Consider the following vector function. r(t) = 6t, 1 2 t2, t2 (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use this formula to find the curvature. κ(t) =
Answers
Using the formula the curvature. κ(t) = \(\frac{\sqrt{900t^2+6480}}{(5t^2+36)^2}\).
The reciprocal of a curve's radius can be used to compute an object's curvature. It is significant to keep in mind that the curvature varies depending on the kind of curve being evaluated.
From the question vector function
r(t) = <6t, t²/2, t²>
Now we have
r'(t) = (6, t, 2t)
and |r'(t)| = √(6)² + (t)² + (2t)²
|r'(t)| = √36 + t² + 4t²
|r'(t)| = √36 + 5t²
Now the unit tangent T(t) is given as:
T(t) = r'(t)/|r'(t)|
T(t) = (6, t, 2t)/√36 + 5t²
Now T'(t) = \(\left < \frac{-30t}{(36+5t^2)^{1/2}}, \frac{36}{(36+5t^2)^{1/2}},\frac{72}{(36+5t^2)^{1/2}}\right >\)
|T'(t)| = \(\sqrt{\frac{900t^2+6480}{(36+5t^2)^{3}}}\)
Therefore the unit normal N(t) is given by;
N(t) = T'(t)/|T'(t)
N(t) = \(\left < \frac{-30t}{\sqrt{900t^2+6480}}, \frac{36}{\sqrt{900t^2+6480}},\frac{72}{\sqrt{900t^2+6480}}\right >\)
Hence,
κ(t) = |T'(t)|/|r'(t)|
κ(t) = \(\frac{\sqrt{900t^2+6480}}{(5t^2+36)^2}\)
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Related Questions
Lara coach told her to run once around the perimeter of the soccer field. The field is 138 yards long and 92 yards wide. How far did Lara run
Answers
Answer:
460
Step-by-step explanation:
138+138+92+92=460
Identify ZABF by clicking and dragging the small yellow dots to shade the
angle.
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y = 2x -1 ( ,9)
The ordered pair is ( , 9)
Answers
Answer:
the ordered pair is (5, 9)
Step-by-step explanation:
using the ordered pair y = 9
9 = 2x - 1
10 = 2x
x = 5
so the ordered pair is (5, 9)
Answer:
the ordered pair is (5,9)
Step-by-step explanation:
........
✌️❤️✌️
g(y)= y - 15/y
h(y) = − 3y
Evaluate.
h(g(5)) =
Answers
Answer: -6
At the end of a fiscal year, a company has made 1.62 x 77 dollars in profit. The company employs 73 people. How much will
each person receive if the company divides the profit equally among its employees?
Each person will receive $___
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hich of the following are most likely to be dependent samples? multiple choice a study that compares the mean wait times at two different hospital emergency rooms a study that compares the salaries earned by men and women in the same job position a study that compares the weight gain for puppies who eat two different brands of food a study that compares standardized test scores before and after a course is taken
Answers
The statement which most likely represent "dependent-samples" is (d) study which compares standardized "test-scores" before and after course is taken.
The scores obtained before and after are linked, as they are obtained from the same group of individuals, and are therefore dependent samples.
For example, suppose a group of students is given a standardized test before and after taking a preparation course.
The scores obtained before the course are likely to be related to the scores obtained after the course, as they are both measures of the same group of students.
If the course has a significant impact on the scores, the before-and-after scores will likely be correlated, and the samples will be dependent.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Which of the following are most likely to be dependent samples?
(a) A study that compares the mean wait times at two different hospital emergency rooms
(b) A study that compares the salaries earned by men and women in the same job position
(c) A study that compares the weight gain for puppies who eat two different brands of food
(d) A study that compares standardized test scores before and after a course is taken.
Will give brainliest, *15 points*
Brian has two rectangular sheets of paper. The length of the larger sheet is 1 1/2 times the length of the smaller sheet. The width of the larger sheet is 1 3/5 times the width of the smaller sheet. By what factor is the area of the larger sheet greater than the area of the smaller sheet?
Answers
240u^2 / 100u^2 = 2.4
A robot can complete 5 task 3/10 in hour. Each task takes the same amount of time.
Answers
Use words and symbols to describe the value of each term as a function as its position. Then find the value of the sixteenth term in the sequence
Position: 2 3 4 5 n
Value of Term: 8 12 16 20 Blank
Answers
Using the value of each term as a function as its position , the value of the sixteenth term in the sequence is 64 .
The value of the terms are : 8, 12, 16, 20 ...
The see that sequence has a constant difference of 4 between any two consecutive terms.
So, we say that the sequence is an arithmetic sequence having common difference of 4.
To find the value of sixteenth term of sequence, we find first term of sequence ;
Let the nth term of the sequence be represented as : "aₙ" ;
It is given that a₂ = 8,
So, a₂ = a₁ + d ,
where a₁ = first term of sequence and d = common difference ;
Solving for a₁,
We get ,
⇒ a₁ = a₂ - d = 8 - 4 = 4 ;
We know that nth term of arithmetic sequence is written as :
⇒ aₙ = a₁ + (n-1)d ;
where a₁ = 4 and d = 4.
