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maria [59]
3 years ago
11

Simplify to create an equivalent expression.

Mathematics
1 answer:
Olin [163]3 years ago
8 0
<span>−y−3(−3y+5)
= </span><span>−y + 9y - 15
= 8y - 15

answer
</span><span>d.8y-15</span>
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Consider the initial value problem y′′+36y=2cos(6t),y(0)=0,y′(0)=0. y″+36y=2cos⁡(6t),y(0)=0,y′(0)=0. Take the Laplace transform
Bingel [31]

Recall the Laplace transform of a second-order derivative,

L(y''(t)) = s^2Y(s)-sy(0)-y'(0)

and the transform of cosine,

L(\cos(at))=\dfrac s{a^2+s^2}

Here, both y(0)=y'(0)=0, so taking the transform of both sides of

y''(t)+36y(t)=2\cos(6t)

gives

s^2Y(s)+36Y(s)=\dfrac{2s}{36+s^2}

\implies Y(s)=\dfrac{2s}{(s^2+36)^2}

4 0
3 years ago
Jo jo has a total amount of $12.45 in quarters and dimes in his pocket. he has a total of 60 coins. how many quarters and dimes
baherus [9]

Given:

Total number of coins (Quarters and dimes) = 60

Total amount = $12.45

To find:

The number of quarters and dimes.

Solution:

Let x be the number of quarters and y be the number of dimes.

We know that,

1 quarter = 0.25 dollar

1 dime = 0.10 dollar

Total coins: x+y=60               ...(i)

Total amount: 0.25x+0.10y=12.45             ...(ii)

From (i), we get

y=60-x          ...(iii)

Putting this value in (ii), we get

0.25x+0.10(60-x)=12.45

0.25x+6-0.10x=12.45

0.25x-0.10x=12.45-6

0.15x=6.45

Divide both sides by 0.15.

x=\dfrac{6.45}{0.15}

x=43

Putting x=43 in (iii), we get

y=60-43

y=17

So, the number of quarters is 43 and the number of dimes is 17.

Therefore, the correct option is b.

8 0
2 years ago
14. A unfair coin has the probability of heads
Hitman42 [59]

Answer :

the probability of tossing three heads in a row

=\left( \frac{3}{8} \right)^{3}  =\frac{27}{512} =0.052734375

…………………………………………

the probability of tossing two heads followed by one tail

=\left( \frac{3}{8} \right)^{2}  \times \left( \frac{5}{8} \right)  =\frac{45}{512}

……………………………

the probability of two heads and one tail in any order

=3\times \left( \frac{3}{8} \right)^{2}  \times \left( \frac{5}{8} \right)  =\frac{135}{512}

3 0
2 years ago
Which of the following statements are true?
Oxana [17]

It is a point hope it helps you

7 0
3 years ago
Read 2 more answers
PLEASE HELP if all correct will give brainliest <br> 15!! POINTS
Vsevolod [243]

1. Linear Pair Postulate

2. Angle 2

3.Angle 3

4.Angle Congruence Postulate


4 0
3 years ago
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