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Veseljchak [2.6K]
3 years ago
12

Find the particular solution that satisfies the differential equation and the initial condition.

Mathematics
1 answer:
Vesnalui [34]3 years ago
7 0

Answer:

1) y =4x^2 +7

2) y =7s^2 -3s^4 +181

Step-by-step explanation:

Assuming that our function is y = f(x) for the first case and y=f(s) for the second case.

Part 1

We can rewrite the expression like this:

\frac{dy}{dx} =8x

And we can reorder the terms like this:

dy = 8 x dx

Now if we apply integral in both sides we got:

\int dy = 8 \int x dx

And after do the integrals we got:

y = 4x^2 +c

Now we can use the initial condition y(0) =7

7 = 4(0)^2 +c, c=7

And the final solution would be:

y =4x^2 +7

Part 2

We can rewrite the expression like this:

\frac{dy}{ds} =14s -12s^3

And we can reorder the terms like this:

dy = 14s -12s^3 dx

Now if we apply integral in both sides we got:

\int dy = \int 14s -12s^3 ds

And after do the integrals we got:

y = 7s^2 -3s^4 +c

Now we can use the initial condition y(3) =1

1 = 7(3)^2 -3(3)^4 +c, c=1-63+243=181

And the final solution would be:

y =7s^2 -3s^4 +181

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A total solar eclipse in 2003 lasted 8 9/20 minutes and was viewed from the southern hemisphere. The next total solar eclipse in
beks73 [17]

Answer:

5/101/180

Step-by-step explanation:

6 0
2 years ago
Given f(x)=4x+5 and g(x)= x^2+x; find (f∘g)(-5)<br> Please show all steps thank you
Greeley [361]

Answer:

(f\circ g)(-5)=85

Step-by-step explanation:

We are given:

\displaystyle f(x)=4x+5\text{ and } g(x)=x^2+x

And we want to find:

(f\circ g)(-5)

This is equivalent to:

\displaystyle =f(g(-5))

So, we will evaluate g(-5) first, which yields:

\displaystyle g(-5)=(-5)^2+(-5)=25-5=20

So:

=f(g(-5))=f(20)

Then:

\displaystyle f(20)=4(20)+5=80+5=85

Therefore:

(f\circ g)(-5)=85

6 0
3 years ago
It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 househo
BartSMP [9]

Complete Question

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

    The sample size is  n  = 120

    The  mean of the proportion is  p =  0.09

   

Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{p(1-p)}{n} }

=>   \sigma  =  \sqrt{\frac{0.09(1-0.09)}{120 } }

=>   \sigma  = 0.02612

Generally the chance that fewer than 3%   of households in the sample recycle their garbage is mathematically represented as

    P(X < 0.03) =  P( \frac{X - p}{\sigma}  <  \frac{0.03 -0.09}{0.02612} )

    P(X < 0.03) =  P( Z  < -2.297 )

From the z-table  

     P( Z  < -2.297 ) = 0.01

=> [tex]P(X < 0.03) = 0.01/tex]

=>   [tex]P(X < 0.03) = 1\% /tex]

4 0
2 years ago
Can someone please help with this asap its worth a lot of points. (: !!!
ladessa [460]

Answer:

8...the value of d variable =45 degree

corresponding angles are equal(reason)

9.

8 0
3 years ago
Read 2 more answers
The volume of a cylinder is 770 cm. It's height is 5 cm. Find its approximate radius.
Alinara [238K]

Hey there,

The equation for the volume of a cylinder is V = πr²h.

The first step into finding the radius is to plug in what you already know into the equation:

  • 770 = πr²5

We divide both sides by 5:

  • 154 = πr²

Now we divide both sides by π:

  • 49.0197224723 = r²

Finally we just do the square root of 49.0197224723:

  • 7.0014086063 = r

The radius therefore would be about 7cm.

Hope I helped,

Amna

3 0
3 years ago
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