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2 years ago

Describe how to write 3x+2y=12 in function notation.assume that y represent the dependent variable.

2 answers:

5 0

To write this function in function notation all you would need to do is rearrange the equation for y.

3x + 2y = 12

3x - 3x + 2y = 12 - 3x

2y = 12 - 3x

2y/2 = 12/2 - 3x/2

Y = 6 - 3/2 X or

Y = -3/2 X + 6.

BARSIC [14]2 years ago

5 0

Answer:

$y=\frac{12-3x}{2}$

Step-by-step explanation:

Given equation,

3x + 2y = 12

For writing an equation in the function notation we need to isolate the dependent variable in the left side of the equation,

Here, the dependent variable is y,

$\implies 2y = 12-3x$

$\implies y=\frac{12-3x}{2}$

Which is the required function formula.

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Find the general solution of {y}''-3y=8e^{3t}+4sin(t) .

babunello [35]

Answer:

$y(x)=C_1e^{\sqrt3t}+C_2e^{-\sqrt3t}-\frac{4}{3}e^{3t}-sint$

Step-by-step explanation:

We are given that linear differential equation

$y''-3y=8e^{3t}+4 sint$

Auxillary equation

$D^2-3=0$

$D=\pm \sqrt3$

C.F= $C_1e^{\sqrt3t}+C_2e^{-\sqrt3}$

P.I= $\frac{8e^{3t}+4sin t}{D^2-3}$

P.I= $\frac{8e^{3t}}{9-3}+4\frac{sint }{-1-3}$

P.I= $e^{ax}{\phi (D+a)}$ and $P.I=\frac{sinax}{(\phi D)}$ where D square is replace by - a square

P.I= $-\frac{4}{3}e^{3t}- sint$

Hence, the general solution

G.S=C.F+P.I

$y(x)=C_1e^{\sqrt3t}+C_2e^{-\sqrt3t}-\frac{4}{3}e^{3t}-sint$

3 0

2 years ago

For the following question, use the equation d = rt, in which d is distance, r is rate, and t is time. How far is Grandmother's

Sergeeva-Olga [200]

You first have to plug in your given numbers to the equation.
d= rt
d=(52)4.5
Then you solve
52*4.5 = 234
So, your distance or d=234

5 0

3 years ago

Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fxg and state its domain.

marissa [1.9K]

Option D: $(f\times g)(x)=12 x^{2}-48 x+21$ ; all real numbers.

Explanation:

Given that the functions are $f(x)=-2 x+7$ and $g(x)=-6 x+3$

We need to determine the value of $(f\times g)(x)$ and its domain.

The value of $(f\times g)(x)$ :

The value of $(f\times g)(x)$ can be determined by multiplying the two functions.

Thus, we have,

$(f\times g)(x)=f(x)\times g(x)$

$=(-2x+7)(-6x+3)$

$=12x^2-6x-42x+21$

$(f\times g)(x)=12 x^{2}-48 x+21$

Thus, the value of $(f\times g)(x)$ is $(f\times g)(x)=12 x^{2}-48 x+21$

Domain:

We need to determine the domain of the function $(f\times g)(x)$

The domain of the function is the set of all independent x - values for which the function is real and well defined.

Thus, the function $(f\times g)(x)=12 x^{2}-48 x+21$ has no undefined constraints, the function is well defined for all real numbers.

Hence, Option D is the correct answer.

3 0

2 years ago

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a_sh-v [17]

Answer:

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3 0

2 years ago

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How do you explain how to find the area of a combined rectangle

Olin [163]

Answer:

I explain down below:

Step-by-step explanation:

First, you divide the combined rectangle into separate parts. Then you find the area of the first rectangle. Then the second and/or third one.

After all the areas have been solved, you add all of the areas together.

Hope this helps!

4 0

2 years ago