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2 years ago

What is the measure of ∠ABC

Mathematics

1 answer:

astraxan [27]2 years ago

4 0

Answer:

Step-by-step explanation:

The measure of the chord- chord angle ABC is half the sum of the arcs intercepted by the angle and its vertical angle, that is

∠ ABC = 0.5( 82 + 44)° = 0.5 × 126° = 63° → B

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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

the front area of a pension house with dimension of 12m by 3m will be covered by bermuda grass.If the bermuda grass with dimensi

stich3 [128]

Answer:

yes

Step-by-step explanation:

and yes

4 0

1 year ago

Consider the isosceles triangle. left side (2x+8)units bottom of triangle (4x-10)units right side of triangle (2x+8) units Part

Blizzard [7]

Complete Question

Consider the isosceles triangle. left side (2z+8)units, bottom of triangle (4z-10)units, right side of triangle (2z+8) units Part A Which expression represents the perimeter of the triangle? a.(4z+16) units b.(6z−2)units c.(8z−16) units d.(8z+6) units

Answer:

d. (8z + 6) units

Step-by-step explanation:

The formula for the Perimeter of a Triangle is :Side A + Side B + Side C

Hence,

(2z + 8)units + (4z - 10) units + (2z + 8)units

= (2z + 8 + 4z - 10 + 2z + 8)units

Collect like terms

= 2z + 4z + 2z + 8 - 10 + 8

= 8z + 6 units

The expression that represents the perimeter of the triangle is (8z +6) units

3 0

2 years ago

What is 8(-9-5x) simplified

VLD [36.1K]

8(-9-5x)
=8(-9) - 8(5x)
= -72 - 40x
= - 40x - 72

expand by using distributive property

hope it helps

8 0

2 years ago

Find the unknown factor. 0= blank x (8 x 3)

algol [13]

I think the answer is 0

8*3=24

24 *0=0

3 0

1 year ago

Read 2 more answers