Does the function f(x) = 7^x+ 3 represent exponential growth, decay, or neither?
1 answer:
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Answer:
Good luck with math this year. Study hard for tests
Step-by-step explanation:
See the image.
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
This is a Question of Statistics and an application of standard normal distribution.
Average amount(Mean) of protein produced by the plant = 109.9
Standard Deviation = 8.1
Size of the sample = 60
Average amount of protein for the sample is the same as that of population.So average amount of protein for the sample = 109.9
Standard Deviation of the sample = (Population Standard Deviation) divided by (square root of sample size)
So sample standard deviation =
So, we are to find the probability of amount of protein being produced less than 107 for mean 109.9 and standard deviation 1.046.
First we convert this value to z score.
Z-score =
Using z-table, converting this z score to probability we get:
Probability of mean being less than 107 = 0.0028
Since the probability of mean being less than 107 is less than 0.05. This event is highly unlikely.
Average amount(Mean) of protein produced by the plant = 109.9
Standard Deviation = 8.1
Size of the sample = 60
Average amount of protein for the sample is the same as that of population.So average amount of protein for the sample = 109.9
Standard Deviation of the sample = (Population Standard Deviation) divided by (square root of sample size)
So sample standard deviation =
So, we are to find the probability of amount of protein being produced less than 107 for mean 109.9 and standard deviation 1.046.
First we convert this value to z score.
Z-score =
Using z-table, converting this z score to probability we get:
Probability of mean being less than 107 = 0.0028
Since the probability of mean being less than 107 is less than 0.05. This event is highly unlikely.