Help ASAP. This is vital to my math grade. I will award 100 points and Brainly to whoever can give me the correct slope. I need this question correct in order to pass my math class. This is for a dual enrollment class. This is timed

As you said, the equation is separable:

dy/dt = 2t / exp(y)

exp(y) dy = 2t dt

Integrate both sides:

∫ exp(y) dy = ∫ 2t dt

exp(y) + C₁ = t ² + C₂

Move the constant terms to one side. When you add them together, you get another constant, so you can ignore the subscript altogether:

exp(y) = t ² + C

Solve for y explicitly by taking the logarithm of both sides:

ln(exp(y)) = ln(t ² + C )

y = ln(t ² + C )

C can be any number; if it happens to be 0, then you have

y = ln(t ²) = 2 ln(t )

so B is the correct choice.

You can also approach this from the opposite angle: Assume y is one of the given solutions, then substitute it into the ODE. (Bit more trial-and-error involved, so not a good idea if you're short on time.)

For example, if y = 2 exp(t ) as in choice A, you have dy/dt = 2 exp(t ), so the ODE would become

2 exp(t ) = 2t / exp(2 exp(t ))

which is clearly (I hope) not true.

Answer:

1/5

Step-by-step explanation:

Answer:

The answer is X = 18

Step-by-step explanation:

2x/3 - 7 = 5

Multiply both sides if the equation by 3 : 2x - 21 = 15

Move the constant to the right hand side and change its sign : 2x = 15 + 21

Calculate 2x = 15 + 21

2x = 36

Divide both sides of the eqaution by 2 : 2x = 36

x = 18

Answer X = 18

Answer:

Step-by-step explanation:

r=6.7

Answer:

No

Step-by-step explanation:

2X + 12=13x - 2x + 5

2X + 12= 11x+5

2x-11x = 5-12

-9x = -7

X = 7/9

so the answer is NO

Answer:

13.8 ounces of salt

Step-by-step explanation:

A restaurant small salt shakers contains 0.6 ounces of salt. The shakers are filled from a container that has 18.6 ounces of salt. If 8 shakers are filled, how much salt will be remaining in the salt container?

Step 1

Note that:

1 shaker = 0.6 ounces of salt

8 shakers = x

Cross Multiply

x = 8 × 0.6 ounces of salt

x = 4.8 ounces of salt

Step 2

The shakers are filled from a container that has 18.6 ounces of salt. If 8 shakers are filled, how much salt will be remaining in the salt container?

This is calculated as:

18.6 ounces of salt - 4.8 ounces of salt

= 13.8 ounces of salt

Answer:

y - 7 =  [tex]-\frac{1}{4}[/tex] (x - 4)

Step-by-step explanation:

Find Slope: m = [tex]\frac{y_{2-}y_{1} }{x_{2-}x_{1} }[/tex]

m = [tex]\frac{6-(7)}{8-(4)}[/tex]

m = [tex]\frac{-1}{4}[/tex]

Point Slope Form: y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

y - 7 = [tex]-\frac{1}{4}[/tex] (x - 4)

Answer:

x<-13

Step-by-step explanation:

−3(x+3)>30

Divide both sides by −3. Since −3 is negative, the inequality direction has changed.

x+3<30/-3

Divide 30 by −3 to get −10.

x+3<−10

Subtract 3 from both sides.

x<−10−3

Subtract 3 from −10 to get −13.

x<−13

Graph for inequality:

Answer:

give me a brainliest now

Step-by-step explanation:

Answer:

60 miles

Step-by-step explanation:

There are two ways to solve this:

1. They tell you that you drive at 60 miles an hour, so , in an hour, you drive 60 miles.

2. Is the way you should use in the future:

Distance = speed * time

Substitute the speed and times.

Distance = 60 * 1

Thus, you drive 60 miles in one hour

The distance that should be traveled be 60 miles

As we know that

[tex]Speed = \frac{distance}{time}[/tex]

Here

speed be 60 miles per hour

And, the time should be one hour

So, the distance should be

[tex]= 60\ miles\ per hour \times one\ hour[/tex]

= 60 miles

Therefore the distance that should be traveled be 60 miles

Learn more about the distance here:brainly.com/question/23774048

Answer:

I think it is the second one haha loll

Answer: 75 ft^2

Step-by-step explanation:

Radius is half of the diameter. Diameter is given as 10.

3 (5)^2

3 x 25 = 75 ft^2

Answer:

i was proud of myself when I finally figured out a difficult math problem. I didn't even ask for help. it was a hard time for me but I eventually came through.

it is gonna be c trust me I know for a fact

Step-by-step explanation:

Hi...

You ask any irrelevant Question, that is why they get deleted.

Answer:

(here i assume that the daily record is another rectangle)

For a rectangle with width W and length L, the perimeter is:

P = 2*W + 2*L

in this case we know that:

P = 125

W = 15

Replacing these in the perimeter equation we get:

125 = 2*15 + 2*L

125 = 30 + 2*L

125 - 30 = 2*L

95 = 2*L

95/2 = L = 47.5

Now we know that the daily record has a scale factor of 60%.

This means that each measure of this rectangle is (60%/100%) times the equivalent measure of the rectangle garden.

Then if the width of the daily record is W' and the length of the daily record is L'

This means that:

L' = (60%/100%)*L = 0.6*L = 0.6*47.5

W' = (60%/100%)*W = 0.6*W = 0.6*15

Then the perimeter is:

P' = 2*0.6*47.5 + 2*0.6*15 = 75

(notice that is exactly the same than multiplying the original perimeter by (60%/100%) = 0.6)

Answer:

122

Step-by-step explanation:

[tex]x^6+y^2[/tex]

Plug in 1 for x and 11 for y

[tex]=1^6+11^2[/tex]

1 to the power of any number will always equal 1

[tex]=1+11^2\\=1+121\\=122[/tex]

I hope this helps!

Answer:

C

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

Sum of the angles in a triangle is 180 so,

35 + 3x + 2x - 20 = 180

35 + 5x - 20 = 180

15 + 5x = 180

5x = 180 - 15

x = 165/5

x = 33

Answer:

is is on the x acsess 2 and go down to -3. Hope this helped!

Step-by-step explanation:

Go to the x acsessw and go to 2 go down to -3 and mark

Answer:

33

Step by step explanation of the answer

Answer:

Step-by-step explanation:

Corresponding parts of congruent triangles are congruent

WX ≅ DC

XY ≅ CY

WY ≅ DY

∠WXY ≅ ∠DCY

∠XWY ≅ ∠CDY

∠WYX ≅ ∠DYC