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At the Earth's surface, warm air expands and rises, creating
what is known as an area of low pressure.
Cold air is dense and sinks to the surface to create what is
known as an area of high pressure.</span>
<em>v</em>² - <em>u</em>² = 2 <em>a</em> ∆<em>x</em>
where <em>u</em> = initial velocity, <em>v</em> = final velocity, <em>a</em> = acceleration, and ∆<em>x</em> = distance traveled.
So
<em>v</em>² - (15 m/s)² = 2 (6.5 m/s²) (340 m)
<em>v</em>² = 4645 m²/s²
<em>v</em> ≈ 68.15 m/s
When designing tires for a car, an engineer must consider the materials that will be used to fabricate the tires ... both the suitability of the materials for the purpose, and their cost.
For example, the engineer should not design car tires to be made of glass or of silk, since these would not hold up well when driving on concrete roads, and they would need to be replaced too often.
For another example, he should not design car tires to be made of gold or polished diamond, since these would be beyond the price range of most car owners, and also, these tires would be very susceptible to being stolen by nefarious and dishonest individuals in the middle of the night.
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I hope this answer is helpful. The question you posted is a very difficult one, because there are no answer choices listed, and also because the question has the mysterious unknown term "the following" in it.
Answer: Electron
In atom, there are proton and neutron inside the nucleus and electron which was moving in orbit outside of the nucleus. The electron is a negatively charged, a proton is positively charged and neutron is neutral. Since there are only proton and neutron in the nucleus it's become positively charged.
I assume you meant to say
Given that <em>x</em> = √3 and <em>x</em> = -√3 are roots of <em>f(x)</em>, this means that both <em>x</em> - √3 and <em>x</em> + √3, and hence their product <em>x</em> ² - 3, divides <em>f(x)</em> exactly and leaves no remainder.
Carry out the division:
To compute the quotient:
* 2<em>x</em> ⁴ = 2<em>x</em> ² • <em>x</em> ², and 2<em>x</em> ² (<em>x</em> ² - 3) = 2<em>x</em> ⁴ - 6<em>x</em> ²
Subtract this from the numerator to get a first remainder of
(2<em>x</em> ⁴ + 3<em>x</em> ³ - 5<em>x</em> ² - 9<em>x</em> - 3) - (2<em>x</em> ⁴ - 6<em>x</em> ²) = 3<em>x</em> ³ + <em>x</em> ² - 9<em>x</em> - 3
* 3<em>x</em> ³ = 3<em>x</em> • <em>x</em> ², and 3<em>x</em> (<em>x</em> ² - 3) = 3<em>x</em> ³ - 9<em>x</em>
Subtract this from the remainder to get a new remainder of
(3<em>x</em> ³ + <em>x</em> ² - 9<em>x</em> - 3) - (3<em>x</em> ³ - 9<em>x</em>) = <em>x</em> ² - 3
This last remainder is exactly divisible by <em>x</em> ² - 3, so we're left with 1. Putting everything together gives us the quotient,
2<em>x </em>² + 3<em>x</em> + 1
Factoring this result is easy:
2<em>x</em> ² + 3<em>x</em> + 1 = (2<em>x</em> + 1) (<em>x</em> + 1)
which has roots at <em>x</em> = -1/2 and <em>x</em> = -1, and these re the remaining zeroes of <em>f(x)</em>.
