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cluponka [151]
3 years ago
9

First-order linear differential equations

Mathematics
1 answer:
garik1379 [7]3 years ago
4 0

Answer:

(a) \frac{dy}{(2y+1)}=tdt (b) y=\frac{e^{t^2}+e^{2c}-1}{2}

Step-by-step explanation:

(1) We have given \frac{dy}{dt}+ycost=0

\frac{dy}{dt}=-ycost

\frac{dy}{y}=-costdt

Integrating both side

lny=-sint+c

y=e^{-sint}+e^{-c}

(2) \frac{dy}{dt}-2ty=t

\frac{dy}{dt}=2ty+t

\frac{dy}{dt}=t(2y+1)

\frac{dy}{(2y+1)}=tdt

On integrating both side  

\frac{ln(2y+1)}{2}=\frac{t^2}{2}+c

ln(2y+1)={t^2}+2c

2y+1=e^{t^2}+e^{2c}

y=\frac{e^{t^2}+e^{2c}-1}{2}

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Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum
IrinaK [193]

Answer:

0.84

Step-by-step explanation:

Given that Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:

P(A) = 0.86, P(B) = 0.79, P(A') = 0.14, P(AUB) = 0.95

We are to find out P(A'UB)

We have

P(AUB) =P(A)+P(B)-P(A\bigcap B)\\0.95=0.86+0.79-P(A\bigcap B)\\P(A\bigcap B)=0.70

P(A'UB) = P(A')+P(B)-P(A' \bigcap B)\\= 1-P(A) +P(B)-[P(B)-P(A \bigcap B)]\\= 1-0.86+0.79-P(B)+[tex]P(A'UB)=0.14+0.79-0.79+0.70\\=0.84P(A \bigcap B)[/tex]

7 0
3 years ago
which is a correct definition for a right angle? a.an angle with a measure that equals the measure of a square corner b.an angle
Sunny_sXe [5.5K]
A. an angle with a measure that equals the measure of a square corner
6 0
3 years ago
40% of the memberships sold by Gym A were gold memberships.
Aneli [31]

Answer:

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

Step-by-step explanation:

Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.  

Which statement must be true?

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.

c) Gym A sold more gold membership than Gym A did.

d) If Gym B sold 50 membership, 25 would be gold memberships.

Given: Gym A have sold 40% gold membership of total membership.

Gym B have sold 25% gold membership of total membership.

Lets take option A first to find if it is true statement.

As per option A, There are total number of membership is 80.

∵ Gym A has sold 40% gold membership.

∴ Gym A gold membership= 40\% \times 80

⇒ Gym A gold membership= \frac{40}{100} \times 80= 32 member.

∴ Gym A gold membership= 32.

Now, Gym B

∵ Gym B has sold 25% gold membership.

∴ Gym B gold membership= 25\% \times 80

⇒ Gym B gold membership= \frac{25}{100} \times 80=20 member.

∴ Gym B gold membership= 20.

Next finding difference gold membership for Gym A and Gym B

32-20= 12 \ membership

Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.

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3 years ago
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The polynomial is not factorable with rational numbers
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