Answer:
<h2>
6.36 cm</h2>
Explanation:
Using the formula to first get the image distance
1/f = 1/u+1/v
f = focal length of the lens
u = object distance
v = image distance
Given f = 16.0 cm, u = 24.8 cm
1/v = 1/16 - 1/24.8
1/v = 0.0625-0.04032
1/v = 0.02218
v = 1/0.02218
v = 45.09 cm
To get the image height, we will us the magnification formula.
Mag = v/u = Hi/H
Hi = image height = ?
H = object height = 3.50 cm
45.09/24.8 = Hi/3.50
Hi = (45.09*3.50)/24.8
Hi = 6.36 cm
The image height is 6.36 cm
Answer:
The speed of the shell at launch and 5.4 s after the launch is 13.38 m/s it is moving towards the Earth.
Explanation:
Let u is the initial speed of the launch. Using first equation of motion as :

a=-g

The velocity of the shell at launch and 5.4 s after the launch is given by :

So, the speed of the shell at launch and 5.4 s after the launch is 13.38 m/s it is moving towards the Earth.
The largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
The given parameters;
- <em>distance between the two black holes, r = 10 AU = 1.5 x 10¹² m</em>
- <em>gravitational force between the two black holes, F = 6.9 x 10²⁵ N.</em>
- <em>combined mass of the two black holes = 5.20 x 10³⁰ kg</em>
The product of the two masses is calculated from Newton's law of universal gravitational as follows;

The sum of the two masses is given as;
m₁ + m₂ = 5.2 x 10³⁰ kg
m₂ = 5.2 x 10³⁰ kg - m₁
The first mass is calculated as follows;
m₁(5.2 x 10³⁰ - m₁) = 2.328 x 10⁶⁰
5.2 x 10³⁰m₁ - m₁² = 2.328 x 10⁶⁰
m₁² - 5.2 x 10³⁰m₁ + 2.328 x 10⁶⁰ = 0
<em>solve the quadratic equation using formula method</em>;
a = 1, b =- 5.2 x 10³⁰, c = 2.328 x 10⁶⁰

The second mass is calculated as follows;
m₂ = 5.2 x 10³⁰ kg - m₁
m₂ = 5.2 x 10³⁰ kg - 4.7 x 10³⁰ kg
m₂ = 5 x 10²⁹ kg
or
m₂ = 5.2 x 10³⁰ kg - 4.9 x 10²⁹ kg
m₂ = 4.7 x 10³⁰ kg
Thus, the largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
Learn more here:brainly.com/question/9373839