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3 years ago

Which of the sequences is an arithmetic sequence?

Mathematics

1 answer:

Alchen [17]3 years ago

3 0

Answer:

Step-by-step explanation:

there is a constant pattern from one term to another

add -7 to get to the next term

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Find the solution of the separable equations a) the general solution: displaystyle dy/dt = t/[y^2] b) the unique solution to: dy

Xelga [282]

Answer:

(a) The general solution of given differential equation is $\frac{y^3}{3}=\frac{t^2}{2}+C$ .

(b) The unique solution is $\frac{y^2}{2}=t-\frac{5}{2}$ .

Step-by-step explanation:

(a)

The given differential equation is

$\frac{dy}{dt}=\frac{t}{y^2}$

Use variable separable method, to solve the above differential equation.

Separate the variables.

$y^2dy=tdt$

Integrate both sides.

$\int y^2dy=\int tdt$

$\frac{y^3}{3}=\frac{t^2}{2}+C$

The general solution of given differential equation is $\frac{y^3}{3}=\frac{t^2}{2}+C$ .

(b)

The given differential equation is

$\frac{dy}{dt}=\frac{1}{y}$

Use variable separable method, to solve the above differential equation.

Separate the variables.

$ydy=1dt$

Integrate both sides.

$\int ydy=\int 1dt$

$\frac{y^2}{2}=t+C$ ... (1)

It is given that y=1 at t=3. Substitute y=1 and t=3 in the above equation.

$\frac{(1)^2}{2}=(3)+C$

$\frac{1}{2}-3=C$

$-\frac{5}{2}=C$

Substitute $C=-\frac{5}{2}$ in equation (1).

$\frac{y^2}{2}=t-\frac{5}{2}$

Therefore the unique solution is $\frac{y^2}{2}=t-\frac{5}{2}$ .

6 0

4 years ago

Which of the following inequalities is true?

leonid [27]

Answer:

B. -3 < -2

Step-by-step explanation:

-3 is less than -2

because -2 is closer to 0 and into being positive than -3,

therefore, -3 < -2.

8 0

3 years ago

Read 2 more answers

All of my points to anyone who can help me with these..! Marking Brainliest as well

maksim [4K]

Answer:

Question one 186

Question two 240

Step-by-step explanation: You multiply the variable (the letter) by the number that the person is using

5 0

4 years ago

Read 2 more answers

Clara is asked to find the surface area of a sphere which has radius r, of 18 in. She says the surface area is 226.08 in. squar

anygoal [31]

Answer:

The surface area of the sphere is approximately 4071.5.

Step-by-step explanation:

You can find the surface area of a sphere using this formula: A=4πr^2!

Answer:

C. Clara did not square the radius when solving.

Step-by-step explanation:

She likely solved it like so:

18 x 3.14 = 56.52

56.52 x 4 = 226.08

Through this process, she forgot to square the radius!

5 0

3 years ago

F(x)=

Ahat [919]

Answer:

The function in the form of fog(x) is written as 48 x² + 336 x + 590

Step-by-step explanation:

Given function as :

f(x) = 3 x² - 6 x + 5

g(x) = - 4 x - 13

So, The function in the form of fog(x) is written as

We, substitute the value of g(x) into f(x)

∴ fog(x) = 3 (g(x))² - 6 (g(x)) + 5

Or, fog(x) = 3 (- 4 x - 13 )² - 6 ( - 4 x - 13 ) + 5

or, fog(x) = 3 (16 x² + 169 + 104 x) + 24 x + 78 + 5

or , fog(x) = 48 x² + 507 + 312 x + 24 x + 78 + 5

or , fog(x) = 48 x² + 336 x + 590

So, The function in the form of fog(x) = 48 x² + 336 x + 590

Hence The function in the form of fog(x) is written as 48 x² + 336 x + 590 Answer

4 0

3 years ago