To find sixteenth term, we substitute n = 16 in the formula:
We get ,
⇒ a₁₆ = 4 + (16-1)4
⇒ a₁₆ = 4 + 15(4)
⇒ a₁₆ = 64
Therefore, the sixteenth term in the sequence is 64.
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member of wanna one?
help me plss
patulong naman po
Answers
Answer:
what yo are telling l can't understand your language
Determine the type of triangle that is drawn below.
Answers
⇒ ΔVWX is a Scalene triangle because all the sides and all the angle are not equal.
if x²+y²=34 and xy=7.5,find the value of 5(x-y)²
Answers
Answer:
It is given that,
x²+y² = 34 ----(1)
xy = 10½ = 21/2 ---(2)
Value of 2(x+y)²+(x-y)²
= (x+y)² + [(x+y)²+(x-y)²]
= x²+y²+2xy + 2(x²+y²)
= 34 + 2×(21/2)+2×34
= 34 + 21 + 68
= 123
If Paula buys 80 T-shirts, what is the maximum number of sweatshirts she can buy?
Answers
Answer:
Step-by-step explanation:
Somebody please solve the Absolute Value Inequality.: |-7b+1|-8<-70
Answers
Answer: the answer is no solution
Step-by-step explanation:
Answer:
No Solution
Step-by-step explanation:
An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.
If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.
See image.
WILLL GIVE BRAINS!!!!!!!!
Answers
Answer:
median = 3 pieces
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is not an exact middle value then the median is the average of the values either side of the middle.
Given the number of pieces then
2 2 4 4 ← pieces of cheese in ascending order
↑ middle is between 2 and 4, thus
median = \(\frac{2+4}{2}\) = \(\frac{6}{2}\) = 3
What is 15% of 90?
A. 14.4
B. 13.5
C. 60.0
D. 16.7
Answers
B.
It's 13.5
---------------
Answer:
multiply 90 by 0.15. and you get 13.5
The number 31 is increased to 44. What is the percentage by which the number was increased, to the nearest tenth of a percent?
.
Answers
Answer:
41.9%
Step-by-step explanation:
percent change = (new number - old number)/(old number) × 100%
new number = 44
old number = 31
percent change = (44 - 31)/31 × 100%
percent change = 13/31 × 100%
percent change = 0.41935 × 100%
percent change = 41.9%
Dan and David win some money and share It into the ratio 5:2 Dan gets £55.how much did they win in total?
Answers
Answer:
$77
Step-by-step explanation:
Answer:
77
Step-by-step explanation:
because den whose part is 5:2 got 55, then you should divide 55 by 5 and get 11, then multiply 11 by 2 equals 22.
55 + 22 = 77
Find the area of the trapezoid.
Answers
Answer:
area = (1/2) · (p + q) · h
Step-by-step explanation:
evaluate the expressin 4c-y when 4 c is 3 -y is -3
Answers
Answer: 0
Step-by-step explanation:
Given 4c-y when 4c = 3 and -y = -3
Now on substitution, we get
3-3 = 0
What is the greatest factor of 16x and 12?
Answers
Answer:
4
Step-by-step explanation:
hope that helps!
4x + 5 ≤ 25 solve for x
Answers
Answer:
\( x \leq 5\)
Step-by-step explanation:
\(4x+5 \leq 25 \\ \\ 4x \leq 20 \\ \\ x \leq 5\)
Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the standard deviation for the number of cells infected was 80 and the mean was 350. What is the standard error
Answers
Thus, standard error for this sample of tissue cells infected in a laboratory treatment is 5.33.
The standard error (SE) is a measure of how much the sample mean deviates from the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
In this case, the sample size is 225, the standard deviation is 80, and the mean is 350. Therefore, the standard error can be calculated as follows:
SE = 80 / √(225)
SE = 80 / 15
SE = 5.33
The standard error for this sample of tissue cells infected in a laboratory treatment is 5.33. This means that the sample mean of 350 is likely to be within 5.33 units of the population mean.
The smaller the standard error, the more precise the estimate of the population mean. In this case, the standard error is relatively small compared to the standard deviation, which suggests that the sample mean is a relatively accurate estimate of the population mean.
However, it is important to note that the standard error only provides information about the precision of the estimate, not its accuracy. Other factors, such as sampling bias or measurement error, could still affect the accuracy of the estimate.
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What was Callie’s mistake? Callie should have added 10 to both sides in step 2. In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly. Callie divided by 2 instead of multiplying by 2 in step 3. Callie should have added 16 to both sides in step 2.
