For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .
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Answer:
The complete answer is explained below.
Step-by-step explanation:
The problem is demanding to simply determine the number of years each color light would last.
We know the following information from the question:
- As it is clear that a red light remains TURNED ON 50% of the time.
- Green remains TURNED ON 42% of the time
- Yellow remains TURNED ON 8% of the time.
Also the bulbs for each color are LED and are designed to last 100,000 hours. So, each light does last 100,000 hours.
lets make conversions
As
Dividing hours by
hours would bring
days
Dividing days by
days would bring
years, meaning 11 years and 4 months.
Keywords: light, conversion, day, hours
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Since this is part of a packet, there's a lot of prior knowledge you need to understand the question.
1) The angle of elevation is the angle between the horizontal and the light of sight from the object to the observer (see picture 1).
2) A lot of the units are from work done by an Indian astronomer. The line of sight (light blue in picture 1) is r = 3438 (I think you might have forgotten to finish writing the number). r, or 3438, is the distance from the earth to the sun used by Indian Astronomers.
3) The table shows units in jya(θ<span>°). Jya is a Sanskrit (ancient Indian language) word. It stands for the length of half of a chord that connects two endpoints of a circle (kinda confusing and more information than you need to know - but it's the green line in picture 2).
What's important is: </span>jya(θ°) = r*sin(θ°)
Now let's tackle the problem:
1) You know that the angle of elevation is 67.5°. Using the chart, the only important value is the second from the bottom. jya(67.5°) = 3177.
2) Remember that jya(θ°) = r*sin(θ°).
Also remember that sine of an angle is
. In this problem, r, the distance from the earth to the sun, happens to be the hypotenuse of the triangle since its the longest edge.
3) Notice that you're dividing jya(θ°) (aka r*sin(θ°)) by r = 3438. That will give you sin(θ°) by itself. Then you're multiplying that sin(θ°) by 1 AU, which we are told is the actual distance of the hypotenuse/distance from earth to sun. Since sine = that gives you the apparent length of the opposite side = apparent height of the sun.
The math is a bit weird, but you're basically multiplying sine by the apparent distance 1AU to get the apparent height, instead of multiplying sine by the estimated height r = 3438. Dividing 3177 by 3438 gives you sin(67.5°). Then multiplying sin(67.5°) by the apparent hypotenuse, 1AU, gives you the apparent height. That's how I'm understanding it!
1) The angle of elevation is the angle between the horizontal and the light of sight from the object to the observer (see picture 1).
2) A lot of the units are from work done by an Indian astronomer. The line of sight (light blue in picture 1) is r = 3438 (I think you might have forgotten to finish writing the number). r, or 3438, is the distance from the earth to the sun used by Indian Astronomers.
3) The table shows units in jya(θ<span>°). Jya is a Sanskrit (ancient Indian language) word. It stands for the length of half of a chord that connects two endpoints of a circle (kinda confusing and more information than you need to know - but it's the green line in picture 2).
What's important is: </span>jya(θ°) = r*sin(θ°)
Now let's tackle the problem:
1) You know that the angle of elevation is 67.5°. Using the chart, the only important value is the second from the bottom. jya(67.5°) = 3177.
2) Remember that jya(θ°) = r*sin(θ°).
Also remember that sine of an angle is
3) Notice that you're dividing jya(θ°) (aka r*sin(θ°)) by r = 3438. That will give you sin(θ°) by itself. Then you're multiplying that sin(θ°) by 1 AU, which we are told is the actual distance of the hypotenuse/distance from earth to sun. Since sine =
The math is a bit weird, but you're basically multiplying sine by the apparent distance 1AU to get the apparent height, instead of multiplying sine by the estimated height r = 3438. Dividing 3177 by 3438 gives you sin(67.5°). Then multiplying sin(67.5°) by the apparent hypotenuse, 1AU, gives you the apparent height. That's how I'm understanding it!