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stealth61 [152]
3 years ago
12

Jan 10, 7:28:48 PM What is the slope of a line parallel to the line whose equation is 3x - 6y = 18. Fully reduce your answer.​

Mathematics
1 answer:
marissa [1.9K]3 years ago
3 0

Answer:

1/2

Step-by-step explanation:

We are given the line:

3x-6y=18

And we want to find the slope of the line parallel to this given line.

Remember that parallel lines have the same slope. So, if we can determine the slope of the given line, we have the slope of its parallel line.

To determine the slope of the given line, we simply have to isolate the <em>y</em>. So, we can first divide everything by 3. This yields:

x-2y=6

Adding 2<em>y</em> to both sides yields:

x=6+2y

And subtracting 6 from both sides yields:

x-6=2y

Finally, dividing everything by 2 gives us:

\displaystyle y=\frac{1}{2}x-3

Hence, the slope of our line is 1/2.

So, the slope of the line parallel to this line must also be 1/2.

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Answer:

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Step-by-step explanation:

The gravitational pull of the Earth on a person or object is given by Newton's law of gravitation as follows;

F =G\times \dfrac{M \cdot m}{r^{2}}

Where;

G = The universal gravitational constant

M = The mass of one object

m = The mass of the other object

r = The distance between the centers of the two objects

For the gravitational pull of the Earth on a person, when the person is standing on the Earth's surface, r = R = The radius of the Earth ≈ 6,371 km

Therefore, for an astronaut in the international Space Station, r = 6,800 km

The ratio of the gravitational pull on the surface of the Earth, F₁, and the gravitational pull on an astronaut at the international space station, F₂, is therefore given as follows;

\dfrac{F_1}{F_2} = \dfrac{ \dfrac{M \cdot m}{R^{2}}}{\dfrac{M \cdot m}{r^{2}}} = \dfrac{r^2}{R^2}  = \dfrac{(6,800 \ km)^2}{(6,371 \ km)^2} \approx  1.14

∴ F₁ ≈ 1.14 × F₂

F₂ ≈ 0.8778 × F₁

Therefore, the gravitational pull on the astronaut by virtue of the distance from the center of the Earth, F₂ is approximately 88% of the gravitational pull on a person of similar mass on Earth

However, the International Space Station is moving in its orbit around the Earth at an orbiting speed enough to prevent the Space Station from falling to the Earth such that the Space Station falls around the Earth because of the curved shape of the gravitational attraction, such that the astronaut are constantly falling (similar to falling from height) and appear not to experience gravity

Therefore, Cory is correct, the astronauts in the International Space Station, 6,800 km from the Earth's center, are not too far to experience gravity.

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Answer:

f(x) has a limited range

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Step-by-step explanation:

Given the function;

f(x) = x^2+2

The domain is the value of the input variables for which the function will exist. According to the expression given, the function exists on all real values of x. The same goes with range which deals with the output values. It also exists on all real values from 2 and above.

Hence f(x) have a limited range (since values less than 2 are not included compare to domain that exists on all real values) and does not have a restricted domain.

For the x intercept, x intercept occur at y = 0

substitute y = 0 into the function and get y

if y = f(x)

y = x^2+2

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Hence  f(x) does not have an x-intercept of (2, 0)

For the y intercept, y intercept occur at x = 0

substitute x = 0 into the function and get y

if y = f(x)

y = x^2+2

y = 0^2 + 2

y = 2

Hence  f(x) has a y-intercept at point (0, 2)

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