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2 years ago

Which expression uses the associative property to make it easier to evalute?

Mathematics

1 answer:

mixas84 [53]2 years ago

6 0

Answer:

The correct option is (c).

Step-by-step explanation:

The given expression is :

$14(\dfrac{3}{2}\times \dfrac{1}{4})$

We need to use the associative property to make it easier.

The associative property for multiplication is as follows :

$A\times (B\times C)=(A\times B)\times C$

We have,

$A=14, B=\dfrac{3}{2}\ and\ C=\dfrac{1}{4}$

$14(\dfrac{3}{2}\times \dfrac{1}{4})=(14\times \dfrac{3}{2})\times \dfrac{1}{4}$

Hence, the correct option is (c).

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

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1 year ago

Percentage:

masha68 [24]

20 percent
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2 years ago

Answer this please it’s for algebra 2

Sergeu [11.5K]

Part a)

P(junior) = (number of juniors)/(number total)

P(junior) = 235/705

P(junior) = 1/3 exactly

P(junior) = 0.33333 approximately

======================================

Part b)

P(freshman and LG) = (number of freshman who have LG)/(number total)

P(freshman and LG) = 70/705

P(freshman and LG) = 14/141 exactly

P(freshman and LG) = 0.09929 approximately

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Part c)

n(junior) = number of juniors = 235

n(samsung) = number of people who have samsung = 274

n(junior and samsung) = number of juniors who have samsung = 93

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n(junior or samsung) = n(junior)+n(samsung)-n(junior and samsung)

n(junior or samsung) = 235+274-93

n(junior or samsung) = 416

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P(junior or samsung) = n(junior or samsung)/n(total)

P(junior or samsung) = 416/705 exactly

P(junior or samsung) = 0.59007 approximately

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Part d)

n(sophomore and apple) = number of sophomores who have apple

n(sophomore and apple) = 80

n(apple) = number of students who have apple

n(apple) = 261

P(sophomore | apple) = n(sophomore and apple)/n(apple)

P(sophomore | apple) = 80/261 exactly

P(sophomore | apple) = 0.30651 approximately

======================================

Part e)

define the events

A = junior who has apple

B = junior who has samsung

C = person is a junior

n(A or B) = number of juniors who have apple or samsung

n(A or B) = n(A) + n(B) ... A and B assumed mutually exclusive

n(A or B) = 87+93

n(A or B) = 180

n(C) = 235

P( (Apple or Samsung) | Junior ) = n(A or B)/n(C)

P( (Apple or Samsung) | Junior ) = 180/235

P( (Apple or Samsung) | Junior ) = 36/47 exactly

P( (Apple or Samsung) | Junior ) = 0.76596 approximately

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3 years ago

the domain of a function f(x) is x > 1, and the range is y < -2. What are the domain and range of its inverse function, f^

Marianna [84]

9514 1404 393

Answer:

domain: x < -2
range: y > 1

Step-by-step explanation:

Domain and range of the inverse function are swapped: the domain of the function is the range of its inverse, and vice versa.

The graph shows an example of a function and its inverse with the given domain and range. The function is red; its inverse is blue.

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3 years ago

The lengths of the sides of a triangle are 5, 12, and 13. What is the length of the altitude drawn to the side with length equal

mario62 [17]

Answer: using A= bh/2 THe height is 9.23

Step-by-step explanation: First, with the Right Angle at the bottom, usr the sides to compute the area: 12*5=60

THen Imagine the side=13 as the base, so you have b=13 for the formula

use the formula A= bh/2

60 = 13h/2 ==> 2(60) =13h --> 120/13 = h

h = 9.23

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2 years ago

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