Answer:
Explanation:
Given
Distance to grandmother's house=100 mi
it is given that during return trip Julie spend equal time driving with speed 30 mph and 70 mph
Let Julie travel x mi with 30 mph and 100-x with 70 mph
![\frac{x}{30}=\frac{100-x}{70}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B30%7D%3D%5Cfrac%7B100-x%7D%7B70%7D)
x=30 mi
Therefore
Julie's Average speed on the way to Grandmother's house![=\frac{100}{\frac{50}{30}+\frac{50}{70}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B100%7D%7B%5Cfrac%7B50%7D%7B30%7D%2B%5Cfrac%7B50%7D%7B70%7D%7D)
=42 mph
On return trip
![=\frac{100}{2\frac{30}{30}}=50 mph](https://tex.z-dn.net/?f=%3D%5Cfrac%7B100%7D%7B2%5Cfrac%7B30%7D%7B30%7D%7D%3D50%20mph)
Answer:
Hey
Your answer would be Radioactive Decay and Heat of formation.
When earth first formed it was very violant. Some planetary scientists believe that the moon was created from a collision involving earth and Thea (a theoretical dwarf planet). these collisions that have formed earth heated it so much that it is still hot from them.
Radioactivce decay is another major fource of internal heat for earth.
Answer:
The angle it subtend on the retina is
Explanation:
From the question we are told that
The length of the warbler is ![L = 14cm = \frac{14}{100} = 0.14m](https://tex.z-dn.net/?f=L%20%3D%2014cm%20%3D%20%5Cfrac%7B14%7D%7B100%7D%20%3D%200.14m)
The distance from the binoculars is ![d = 18cm = \frac{18}{100} = 0.18m](https://tex.z-dn.net/?f=d%20%3D%2018cm%20%3D%20%5Cfrac%7B18%7D%7B100%7D%20%3D%200.18m)
The magnification of the binoculars is ![M =8](https://tex.z-dn.net/?f=M%20%3D8)
Without the 8 X binoculars the angle made with the angular size of the object is mathematically represented as
![\theta = \frac{L}{d}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Cfrac%7BL%7D%7Bd%7D)
![\theta = \frac{0.14}{0.18}](https://tex.z-dn.net/?f=%5Ctheta%20%20%3D%20%5Cfrac%7B0.14%7D%7B0.18%7D)
![= 0.007778 rad](https://tex.z-dn.net/?f=%3D%200.007778%20rad)
Now magnification can be represented mathematically as
![M = \frac{\theta _z}{\theta}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B%5Ctheta%20_z%7D%7B%5Ctheta%7D)
Where
is the angle the image of the warbler subtend on your retina when the binoculars i.e the binoculars zoom.
So
![\theta_z = M * \theta](https://tex.z-dn.net/?f=%5Ctheta_z%20%3D%20M%20%2A%20%5Ctheta)
=> ![\theta_z =8 * 0.007778](https://tex.z-dn.net/?f=%5Ctheta_z%20%3D8%20%2A%200.007778)
![= 0.0622222224](https://tex.z-dn.net/?f=%3D%200.0622222224)
Generally the conversion to degrees can be mathematically evaluated as
![\theta_z = 0.062222224 * (\frac{360 }{2 \pi rad} )](https://tex.z-dn.net/?f=%5Ctheta_z%20%3D%200.062222224%20%2A%20%28%5Cfrac%7B360%20%7D%7B2%20%5Cpi%20rad%7D%20%29)
the force that the planet exerts on the moon is equal to the force that the moon exerts on the planet
Explanation:
In this problem we are analzying the gravitational force acting between a planet and its moon.
The magnitude of the gravitational attraction between two objects is given by
where
:
is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
In this problem, we are considering a planet and its moon. According to Newton's third law of motion,
"When an object A exerts a force (action force) on an object B, then object B exerts an equal and opposite force (reaction force) on object A"
If we apply this law to this situation, this means that the force that the planet exerts on the moon is equal to the force that the moon exerts on the planet.
Learn more about gravitational force:
brainly.com/question/1724648
brainly.com/question/12785992
#LearnwithBrainly
Answer:
Explanation:
I is the moment of inertia of the pulley, α is the angular acceleration of the pulley and T is the tension in the rope. Let a is the linear acceleration.
The relation between the linear acceleration and the angular acceleration is
a = R α .... (1)
According to the diagram,
T x R = I x α
T x R = I x a / R from equation (1)
T = I x a / R² .... (2)
mg - T = ma .... (3)
Substitute the value of T from equation (2) in equation (3)
![mg - \frac{Ia}{R^{2}}=ma](https://tex.z-dn.net/?f=mg%20-%20%5Cfrac%7BIa%7D%7BR%5E%7B2%7D%7D%3Dma)
![a=\frac{mg}{m+\frac{I}{R^{2}}}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bmg%7D%7Bm%2B%5Cfrac%7BI%7D%7BR%5E%7B2%7D%7D%7D)
T is the acceleration in the system
Substitute the value of a in equation (2)
![T = \frac{I}{R^{2}}\times \frac{mg}{m+\frac{I}{R^{2}}}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7BI%7D%7BR%5E%7B2%7D%7D%5Ctimes%20%5Cfrac%7Bmg%7D%7Bm%2B%5Cfrac%7BI%7D%7BR%5E%7B2%7D%7D%7D)
![T=\frac{I\times mg}{I+mR^{2}}](https://tex.z-dn.net/?f=T%3D%5Cfrac%7BI%5Ctimes%20mg%7D%7BI%2BmR%5E%7B2%7D%7D)
This is the tension in the string.