Please help me!
14
33
46
60
200

(1) Both equations in (a) and (b) are separable.

(a)

[tex]\dfrac xy y' = \dfrac{2y^2+1}{x+1} \implies \dfrac{\mathrm dy}{y(2y^2+1)} = \dfrac{\mathrm dx}{x(x+1)}[/tex]

Expand both sides into partial fractions.

[tex]\left(\dfrac1y - \dfrac{2y}{2y^2+1}\right)\,\mathrm dy = \left(\dfrac1x - \dfrac1{x+1}\right)\,\mathrm dx[/tex]

Integrate both sides:

[tex]\ln|y| - \dfrac12 \ln\left(2y^2+1\right) = \ln|x| - \ln|x+1| + C[/tex]

[tex]\ln\left|\dfrac y{\sqrt{2y^2+1}}\right| = \ln\left|\dfrac x{x+1}\right| + C[/tex]

[tex]\dfrac y{\sqrt{2y^2+1}} = \dfrac{Cx}{x+1}[/tex]

[tex]\boxed{\dfrac{y^2}{2y^2+1} = \dfrac{Cx^2}{(x+1)^2}}[/tex]

(You could solve for y explicitly, but that's just more work.)

(b)

[tex]e^{x+y}y' = 3x \implies e^y\,\mathrm dy = 3xe^{-x}\,\mathrm dx[/tex]

Integrate both sides:

[tex]e^y = -3e^{-x}(x+1) + C[/tex]

[tex]\ln(e^y) = \ln\left(C - 3e^{-x}(x+1)\right)[/tex]

[tex]\boxed{y = \ln\left(C - 3e^{-x}(x+1)\right)}[/tex]

(2)

(a)

[tex]y' + \sec(x)y = \cos(x)[/tex]

Multiply both sides by an integrating factor, sec(x) + tan(x) :

[tex](\sec(x)+\tan(x))y' + \sec(x) (\sec(x) + \tan(x)) y = \cos(x) (\sec(x) + \tan(x))[/tex]

[tex](\sec(x)+\tan(x))y' + (\sec^2(x) + \sec(x)\tan(x)) y = 1 + \sin(x)[/tex]

[tex]\bigg((\sec(x)+\tan(x))y\bigg)' = 1 + \sin(x)[/tex]

Integrate both sides and solve for y :

[tex](\sec(x)+\tan(x))y = x - \cos(x) + C[/tex]

[tex]y=\dfrac{x-\cos(x) + C}{\sec(x) + \tan(x)}[/tex]

[tex]\boxed{y=\dfrac{(x+C)\cos(x) - \cos^2(x)}{1+\sin(x)}}[/tex]

(b)

[tex]y' + y = \dfrac{e^x-e^{-x}}2[/tex]

(Note that the right side is also written as sinh(x).)

Multiply both sides by e ˣ :

[tex]e^x y' + e^x y = \dfrac{e^{2x}-1}2[/tex]

[tex]\left(e^xy\right)' = \dfrac{e^{2x}-1}2[/tex]

Integrate both sides and solve for y :

[tex]e^xy = \dfrac{e^{2x}-2x}4 + C[/tex]

[tex]\boxed{y=\dfrac{e^x-2xe^{-x}}4 + Ce^{-x}}[/tex]

(c) I've covered this in an earlier question of yours.

(d)

[tex]y'=\dfrac y{x+y}[/tex]

Multiply through the right side by x/x :

[tex]y' = \dfrac{\dfrac yx}{1+\dfrac yx}[/tex]

Substitute y(x) = x v(x), so that y' = xv' + v, and the DE becomes separable:

[tex]xv' + v = \dfrac{v}{1+v}[/tex]

[tex]xv' = -\dfrac{v^2}{1+v}[/tex]

[tex]\dfrac{1+v}{v^2}\,\mathrm dv = -\dfrac{\mathrm dx}x[/tex]

[tex]-\dfrac1v + \ln|v| = -\ln|x| + C[/tex]

[tex]\ln\left|\dfrac yx\right| -\dfrac xy = C - \ln|x|[/tex]

[tex]\ln|y| - \ln|x|  -\dfrac xy = C - \ln|x|[/tex]

[tex]\boxed{\ln|y| -\dfrac xy = C}[/tex]

Answer:

P(S or T) = 3/4

Step-by-step explanation:

for the given A.P

5,9,13,...

First term (a)=5

common difference (d) = 9-5=4

Let Tn=2012

a +(n-1) d=2012

5 +(n-1) 4=2012

(n-1) 4=2012-5

(n-1)4=2007

n-1=501.75

n=1+501.75

n=502.75 -- - - - - -> which is not possible.

No.of terms can never in fraction.

Hence, 2012 is not a term of given A.P

Answer:

expected value is the mean : 10.5

Standard error for the sampling distribution : 0.375

it has a bell-shaped curve  with 99.7%  of the values between  9.375  and 11.625

Step-by-step explanation:

Answer:

15y -9

Step-by-step explanation:

3(5y-3)

Distribute

3*5y -3*3

15y -9

Answer:

270 degrees

Step-by-step explanation:

If you plug in 270 in place of the x's, the function is true!

This is correct for Plate/Edmentum users!! Hope I could help :)

5x + 8

I used long division

Answer:

Scatter plot charts are good for relationships and distributions, but pie charts should be used only for simple compositions — never for comparisons or distributions.

Answer:

A) The diameter is approximately 12 feet.

