Physics, 20.07.2021 14:00 hedaya

Derive this please as fast as u can

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Answer from: starsinopoli13

Derived in explanation

Explanation:

The law of universal gravitation was discovered by Newton in 1686. According to this law:

“Every object in this universe attracts other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.”

Consider two bodies ‘A’ and ‘B’ having masses ‘m1’ and ‘m2’, respectively. They are placed with their centers at distance ‘r’ from each other.

According to this law, force is directly proportional to the product of their masses, that is:

$F\ \alpha\ (m_1)(m_2)$

Also, the force is inversely proportional to the square of the distance between them, that is:

$F\ \alpha\ \frac{1}{r^2}$

On combining both equations we get:

Where ‘G’ is called ‘Gravitational Constant’ and its value is 6.67 x 10⁻¹¹ Nm²/kg².

Answer from: Quest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

Answer from: Quest

we have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is $[2,\infty)$ .

if we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

let us know find its inverse.

$y=(x-5)^{2}+2$

upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

let us now solve this function for y.

$(y-5)^{2}=x-2\\ y-5=\pm \sqrt{x-2}\\ y=5\pm \sqrt{x-2}\\$

hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

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