Answer: 34.9 cm
Explanation:
You are given the following parameters;
Object distance U = 32 cm
Magnification M = - 12.0
According to formula for magnification;
M = V/U
Where V = image distance.
Substitute V and M into the formula
-12 = V/32
Cross multiply
V = -12 × 32
V = - 384
You can use the formula
1/f = 1/V + 1/U
Where f = focal length
Substitute V and U into the formula
1/f = - 1/384 + 1/32
Find the lowest common factor of the denominator at Left hand side
1/f = ( -1 + 12 ) / 384
1/f = 11/384
Reciprocate both sides
F = 384/11
F = 34.9 cm
He should therefore use the focal length of 34.9 cm
Answer: b. Salt lakes are formed when river bends are cut off.
Salt lakes are formed when water from water sourced gets accumulated in a shallow region and the supply of water is cut. These salt lakes are terminal which means water does not flow to other locations. Therefore, salt lakes are formed when river bends are cut off.
UV waves are the wave that is just above human eyesight from the naked eye. Ultra violet for real means more violet. As the radio waves, you will have to wait for the next commenter as I have no idea. Sorry!
A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production costs.
h: height of the cylinder, r: radius of the cylinder
The volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
The cost of packaging, C=2πrh*0.02+ πr^2*0.02+ πr^2*0.05 subject to the constraint πr^2h=600
C=πr(0.04h+.07r) and the constraint implies h=600/ πr^2
So C=πr(24/πr^2+.07r)=24/r+.07πr^2
C'=-24/r^2+0.14πr=0
r^3=24/0.14π r=3.79 cm
h=600/πr^2=13.3 cm
C=π*3.79*(0.04*13.3+.07*3.79)=9.48cents
C''=0.14π+48/r^3>0 for all r>=0 so our solution is indeed a minimum.
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Question no. 1. Compare the planets Mars and Saturn. Describe how their common characteristics are similar:
Answer: Our solar system is located in the outer spiral arm of the milky way galaxy. our solar system has one sun and nine revolving planets and . namely
- Mercury
- Venus
- Earth
- Mars
- Jupiter
- Saturn
- Uranus
- Neptune
- Pluto (small planet usually refer as dwarf)
Each star has its on moon/moons and has its own characteristics i.e , planet must be a celestial body , must have orbit around sun, have enough mass for self gravity, big enough to have gravity that clear its path from other same size object close to its orbit around sun.
Mars is the fourth from the sun and sixth is the Saturn from the sun in our solar system.
<u>Common in Characteristics of Mars and Saturn:</u>
- Mars and Saturn both have celestial body.
- Mars and Saturn both have enough mass for the gravity to get rid of rigid body forces.
- Mars and Saturn both revolve around the sun in their own orbits.
- Mars is the second smallest in the solar system while Saturn is second largest in the solar system.
- Mars and Saturn both have their own moons. Mars has two while Saturn has 83 moons
- Mars and Neptune both do not support life.
Question no. 2. Compare the planets Earth and Neptune. Describe how are they different from each other
Answer:
Earth our home planet is the third from the sun and Neptune on the other hand is the eighth from the sun in the solar system.
<u>Common differences between Earth and Neptune</u>
- Earth is the terrestrial planet while Neptune (Ice giant) is the Jovian planet.
- Earth has no ring around it, Neptune has ring around it.
- Earth is closer to the sun and Neptune is far distant from the sun.
- Earth consists of rocks and metals on the other hand Neptune contain gases
- Earth is smaller than the Neptune in the solar system.
- Earth rotates slower and Neptune rotates faster.
