Find B and for the space curve r(t) = j, t> 0. 3 т 11 i + j N = i + . The binormal vector is B = i+i+Ok. (Simplify your answers. Use integers or fractions for all numbers in the expression.) The torsion is t= (Type an integer or a simplified fraction.)
Answers
To find B and the torsion for the space curve r(t) = <3t, 1, 0>, we can first find the tangent and normal vectors:
r'(t) = <3, 0, 0>
| r'(t) | = 3
T(t) = r'(t) / | r'(t) | = <1, 0, 0>
N(t) = ( T'(t) / | T'(t) | ) = <0, 1, 0>
Next, we are given that the binormal vector is B = <1, 1, 0>. We can check that B is indeed perpendicular to both T and N:
T dot B = <1, 0, 0> dot <1, 1, 0> = 1
N dot B = <0, 1, 0> dot <1, 1, 0> = 0
Finally, we can use the formula for torsion:
t = - ( B'(t) dot N(t) ) / | r'(t) |
We have B(t) = B = <1, 1, 0>, and B'(t) = 0 since B is constant. Therefore:
t = 0 / ( 3 ) = 0
So the torsion for the space curve is 0.
To find the binormal vector B and torsion τ for the given space curve r(t) = j, we need to compute the tangent vector T, normal vector N, and their derivatives. Given N = i + 3tj, we'll start by finding T.
1. Compute the derivative of r(t) with respect to t to get the tangent vector T.
dr/dt = 0i + 1j => T = j (since T = dr/dt)
2. Normalize T.
Since T = j, its magnitude is |T| = 1. So, the unit tangent vector is T = j.
3. Compute the derivative of T with respect to t to find the normal vector N.
dT/dt = 0i + 0j => N = 0 (since N = dT/dt)
However, the given N is i + 3tj, which contradicts our computed N. Therefore, there seems to be an error in the question's information, and we cannot proceed further to find the binormal vector B and torsion τ with the provided data.
Please double-check the given information and provide the correct details for the space curve and normal vector.
To know more about Curve click here .
brainly.com/question/28793630
#SPJ11
Related Questions
Leah Deposited $7000 in an account that earns 2% interest compounded annually. How much interest will she have earned after 6 years?
Answers
Answer:
840
Step-by-step explanation:
7000×2×6 ÷ 100. since it is 2%
= 840
If g(x) = x2 + 2, find g(3).
Answers
Answer:
8
Step-by-step explanation:
g(3)=3(2)+2
g(3)=6+2
g(3)=8
12. Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 18.
A. 7
B. 12
C. 15
D. 5
Answers
Answer:
12
Step-by-step explanation:
the points at which the parabola intersects the x-axis
Answers
The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.
What is parabola?A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.
To know more about parabola,
https://brainly.com/question/28973830
#SPJ4
Carla served her mango pie on a 14 inches diameter dish. She wanted to tie a ribbon around the dish to make it a little more attractive. How long does the ribbon need to be in order to fit around the dish?
Answers
By finding the circumference of the plate, we conclude that the ribbon must be 43.96 in long.
How long does the ribbon need to be?
Remember that for a circle of radius R, the circumference is:
C = 2*pi*R
In this case, the ribbon must be equally long to the circumference of the plate. We know that the diameter of the plate is 14 inches, and the radius is half of that, then we get:
R = 14in/2 = 7in
Replacing that on the circumference equation we get:
C = 2*3.14*7in = 43.96 in
The ribbon must be 43.96 in long.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Homework: Section 11.1 Question 7. Complete the square to find the x-intercepts of the function given by the equation listed. f(x)=x² +34x+104 What are the x-intercepts? **** (Simplify your answer. T
Answers
Answer:
x² + 34x + 104 = 0
x² + 34x = -104
x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²
x² + 34x + 17² = -104 + 17²
x² + 34x + 289 = 185
(x + 17)² = 185
x + 17 = +√185
x = -17 + √185
Anything is appreciated I will give you Brinley
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
7/3 + 3 (2/3 - 1/3)^2
Answers
Answer:
20/9
Step-by-step explanation:
Not sure what you need, but here is that simplified as much as possible:
(given) 7/3 + 3 (2/3 - 1/3)^2
(subtract) 7/3 + 3 (1/3)^2
(square) 7/3 + 3 (1/9)
(mixed number to improper fraction) 7/3 + 38/9
(changing 7/3 into 1/9s) 7/3 = 21/9
(expression) 21/9 + 38/9
(adding) 40/9
(simplify) 20/9
Find the product of 2/3 and 9/10
Answers
Answer:
3/5
Step-by-step explanation:
PLZ MARK AS BRAINLIEST
To find the product of 2/3 and 9/10, multiply the numerators and denominators together: \(\frac{2}{3} * \frac{9}{10} = \frac{18}{30}.\) This simplifies to \(\frac{3}{5}\), which is the answer.
Nina mixes 200 mL of cranberry juice, 300 mL of grapefruit juice,and 700 mL of spring water to make fruit punch. What is the ratio of cranberry juice to grapefruit juice to spring water
Answers
find three consecutive integers whose sum is 21
Answers
Answer:
6 + 7 + 8 = 21
Step-by-step explanation:
6, 7, and 8 are consecutive integers.
