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3 years ago

What is 28/3 as a mixed number

Mathematics

1 answer:

svlad2 [7]3 years ago

6 0

Answer:

9 1/3

Step-by-step explanation:

First, note that 3 goes into 27 9 times, with a remainder of 1.

Thus, 28/3 = 9 1/3

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

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

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

If x = 3 /4 and y = 8, consider the sum of x and y. Which statement describes the sum of x and y? A) The sum of x and y is a rat

maksim [4K]

Answer: A is the correct one

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3 years ago

Dana needs 6 meters of ribbon to make bows. She has 160 centimeters of ribbon. Does Dana have enough ribbon to make bows? Explai

ozzi

No; to make a bow, you need 6 meters and 6 meters = 600 centimeters. If Dana only has 160 centimeters of ribbon, bows cannot be made because 600 cm is more than 160 cm.

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3 years ago

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Gwar [14]

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Step-by-step explanation:

Just multiply 0.23 with 32

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