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3 years ago

Solve the following system of equations:

1 answer:

3 0

3x-2y=6
6x-4y=14

Simplifying equation II
3x-2y=7
Subtracting the simplified equation from equation1
0=-1
There is no solution.

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A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?

professor190 [17]

Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let $x\cdot y = 18$ , we get an additional equation by implicit differentiation:

$x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (1)

From the first equation we find that:

$x = \frac{18}{y}$ (2)

By applying (2) in (1), we get the resulting expression:

$\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (3)

$y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}$

$\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}$

If we know that $y = 6$ and $\frac{dy}{dt} = 8$ , then the first derivative of x in time is:

$\frac{dx}{dt} = -\frac{18}{6^{2}} \cdot (8)$

$\frac{dx}{dt} = -4$

From (1) we determine the value of x at this instant:

$x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}$

$x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)$

$x = -6\cdot \left(\frac{-4}{8} \right)$

$x = 3$

The value of x at this instant is 3.

4 0

3 years ago

Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the f

kompoz [17]

In the question "Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days?" The correct answer is 6271 because given the function f(x) = 33(1.3)^x where x is the number of days the video has been online. For x = 20 days: f(20) = 33(1.3)^20 = 33(190.0496377) = 6,271

3 0

4 years ago

Read 2 more answers

State the conclusion based on the results of the test. The standard deviationstandard deviation inin the pressure required to op

inysia [295]

Answer:

B. There is sufficient evidence that the mean of the pressure required to open a certain valve has changed.

Step-by-step explanation:

We make this conclusion based on these reasons:

We are told that the "null hypothesis was rejected" after the "manager feels that the pressure variability has changed., meaning the null hypothesis was the opposite of what occurred; that is to say, it is the alternate hypothesis that proved true instead.
"changes in the manufacturing process" form what can be called "sufficient evidence" that the mean of the pressure required to open the valve has changed, thereby going against the null hypothesis.

It is based on the above reasons that the null hypothesis was rejected.

4 0

3 years ago

I hunder percent agree.

Black_prince [1.1K]

I too hunder percent agree

7 0

2 years ago

PLEASE ANSWER THiS MATH QUESTION !! 20 POINTS AND BRAINLIEST !!

RoseWind [281]

Answer:

Step-by-step explanation:

Plug in the values of each of the coordinate pairs into the linear system.

2x - 8y = 0, -3x - 8y = 20

2*-4 - 8*-1 = 0

- 8 - (-8) = 0 -> CORRECT!

-3x - 8y = 20

-3*-4 - 8*-1 = 20

12 - (-8) = 20 -> CORRECT!

You don't need to try any other pairs, you already know that this is the solution to the problem! Remember, in the future, just plug all the coordinate pairs into the equation. Whichever one makes the equation true is the correct solution! Hope this helps!

4 0

3 years ago

Read 2 more answers