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3 years ago

Which numbers should be multiplied to obtain 175^2 − 124^2?

Mathematics

2 answers:

Tomtit [17]3 years ago

7 0

Hi There! :)

Which numbers should be multiplied to obtain 175^2 − 124^2?

51 and 299

Ahat [919]3 years ago

5 0

Answer:

it is A

Step-by-step explanation:

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erik [133]

The first thing I would do is convert that 1.2 kilograms of salt to grams; that would ensure that all the units are the same so we can perform calculations on them.

1.2kg = 1200g

Next, I would find out how many students can do the experiment with 1200g of salt, by finding it how many 25g are in 1200g (by dividing them).

$\frac{1200g}{25g}=48students$

That means we still have 80 students left to provide salt for (128 - 48).
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Please simplify the following equation and show how: (2x+2)^3

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You can use (a+b)2 = a2+2ab+b2.
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3 years ago

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

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

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3 years ago