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2 years ago

Which set of ordered pairs could be generated by an exponential function?

Mathematics

1 answer:

Marrrta [24]2 years ago

7 0

The set that can represent an exponential function is the one in option c.

<h3></h3><h3>Which set of ordered pairs could be generated by an exponential function?</h3>

An exponential function is of the form:

$f(x) = A*(b)^x$

So, as x increases by one unit, we multiply the previous number by b.

From the given options, the only one that can represent an exponential function is the third one:

(1, 1/2) , (2, 1/4) , (3, 1/8) ( 4, 1/16)

As you can see, as x increases, the value of y keeps being divided by 2.

This exponential function is:

$f(x) = 1*(1/2)^x = (1/2)^x$

Evaluating it, we get:

$f(1) = (1/2)^1 = 1/2\\\\f(2) = (1/2)^2 = 1/4\\\\f(3) = (1/2)^3 = 1/8\\\\etc...$

Then we conclude that the correct option is the third one.

If you want to learn more about exponential functions:

brainly.com/question/11464095

#SPJ1

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If the first term is 3 (A1=3) and the common difference is 4 (d=4) what is the fifth term? (A5=?)

omeli [17]

Answer:

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Step-by-step explanation:

Pov:شما به ترجمه گوگل رفت برای دیدن آنچه من گفتم و دیدم این xD

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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.

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3 years ago

I’ll give you all my love and affection if you help me with this ASAP PLEASE ;)

guapka [62]

Answer: (12,0)

Steps:

First, put the equation in slope-intercept form.

y=mx+b

1.5x + 4.5y =18

Subtract 1.5x from both sides.

4.5y =-1.5x +18

Divide both sides by 4.5 to isolate y.

y = -1/3x + 4

Then replace y with 0 because the point for the x-intercept is exactly on the x-axis so the y=0.

0 = -1/3x + 4

Subtract 4 from both sides

-4 = -1/3x

Divide both sides by -1/3 to isolate the x

12=x

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3 years ago

parking garage has 5 floors. If 117 cars can be parked on each floor, how many total cars can park in the garage? Drag numbers t

mr Goodwill [35]

Answer:

585 cars

Step-by-step explanation:

Given

$Floors = 5$

$Cars = 117$ per floor

Required

Determine the total number of cars

This is calculated by multiplying number of cars per floor by number of floors.

$Total = Floors*Cars$

$Total = 5 * 117$

$Total = 585$

Hence, there are 585 cars in total

6 0

3 years ago

Triangle A B C is reflected over side A C and then is dilated to form smaller triangle D E C. Angles B C A and D C E are right a

andreyandreev [35.5K]

Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

Transformation involves the reshaping or resizing of a given figure. The types are: reflection, dilation, rotation and translation.

In the given question, the two operations performed on triangle ABC are reflection and dilation to form triangle DEC. The length of each side of triangle DEC is two-third of that of ABC. Therefore, the correct statements about the two triangles are:

i. △ABC ~ △DEC

ii. ∠B ≅ ∠E

iii. 3DE = 2AB

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4 years ago