6 + 7 is 13. 13 + 8 = 21. So, 6 + 7 + 8 are consecutive integers that equal 21.
Answer:
6+7+8= 21
Step-by-step explanation:
6,7,8 follow consecutively. and if you add them, the sum is 21
can someone help me with this
Answers
Answer:
i cant see the pic please send a better one and i reloaded it and it still does not work
Step-by-step explanation:
6. Excel functions to be used for the following methods. a) Straight Line: b) Double Declining Balance: c) Sum of Years Digits: d) Variable Declining Balance:
Answers
a) Straight Line: The Excel function used for the straight-line method is "SLN." b) Double Declining Balance: The Excel function used for the double declining balance method is "DDB." c) Sum of Years Digits: The Excel function used for the sum of years digits method is a combination of "SYD" and other mathematical functions. d) Variable Declining Balance: The Excel function used for the variable declining balance method may vary depending on the specific calculation required.
a) Straight Line: The straight-line method calculates depreciation by dividing the asset's cost by its useful life. In Excel, the "SLN" function is used, which takes three arguments: cost, salvage value, and useful life. The formula is "=SLN(cost, salvage, life)."
b) Double Declining Balance: The double declining balance method applies a constant depreciation rate to the asset's book value. In Excel, the "DDB" function is used, which takes five arguments: cost, salvage value, useful life, period, and factor. The formula is "=DDB(cost, salvage, life, period, [factor])."
c) Sum of Years Digits: The sum of years digits method calculates depreciation by assigning weights to each year based on the asset's useful life. In Excel, the "SYD" function is used, which takes four arguments: cost, salvage value, useful life, and period. The formula is "=SYD(cost, salvage, life, period)."
d) Variable Declining Balance: The variable declining balance method calculates depreciation using a varying depreciation rate based on the asset's expected usage or production levels. The Excel function to be used may depend on the specific calculation or formula required for the variable declining balance method.
Conclusion:
Excel provides specific functions to facilitate the calculations for different depreciation methods. The "SLN" function is used for straight-line depreciation, "DDB" function for double declining balance, and "SYD" function for sum of years digits method. These functions simplify the calculations by taking relevant arguments and producing accurate results. However, for the variable declining balance method, the specific Excel function may vary depending on the formula or calculation required. By utilizing the appropriate Excel functions, depreciation calculations can be performed efficiently and accurately within the chosen depreciation method.
To know more about SLN, visit;
https://brainly.com/question/31957875
#SPJ11
Find the angle measure G.
Answers
Answer:
∠ G = 85°
Step-by-step explanation:
∠ G is an inscribed angle whose measure is half the measure of its intercepted arc.
the sum of the arcs in a circle = 360° , then
arc DF = 360° - 120° - 70° = 360° - 190° = 170° , then
∠ G = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 170° = 85°
How do you solve algebraic expressions in simplest form?
Answers
Answer:
Step-by-step explanation:
To solve an algebraic expression in simplest form, you can follow these steps:
1. Use the order of operations (PEMDAS) to simplify any arithmetic in the expression (parentheses, exponents, multiplication and division, addition and subtraction).
2. Combine like terms by adding or subtracting any coefficients in front of similar variables.
3. Divide or multiply both sides of the equation by the same non-zero number to solve for the variable.
4. If possible, factor the expression to make it simpler.
5. If the expression is a fraction, check for a common denominator and then simplify by canceling any common factors in the numerator and denominator.
6. If the expression is a radical, check for a perfect square and simplify by taking the square root of the number inside the radical.
7. Use the properties of exponents and logarithms to simplify the expression.
8. Evaluate the expression by plugging in the values of any known variables.
It's important to keep in mind that there may be multiple ways to simplify an algebraic expression and the solution that is in simplest form may not always be obvious.
Solve #1 pls, I need to find the shortest side, median side, and longest side
Answers
Answer:
Shortest side = 39 cm.
Median side = 65 cm.
Longest side = 91 cm.
Step-by-step explanation:
The perimeter in total is 195 cm. The ratio of the sides are 3 : 5 : 7.
First, find how much parts there are as a whole, by combining the ratios:
3 + 5 + 7 = 15 parts.
Divide the total of parts from the total measurement:
195/15 = 13
Each part has the measurement of 13 cm.
1 part = 13 cm.
Use the following ratio to solve for each of the sides:
Shortest side: 3
3 x 13 = 39
Shortest side = 39 cm.
Median side: 5
5 x 13 = 65
Median side = 65 cm.
Longest side: 7
7 x 13 = 91
Longest side = 91 cm.
Check. Combine all side measurements together. They should equal 195:
39 + 65 + 91 = 195
(39 + 65) + 91 = 195
(104) + 91 = 195
195 = 195 (True).
~
Density =8g/ml, Volume = 10ml, what is the mass?
