20}{5}$

Z=-1.0

We have to find Probability at Z less than -1

P(Z<-1.0) which can be written as:

=1-P(Z>1.0)

From Cumulative distribution table:

=1-(0.3413+0.5)

=0.1587 or 15.87%

So option A is correct answer so 15.87% of the invoices were paid within 15 days of receipt.

7 0

3 years ago