Answers
Answer:
In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly
Answer:
B
Step-by-step explanation:
nae nae before u get a whoopin
Considerable research is being done in bioremediation - the use of living organisms to clean up pollution. In a recently conducted experiment, researchers used fungi to degrade hydrocarbons, the by-products of incomplete combustion of fossil fuels. These by-products can cause cancer, and their accumulation in water and soil poses an environmental hazard. 0.83 0.91 1.00
1.08 1.08 1.09
1.10 1.23 1.36 In order to be cost-effective, a minimum of 1.00 micromoles/minute/gram of soil of a particular hydrocarbon must be degraded. The researchers added fungi and growth media (essentially sugar) to the soil in 9 containers with random samples of soil and obtained the following degradation rates in micromoles/min/gram:
(a) The sample mean =1.076 and the sample standard deviation=0.158. Calculate and interpret the standard error of the mean for these data.
(b)Construct and interpret a 90% confidence interval for the mean degradation rate. Can the researchers be confident that this process will be cost-effective?
Answers
Standard error of the mean is 0.05267 in (a). The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to (b).
What does standard error mean?The group mean's likelihood to vary from a sampling distribution is indicated by the standard deviation of a mean, or merely standard error. It reveals how much is the sample imply would change if a research were to be repeated with fresh samples drawn from a particular population.
(a)
Sample size, n = 9
Sample standard deviation, S = 0.158
Standard error of the mean,
\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)
(b)
Since we do not know the distribution of the parent population or the population standard deviation, and further the sample size, n = 8 < 30,
Therefore we will use the t-distribution to construct the confidence interval for the true population mean α
Sample size, n = 9
Sample mean, r = 1.076
Sample standard deviation, S = 0.158
Standard error of the mean,
\(\sigma_{\bar{x}}=\frac{S}{\sqrt{n}}=\frac{0.158}{\sqrt{9}}=0.05267\)
Level of confidence, c (in percentage) = 90
α = (1-(c/100) = 0.1
Degrees of freedom, df = n-1 = 9 - 1 = 8
The critical t-score, \(\mathrm{t}_{\mathrm{c}}\) is the
t-score corresponds to the given level of confidence and degrees of freedom :
\(\begin{aligned}& P\left(x > t_{d f}\right)=\Rightarrow / 2 \\& \Rightarrow \\& P\left(x > t_8\right)=0.1 / 2=0.05 \\& \Rightarrow t_c=1.86\end{aligned}\)
The confidence interval is calculated as:
\(\mathrm{Cl}=\bar{x} \pm\left(\mathrm{t}_{\mathrm{c}}\right)^*\left(\sigma_{\bar{x}}\right)\)
= 1.076 ± (1.86)*(0.05267)
= 1.076± 0.098
= (1.076 - 0.098, 1.076 + 0.098)
= (0.978, 1.174)
The actual mean degradation rate has a 90% probability of being between 0.978 and 1.174 micromoles/minute/gram, according to this information.
The mean degradation rate must be higher than 1 for the process to be cost-effective.
However, because the 90% confidence interval does not completely fall above 1, the experts cannot be certain that the process will be cost-effective.
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Rose saved up her money and bought a model train. Each of the cars were 8 was the same length when rose put the car together it was 3 feet long
How long were the cars
Answers
The length of each car that Rose bought for her model train was 3/8 feet or 0.375 feet.
How is the length determined?To determine the length, we use the mathematical operation of division.
Given that the train was 3 feet in length and made up of 8 cars, the length of each car will be a quotient of 3 feet by 8.
Data and Calculations:The number of cars of the same length = 8
The length of the train of 8 cars = 3 feet
Therefore, the length of each car = 3/8 or 0.375 feet
Thus, the length of each car was 3/8 feet or 0.375 feet.
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Complete Question:Rose saved up her money and bought a model train. Each of the 8 cars on the train was the same length. When Rose put all the cars together, the train was 3 feet long. How long was each car?
Je n'arrive pas a faire cette exercice donne moi les réponse s'il te plait
Answers
Answer:
a) Non car si le fils a 10 ans la mère a 30 ans et le père 33 or 10+30+33=73
b) Oui car si le fils a 12 ans la mère a 36 ans et le père 39 et 12+36+39=87
Step-by-step explanation:
the scores on a mathematics exam have a mean of 70 and a standard deviation of 5. find the x-value that corresponds to the z-score 2.33.
Answers
x-value that corresponds to the z-score of 2.33 is 81.65.
Mean = 70
Standard deviation = 5
z score = 2.33
Using the z-score formula:
z = (x - mean) / SD
Plug the values:
2.33 = (x-70)/5
x = 5(2.33) +70
x = 81.5
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Please help!!!!!!!!! I'll mark brainliest if you give an explanation!!!!
Each solar array wing on the International Space Station measures 39 feet by 112 feet. The scale drawing of a solar array wing shown below was made using a scale of 1 inch: 8 feet.
Write the ratio of the area of the wing in the drawing (square inches) to the area of an actual solar array wing (square feet) as a unit fraction.
The drawing is just a large rectangle with the length being 4.875 and there is noting for the width.
Answers
Answer:
39-112= -73 or 73
so 73+1/8= 81
Step-by-step explanation:
b) Find the standard deviation of the number of nights potential customers will need.
Answers
Answer:
ok
Step-by-step explanation: