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pashok25 [27]
3 years ago
8

.5(x + 3) ^{2} " alt="x + 5 = 0.5(x + 3) ^{2} " align="absmiddle" class="latex-formula">
Physics
1 answer:
nikitadnepr [17]3 years ago
6 0
Solve for x over the real numbers = complete the square
x + 5 = 0.5 (x + 3)^2

0.5 (x + 3)^2 = 1/2 (x + 3)^2:
x + 5 = 1/2 (x + 3)^2

Expand out terms of the right hand side:
x + 5 = x^2/2 + 3 x + 9/2

Subtract x^2/2 + 3 x + 9/2 from both sides:
-x^2/2 - 2 x + 1/2 = 0

Multiply both sides by -2:
x^2 + 4 x - 1 = 0

Add 1 to both sides:
x^2 + 4 x = 1

Add 4 to both sides:
x^2 + 4 x + 4 = 5

Write the left hand side as a square:
(x + 2)^2 = 5

Take the square root of both sides:
x + 2 = sqrt(5) or x + 2 = -sqrt(5)

Subtract 2 from both sides:
x = sqrt(5) - 2 or x + 2 = -sqrt(5)

Subtract 2 from both sides:
Answer:  x = sqrt(5) - 2 or x = -2 - sqrt(5)
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What happens when the data in an investigation does not support the origanal hypothesis
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Answer: The scientist gives up and starts an investigation on a new topic.

Explanation:

The data is altered so that it supports the original hypothesized. The data is then altered so that it supports the original hypothesis.

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2 years ago
Which law states that for any closed loop, the sum of the length segments times the magnetic field in the direction of the segme
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Read 2 more answers
A gang of robbers is escaping across city roofs at night. They come to the edge of one building and need to drop down to their g
REY [17]

Answer:

a) They will hit the ground with a speed of 19.6 m/s.

b) They are at a height of 20 m.

c) It is not a safe jump.

Explanation:

Hi there!

a) The equations of height and velocity in function of time of a free falling body are the following:

h = h0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

h = height of the object at time t.

h0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity (-9.8 m/s² considering downward as negative direction).

v = velocity of the object at time t.

Using the equation of velocity, let's find the velocity at which they will hit the ground. The pebble is dropped (initial velocity = 0) and it takes 2 s to reach the ground:

v = v0 + g · t     (v0 = 0)

v = g · t

v = -9.8 m/s² · 2.0 s

v = -19.6 m/s

They will hit the ground with a speed of 19.6 m/s.

b)Now, we have to use the equation of height:

h = h0 + v0 · t + 1/2 · g · t²

If we place the origin of the frame of reference on the ground, we have to find the initial height (h0) knowing that at t = 2.0 s, h = 0 m

0 m = h0 - 1/2 · 9.8 m/s² · (2.0 s)²

h0 = 1/2 · 9.8 m/s² · (2.0 s)²

h0 = 20 m

They are at a height of 20 m.

c)According to a NASA paper (Issues on Human Acceleration Tolerance After Long-Duration Space Flights, figure 10), if you fall with a vertical velocity greater than 17 m/s it is unlikely that you will survive. So, it is not a safe jump.  

3 0
3 years ago
How is the lifetime of a star related to its mass?
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Stars having less mass collapses early than those with more mass. This can be explained by Einstein's equation E=mc².
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6 0
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If a car travels 40 km/hr for hours how far has it traveled
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It depends on how many hours!
1 hour = 40km
2 hours = 80km
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