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2 years ago

11

. Beth is making gingerbread men. She uses 2 raisins for eyes and 3 raisins for buttons for each gingerbread man. She buys 4 box

es of raisins, each with 120 raisins in it. How many dozens of gingerbread men can she make

1 answer:

vagabundo [1.1K]2 years ago

3 0

I think the answer is Beth can make 8 dozen gingerbread men

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umka2103 [35]

Answer:

0.1666666666

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3 years ago

Solve for x<br><br><br><br><br> Thankyouhjg

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2 years ago

Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview

mario62 [17]

Answer: The required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.$

So, the general solution of the given equation is

$y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.$

According to the given conditions, we have

$y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.$

From equation (ii), we get

$B=\dfrac{7}{3}.$

Thus, the required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

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3 years ago

Which fraction is equal to 0.5 7

Andrei [34K]

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3 years ago

Which of the following is not a factor of x^3 – 3x^2 – 4x + 12?

Slav-nsk [51]

Answer:

c. (x + 3)

Step-by-step explanation:

using factor theorem

if x - 3 is a factor then p(a) = 0

p(a)= x^3 - 3x^2 - 4x + 12

a.(x-3)

p(3) = (3)^3 - 3(3)^2 - 4(3) + 12

= 27 - 27 - 12 + 12

= 0

therefore x-3 is a factor

b.(x + 2)

p(-2) = (-2)^3 - 3(-2)^2 - 4(-2) + 12

= -8 -12 + 8 + 12

,= 0

therefore x + 2 is a factor

c.(x + 3)

p(-3) = (-3)^3 - 3(-3)^2 - 4(-3) + 12

= -27 -27 + 12 + 12

= -30

therefore x + 3 is not a factor

d.(x-2)

p(2) = (2)^3 - 3(2)^2 - 4(2) + 12

= 8 -12 - 8 + 12

= 0

therefore x - 2 is a factor

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3 years ago