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3 years ago

Answer this please. Identify the vocabulary word that matches the picture. *

Mathematics

1 answer:

Greeley [361]3 years ago

4 0

Answer:

Step-by-step explanation:

The line BD divides a right angle into two acute angles <CBD + <DBA

They add to 90.

They are therefore complementary.

The word you are looking for is complementary.

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Rudik [331]

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2 years ago

Emily goes to the store with $56. She buys pants for $19, a shirt for $17 and 2 bracelets for $4. Does she have enough for a pai

Sergeu [11.5K]

19+17+4+4=44

56-44=12

20-12=8

No, and she needs 8 more dollars.

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3 years ago

can someone help me?, I had the notes in my notebook but the notebook got full, so I threw it away not thinking I was gonna need

Natalija [7]

Step-by-step explanation:

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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

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