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givi [52]
3 years ago
14

Factor completely.

Mathematics
1 answer:
erik [133]3 years ago
3 0
(n-4)(n+11) so pretty much B
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That is rational number.
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2,000.....................
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Find the first, fourth, and eighth terms of the sequence. A(n) = –5 • 3n–1
jeka94

Answer:

<h2>C. -5; -135, -10,935</h2>

Step-by-step explanation:

\text{Substitute}\ n=1,\ n=4\ \text{and}\ n=8\ \text{to}\ A(n)=-5\cdot3^{n-1}:\\\\A(1)=-5\cdot3^{1-1}=-5\cdot3^0=-5\cdot1=-5\\\\A(4)=-5\cdot3^{4-1}=-5\cdot3^3=-5\cdot27=-135\\\\A(8)=-5\cdot3^{8-1}=-5\cdot3^7=-5\cdot2,187=-10,935

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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
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