Answers
Answer:
mass = 0.8g
Step-by-step explanation:
d=m/v isolate m
m×d=v
m=d/v
m= 8/10
m = 0.8 g
Answer:
mass = 0.8g
Step-by-step explanation:
d=m/v isolate m
m×d=v
m=d/v
m= 8/10
m = 0.8 g
brainliest plz!!
please help i’m sorry!!! 15 points again!
Answers
Answer:
Guess I'll agree with the other person.
Step-by-step explanation:
Runner a averages 5 mph and run it B rat averages 6 mph these rates how much longer does it take runner A then runner be to run 15 miles
Answers
How do you find the mean and standard deviation of a simple random sample?
Answers
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
To know more about mean and standard deviation, click on the link
https://brainly.com/question/475676
#SPJ4
A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?
Answers
Answer:
49.6 minutes to create 308 bolts
Step-by-step explanation:
hope this helps :)
49Answer:
Step-by-step explanation:
The asymmetric cryptography algorithm most commonly used is:
O GPG
O RSA
O ECC
O AES
Answers
Answer
Step-by-step explanation:
602.88 rounded to 2 decimal place is ?
Answers
Answer:
it will be 603.00
it will. e counted from the right to the left
Alaina is giving a presentation about how the average college student spends their day. Through her research, she finds that most college students spend 30% of their day sleeping, 20% in class, 20% studying, and 30% socializing/participating in extracurricular activities. How should she graphically display this information in her presentation?
Answers
In her presentation, Alaina can use a pie chart to show information about how the typical college student spends their day.
A circular chart that has been divided into sectors or "pie slices" to represent numerical proportions is known as a pie chart. Each pie slice symbolises a percentage, and each slice's size is proportional to the percentage it represents.
In this instance, Alaina can separate the pie chart into four segments that stand in for the various activities that college students engage in throughout the day: sleeping, attending classes, studying, and participating in extracurricular activities. She can give each slice a unique colour and a label indicating the proportion it represents.
The pie chart, for instance, might have the following slices:
-30% of people are sleeping (blue).
- 20% of the class (in green)
20% of study time (coloured)
30% of time for socializing
Know more about pie chart here:
https://brainly.com/question/1109099
#SPJ11
what value of x makes 1/2 (3x+ 4) = 1/2 x true
Answers
The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2
We have to simplify the given expression to find the value of x
1/2(3x + 4) = 1/2x
Cancel 1/2 from both sides
⇒ 3x + 4 = x
⇒ 2x = -4
⇒ x = -2
Hence, the value of x is -2 which makes the given expression true.
Learn more about value here
https://brainly.com/question/4806080
#SPJ1
The philanthropic organization in Exercise 1 expects about a 5%success rate when they send fundraising letters to the people on their mailing list. In Exercise 1 you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of size and The sample statistics from each simulation were as follows:a) According to the Central Limit Theorem, what should the theoretical mean and standard deviations be for these sample sizes?b) How close are those theoretical values to what was observed in these simulations?c) Looking at the histograms in Exercise at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?d) What does the Success/Failure Condition say about the choice you made in part c?
Answers
The Normal model is a good approximation for the sampling distribution.
a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.
b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.
c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.
d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.
The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.
Learn more about sampling distribution here:
https://brainly.com/question/30007465
#SPJ4
A bowl contains blueberries and strawberries. There are a total of 48 berries in the bowl. The ratio of blueberries to strawberries is 9 to 3. How many of each berry are in the bowl?
Answers
There are 48 berries and the ratio is for every 9 blueberries there is 3 strawberries. 9 x4 is 36 and 3x4 is 12 which is 48 berries in total.
The length of a rectangle is 5 centimeters more than twice the
width. The perimeter is 82 centimeters. Find the length and width.
Answers
Answer:
The length is 29 cm while the width is 12cm
Step-by-step explanation:
Given that the length l of a rectangle is 5cm more than twice the width w then
l = 5 + 2w
If the perimeter p of the rectangle is 82cm, recall that the perimeter p of a rectangle is given as
p = 2(l + w)
substituting for l into the equation
82 = 2(5 + 2w + w)
82 = 2(5 + 3w)
Divide both sides by 2
41 = 5 + 3w
41 - 5 = 3w
36 = 3w
Divide both sides by 3
w = 12cm
recall that
l = 5 + 2w
l = 5 + 2(12)
l = 5 + 24
l = 29cm
Which best describes why these two figures are similar or not similar?
Answers
Answer:
first one top left
Step-by-step explanation:
PLEASE HELP
Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How old is Ricardo?
Answers
Given:
Ricardo is 4 years less than twice as old as his sister.
The sum of their ages is 20.
To find:
Ricardo's age.
Explanation:
Let R be Ricardo's age.
Let S be his sister's age.
According to the question,
\(\begin{gathered} R=2S-4............(1) \\ R+S=20...........(2) \end{gathered}\)Substituting equation (1) in (2) we get,
\(\begin{gathered} 2S-4+S=20 \\ 3S-4=20 \\ 3S=24 \\ S=8 \end{gathered}\)Substituting S = 8 in equation (2) we get,
\(\begin{gathered} R+8=20 \\ R=12 \end{gathered}\)Therefore, Ricardo's age is 12.
Final answer:
Ricardo's age is 12.