Step-by-step explanation:

C= piD

sq ft would be wrong bc this is not talking ab area

Answer:

The expected value of the lottery is $80

Step-by-step explanation:

To get the expected value, we have to multiply each outcome by its probability

Then we proceed to add up all of these to get the expected value of the lottery

we have this as ;;

125(0.2) + 100(0.3) + 50(0.5)

= 25 + 30 + 25 = $80

Answer:

A scatter plot shows a negative trend if y tends to decrease as x increases. A scatter plot shows no trend if there is no obvious pattern.

Answer:

the missing side is 21!!!!!!!!

The probability that one of them will win will be 9/14.

Since the probability that Jack will win is 1/7 and the probability that Bill will win is 1/2, then the probability that one of them will win will be:

= 1/7 + 1/2

= 7/14 + 2/14

= 9/14

Therefore, the probability that one of them will win will be 9/14.

Read related link on:

https://brainly.com/question/21689780

Answer:

it's. is now the MA plz I miss you

si pudiera escoger entre vivir eternamente y vivir dos veces

yo escogeria vivir dos veces porque vivir una vida eterna sin ti a mi lado seria el mayor sufrimiento, ahora vivir dos veces me dejaria tranquilo porque despues del final de mi vida podria volver a encontrarme contigo y vivir todos los momentos bellos una vez mas y eso seria un sueño volviendose realidad

9514 1404 393

Answer:

  (c)  3x - 2y

Step-by-step explanation:

Use the distributive property to eliminate parentheses, then collect terms.

  3(x -y) +y = 3x -3y +y = 3x +(-3+1)y = 3x -2y

Now we have to find,

The expression which is equivalent to,

→ 3(x - y) + y

Let's get the solution,

→ 3(x - y) + y

→ 3x - 3y + y

→ 3x - 2y

Hence, required expression is 3x - 2y.

Answer:

5

Step-by-step explanation:

(625 ^2)^(1/8)

Rewriting 625 as 5^4

(5^4 ^2)^(1/8)

We know that a^b^c = a^(b*c)

5^(4*2)^1/8

5^8 ^1/8

5^(8*1/8)

5^1

5

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex] { {(625}^{2} )}^{ \frac{1}{8} } \\ { ({25}^{2 \times 2} )}^{ \frac{1}{8} } \\ {25}^{4 \times \frac{1}{8} } \\ {5}^{2 \times 4 \times \frac{1}{8} } \\ {5}^{ \frac{8}{8} } \\ {5}^{1} \\ = 5[/tex]

Tangent = opposite / adjacent, or in this case Tangent = y / x.

Tan = (1/2) / ([tex]\sqrt{3}[/tex] / 2)

1 / [tex]\sqrt{3}[/tex]

[tex]\sqrt{3}[/tex] / 3

Hope this helps!

Answer:

x (-8,0)

y (0,6)

Step-by-step explanation:

at the x-intercept, y = 0

at the y-intercept x=0

sub those values into your equation!

for the x-intercept,

-3x = 24

x = -8

for the y-intercept,

4y = 24

y = 6

Answer:

6. x = 4

8. x = 13

Step-by-step explanation:

Using similar triangles theorem,

6. (5+4)/5 = (4x + 2)/(4x + 2 - 8)

9/5 = (4x + 2)/(4x - 6)

Cross multiply

9(4x - 6) = 5(4x + 2)

36x - 54 = 20x + 10

Collect like terms

36x - 20x = 54 + 10

16x = 64

16x/16 = 64/16

x = 4

8. (4x + 13)/20 = 52/16

(4x + 13)/20 = 13/4

Cross multiply

4(4x + 13) = 13(20)

16x + 52 = 260

16x = 260 - 52

16x = 208

x = 208/16

x = 13

Answer:

8

Step-by-step explanation:

=z²-3z+4 when z is 4

=4²-3(4)+4

=16-12+4

=8

Answer:

Building A is 660 feet and Building B is 830 feet

Step-by-step explanation:

Let x represent the height of building B.

Since building A is 170 feet shorter than building B, it can be represented by x - 170.

Create an equation and solve for x:

(x) + (x - 170) = 1490

2x - 170 = 1490

2x = 1660

x = 830

So, the height of building B is 830 feet.

Subtract 170 from this to find the height of building A:

830 - 170

= 660

Building A is 660 feet and Building B is 830 feet

Answer:

inequality is mostly represented on a number line but equation is not.

Answer:

the Ans is c

Step-by-step explanation:

actually I don't know how to explain

Step-by-step explanation:

2x+3x+x+20=180

6x+20=180

6x=160

x=160/6

x=26.667

Answer:

2X=53.2 , 3X=79.8 , X+20=46.6

Step-by-step explanation:

3X+2X+X+20=180

therefore,

6X+20=180

6X       =180-20

6X       =160

X        = 160 over 6

X        =26.6

now,

3X      = 26.6 x3

          =79.8

2X       =26.6 x2

          =53.20

X+20  =26.6+20

          =46.6

Im not sure if it's right. Because the total does not make 180 degrees.

Answer: b

Step-by-step explanation:

Answer:

1 cup per 8 oz

48/6 = 8

every 1 cup of water 8 oz of tomato paste.

Step-by-step explanation:

can i brainlist

Answer:

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Step-by-step explanation:

For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5% of calculators coming out of the production lines have a defect.

This means that [tex]p = 0.05[/tex]

Fifty calculators are randomly selected from the production line and tested for defects.

This means that [tex]n = 50[/tex]

What is the probability that exactly 2 calculators are defective?

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{50,2}.(0.05)^{2}.(0.95)^{48} = 0.2611[/tex]

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Answer:

f(- 5) = 13

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(x) = - 3x - 2 , then

f(- 5) = - 3(- 5) - 2 = 15 - 2 = 13

Answer:

The answer is D.

Step-by-step explanation: