Answer:
The sum of the lengths of the sides is 2292 yards and the sum of the lengths of the triangle is 3056 yards
Explanation:
Since y represents the length of fence that is opposite (parallel) to the river and x represent the length of fence perpendicular to the river.
Therefore since we can use 3,056 yards of fencing
Side perpendicular to the river = x and,
Side opposite to the river = y = 3056 - 2x
The area of the rectangle formed (A) = Perpendicular side × Parallel side
∴ A = x(3056 - 2x) = 3056x - 2x²
A = 3056x - 2x²
To maximize the area, A' (dA/dx) = 0
∴ A' = 3056 - 4x = 0
3056 - 4x = 0
4x = 3056
x = 764 yards
y = 3056 - 2x = 3056 - 2(764) = 1528 yards.
Side perpendicular to the river = 764 yards and,
Side opposite to the river = 1528 yards
The sum of the lengths of the sides = 764 + 1528 = 2292 yard and the sum of the lengths of the triangle = 764 + 764 + 1528 = 3056 yards
Answer: 250n
Explanation:
The formula for gravitational force is: F = (gMm)/r^2
There are two factors at play here:
1) The mass of the planet 'M'
2) The radius 'r'
We can ignore the small M and the g, they are constants that do not alter the outcome of this question.
You can see that both M and r are double that of earth. So lets say earth has M=1 and r=1. Then, new planet would have M=2 and r=2. Let's sub these two sets into the equation:
Earth. F = M/r^2 = 1/1
New planet. F = M/r^2 = 2/4 = 1/2
So you can see that the force on the new planet is half of that felt on Earth.
The question tells us that the force on earth is 500n for this person, so then on the new planet it would be half! So, 250n!
Explanation:
- Speed is the rate of change of distance with time.
Speed = 
- Velocity is given as the displacement per unit of time:
Velocity = 
Speed and velocity are similar but speed is a scalar quantity while velocity is a vector quantity. Speed has magnitude but does not point towards a specific direction. Velocity shows both magnitude and direction and it is a vector quantity.
- Acceleration is given as the change in velocity with time. It is a vector quantity:
Acceleration = 
- Distance is how far a body moves. It is scalar quantity.
- Time is the duration of an event. It is a scalar quantity.
Learn more:
Vector calculation brainly.com/question/2678571
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The speed of sound at
is approximately v=343 m/s. The distance covered by the sound wave is
And the time it takes is
Now we want to find how far the light travels during this time. Light travels at speed
, therefore the distance it covers during this time is
<u>Galileo's discovery shows that, to an observer on Earth, Venus has phases just like Earth's moon. This observation provide support for the heliocentric model of the solar system as follows:</u>
- Galileo noticed the Moon is not flat, but rocky and rugged-just like the Earth did.
- He used his telescope to observe the Venus phases. Galileo's findings confirmed his confidence in the concept of Copernicus that Earth and remaining planets revolve around the Sun, i.e. Heliocentrism.
- While most individuals in Galileo's days assumed that the Earth was the center of the universe and that the Sun and planets revolved around it, i.e. geocentrism.
- The idea of geocentric was generally preferred by the prominent and strong Catholic Church, and when Galileo started writing papers on his belief in a heliocentric with a valid explanation, he was called to Rome to face the inquisition's charges towards him.
- Thus in early 1616 he was accused of being a heretic, but later he cleared of charges of "heresy" with warning that he should not spread his belief.
- But he pursued his astronomy research, and was increasingly confident that all planets revolved around the Sun. Therefore he published a book in 1632 which explained that Copernicus' heliocentric theory was appropriate.
- Thus after this finally he was charged by "heresy" and sentenced to life imprisonment in 1633, but due to his poor health he lived imprisonment under house arrest and finally died on January 8, 1642.
