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3 years ago

If a= 11, solve for b and c.

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

8 0

Step-by-step explanation:

b = 11

c = 11✓2 because the properties of 45 45 90 triangle

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Pla help pls : What is the first step to solving the following equation? 5x – 11 = 42

kow [346]

Answer:

x = 10.6

Step-by-step explanation:

5x - 11 = 42

first +11 so,

5x = 53

then ÷5

x = 10.6

3 0

3 years ago

Justify your answer

BaLLatris [955]

Answer:

8cm

Step-by-step explanation:

x is similar to the side 12cm.

We know the second triangle is rotated counter-clockwise from the first because similar triangles have the same angle measurements.

Since the angle in the first triangle between 9cm and 15cm is 53°, it can't be similar to the angle between x and the hypotenuse in the second triangle.

Find the scale factor:

Triangle 1/Triangle 2

Divide two similar sides.

6/9 = 2/3

Multiply the scale factor by the similar side to find x.

x = 12*(2/3)

x = 8

7 0

3 years ago

HELP ME PLEASE

Mashutka [201]

Answer:

$9 + \frac{n}{3} - 6 = 7$

Step-by-step explanation:

Given

$9 + \frac{n}{3} - 6$

Required

Evaluate when n = 12

Substitute 12 for n in $9 + \frac{n}{3} - 6$

$9 + \frac{n}{3} - 6 = 9 + \frac{12}{3} - 6$

Simplify the fraction

$9 + \frac{n}{3} - 6 = 9 + 4 - 6$

$9 + \frac{n}{3} - 6 = 7$

4 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

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