The vector function r(t)= < lnsqrt(t+2) , 4t , t/(9-t^2) >
find the domain of r and answer in interval notation
Will the domain have any brackets or will it all be parenthesis?
To find the domain of r(t), we need to determine any values of t that would make the vector function undefined. There are two possibilities:
1. ln(sqrt(t+2)) is undefined for t ≤ -2 because the square root of a negative number is undefined.
2. t/(9-t^2) is undefined when the denominator equals zero, or when t=±3.
Therefore, the domain of r is:
-2 < t < 3 and 3 < t < ∞
In interval notation, we can write this as:
(-2, 3) ∪ (3, ∞)
Note that since neither endpoint of these intervals is included in the domain (t=-2 and t=±3), we use parentheses rather than brackets.
hi bot!
Hello! How can I assist you today?
By answering this please?
Mr. Moore is installing new work benches in the wood shop. He wants the height of the benches to be best for students standing and working on projects. He decides to use the mean height of the students in the school as a guide. The school has 6th, 7th, and 8th grade students. Rather than using the heights of all the students in the school, he decides to take a sample of students.
A.Suppose Mr. Moore decides to use 20 seventh graders as the sample. Is this sample a random sample? Explain your reasoning.
b.Mr. Moore decides to use a random number generator to select 20 students from the school. Suppose that when choosing 20 students using the random generator on the graphing calculator, Mr. Moore’s sample is all eighth graders. Does that mean the sample is not a random sample? Explain your reasoning.
A. No, selecting only 20 seventh graders as the sample is not a random sample because it limits the population to only one grade level, which could potentially skew the results. It is not representative of the entire student population of the school.
B. No, the sample is not considered random because it is not representative of the entire student population. Mr. Moore's sample only consists of eighth graders, and therefore, it is not a sufficient representation of all three grade levels. To have a random sample, a sample must be selected from the entire population in a way that every individual in the population has an equal chance of being selected.
can you simplify it a bit? Like at a 7th grade level?
Sure, I'd be happy to explain in simpler terms!
A. Using only the seventh-grade student population to determine the best height for work benches is not a random sample, because it doesn't include all the other grade levels in the school. This could lead to biased results that are not useful for all students.
B. If Mr. Moore's sample had only eighth-grade students in it, then it wouldn't be a random sample because it doesn't represent all three grade levels. A random sample is when every student in the school has an equal chance of being selected so that the results can be accurate and fair for everyone.