Find the Principal unit normal for r(t) = sintit cost; + tk Evaluate it at t = Tyz Sketch the situation
Answers
We can plot the vector r(t) and the vector N(T) at the given value of t = T.
To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.
First, let's find the derivative of r(t):
r'(t) = cos(t)i + (cos(t) - tsin(t))j + k
Next, we'll normalize the vector r'(t) to obtain the unit vector:
||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)
Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:
N(t) = r'(t) / ||r'(t)||
Let's evaluate the principal unit normal at t = T:
N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||
To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.
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Related Questions
Use any method to solve the following system of equations: Equation #1: 2y = x - 4 Equation #2: 4x + 3y = 5 *
(2, -1)
(-2, -1)
(2, 1)
(-2, 1)
help please!!
Answers
Answer:
Step-by-step explanation:
the answer is (2,1)
Answer
Of
This
Question
Is
(2,1)
Using the divergence theorem, find the outward flux of f across the boundary of the region d, where d is the region cut from the solid cylinder (y-x)i (z-y)j (z-x)k
Answers
The outward flux of F across the boundary of the region D is 0 (C. 0).
To find the outward flux of the vector field F = (y - x)i + (2 - y)j + (z - x)k across the boundary of the region D, we can use the Divergence Theorem. The Divergence Theorem relates the outward flux of a vector field across a closed surface to the volume integral of the divergence of the vector field over the region bounded by that surface.
The divergence of F (div F) can be computed as follows:
div F = (∂/∂x)(y - x) + (∂/∂y)(2 - y) + (∂/∂z)(z - x)
= -1 - 1 + 1
= -1
Now, let's consider the region D that is cut from the solid cylinder x² + y² = 9 by the planes z = 0 and z = 5. The region D consists of the curved surface of the cylinder, the top and bottom circular surfaces, and the two flat surfaces at z = 0 and z = 5.
According to the Divergence Theorem, the outward flux of F across the boundary of D is given by the volume integral of the divergence of F over the region D:
Flux = ∭D div F dV
Now, we need to set up the triple integral to evaluate the flux over the region D.
Since the divergence of F is -1, the flux simplifies to:
Flux = - ∭D dV
To evaluate this triple integral over the region D, we need to determine the limits of integration.
The region D is bounded by the cylinder x² + y² = 9 and the planes z = 0 and z = 5. The region D lies between z = 0 and z = 5, and within the circle of radius 3 (x² + y² = 9) in the xy-plane.
Therefore, the limits of integration are:
-3 ≤ x ≤ 3
-3 ≤ y ≤ 3
0 ≤ z ≤ 5
Now, we can set up the triple integral:
Flux = - ∭D dV
= - ∫[0 to 5] ∫[-3 to 3] ∫[-3 to 3] dx dy dz
The limits are constant, so we can pull them out of the integral:
Flux = - 5 ∫[-3 to 3] ∫[-3 to 3] dx dy
Now, integrate with respect to x and y:
Flux = - 5 ∫[-3 to 3] [xy] from -3 to 3 dy
= - 5 ∫[-3 to 3] (3y - 3y) dy
= - 5 ∫[-3 to 3] 0 dy
= 0
Thus, the outward flux of F across the boundary of the region D is 0 (C. 0).
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The question is incomplete the complete question is :
Using the Divergence Theorem find the outward flux of F across the boundary of the region D. F = (y - X)i + (2-y)j + (z - X)k, D the region cut from the solid cylinder x² + y² ≤ 9 by the planes z = 0 and z = 5
A. -45π B - 45 C.0 D. 45π
Question 3
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
There are 20 marbles in a bag: 8 purple, 5 gold, and 7 silver.
Part A: What is the probability that you select a silver marble? Reduce fractions if possible.
O
A) 20
O B)
O
c)
O D) 70
Answers
home within our geographic footprint.
Goals: Increase awareness of key homes for sale in our portfolio and generate traffic to the website for more information.
Step-by-step explanation:
the total is 8+5+7=20
the probabliliy that its gonna be 7/20
this fraction cannot be reduced
Book club A charges $20 for membership and $2 per book rental. Book club B charges $10 for membership and $3 per book rental. For how many movie rentals will the cost be the same at both book clubs? What does that cost?
Answers
Given:
Book club A charges $20 for membership and $2 per book rental.
Book club B charges $10 for membership and $3 per book rental.
To find:
The number of books for which the cost be the same at both book clubs.
Solution:
Let x be the number of books.
Book club A charges $20 for membership and $2 per book rental. So, the total cost is
\(C_1=20+2x\) ...(i)
Book club B charges $10 for membership and $3 per book rental. So, the total cost is
\(C_2=10+3x\) ...(ii)
Equating (i) and (ii), we get
\(10+3x=20+2x\)
\(3x-2x=20-10\)
\(x=10\)
The total cost is
\(C_1=20+2(10)\)
\(C_1=20+20\)
\(C_1=40\)
Therefore, the total cost at both book clubs are same for 10 rental books and that cost is $40.
find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
Answers
the slope is 0.288
Explanation
Step 1
given
\(xcosy=1\)a) find the implicit derivate
\(\begin{gathered} xcosy=1 \\ cosy-xsiny*y^{\prime}=0 \\ y^{\prime}=\frac{-cosy}{-xsiny} \\ y^{\prime}=\frac{cosy}{xs\imaginaryI ny} \end{gathered}\)b), now ,Plug x value of the indicated point into f '(x) to find the slope at x
\(\begin{gathered} y^{\prime}=\frac{cosy}{xs\imaginaryI ny} \\ y^{\prime}=\frac{cos(\frac{\pi}{3})}{2sin(\frac{\pi}{3})}= \\ y^{\prime}=0.288 \end{gathered}\)so, the slope is 0.288
I hope this helps you
Which three points are collinear?
Answers
according to defination of collinear points :Three or more points are said to be collinear if they all lie on the same straight line.
therefore, A,B,C points are collinear.
determine the measure of each missing angle in the triangle! HELPPP PLEASSEEEE!!!
Answers
Please answer I will make you brainliest
Answers
Answer:
3 times as great
Step-by-step explanation:
The most amount of water is 3/4 full
The least amount of water 1/4 full
To get from 1/4 to 3/4, you multiply by 3:
\(\frac{1}{4} * \frac{3}{1} = \frac{3}{4}\)
(I made 3 into 3/1 to show how you multiply across easier)
Find x and y in each figure.
Answers
Answer:
\(by \:alternate \: interiar \: angle \: \\ (8y + 2) + (25y - 20) = 180 \\ 8y + 2 + 25y - 20 = 180 \\ 33y - 18 = 180 \\ 33y = 180 + 18 \\ 33y = 198 \\ y = 6 \\ \\ now \\ by \: \: linear \: pair \: \\ 10x + 8y + 2 = 180 \\ 10x + 48 + 2 = 180 \\ 10x = 180 - 50 \\ 10x = 130 \\ x = 13\)
so finallyX=13and y=6-------------------------Pls help due asap. Please
Answers
Answer:
15.73
Step-by-step explanation:
Straight angle is 180 degrees. So the given angles add up to 180.
(6x - 3) + (5x + 10) = 180
11x + 7 = 180
-7 -7
11x = 173
helpppppppppppppppppppppp plsssssssssssssssss
m∠b= 25°
Answers
Answer:
Step-by-step explanation:
The total of all angles in the triangle is 180
You already know 2 values for the triangle, Angle A 25 as well as Angle C 90
Your formula is
180 - 90 -25
HI! please help out ASAP this is due today! Explain it the best you can and send a picture explaining it so I won’t get confused. Thank u!
Answers
(0,-1)
(3,-2)
(1,-4)
Which angles are supplementary?
Group of answer choices
Alternate Interior
Same Side Interior (Consecutive)
Corresponding
Vertical
Answers
Same Side Interior (Consecutive) angles are supplementary and are formed when two parallel lines are intersected by a transversal.
What are angles?Angles are been formed when two or more lines intersect at a point. Types of angles are acute, obtuse and right angle.
Supplementary angles are angles that add up to 180 degrees.
Same Side Interior (Consecutive) angles are supplementary and are formed when two parallel lines are intersected by a transversal.
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The difference of a number and 8 is 46 less the number. Find the number
Answers
Answer:
unsolvable
Step-by-step explanation:
n-8=46-n
n=(46-n)+8
n=54-n
Answer:
54
Step-by-step explanation:
you add 8+46 and you can check with 54-46=8
In the diagram below, points E, F, and G are collinear. If FH bisects ZEFI and m/IFG=38°, then which
of the following is the measure of ZHFG?
Answers
Where the above conditions are given, note that ∠AFB and ∠EFD are not vertical angles neither are they linear pair angles.
How is this so?Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines.
They are equal in measure and are formed opposite to each other. An example of vertical angles is when two intersecting roads create an "X" shape, and the angles formed at the intersection points are vertical angles.
Linear pair angles are a pair of adjacent angles formed by intersecting lines. They share a common vertex and a common side.
An example of linear pair angles is when two adjacent walls meet at a corner, and the angles formed by the walls are linear pair angles.
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Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Answers
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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Select all that are correct. An activity relationship diagram reveals qualitative factors which may be crucial to the workstation placement decision Systemic layout planning is most appropriate when the numerical flow of items between workstations is not know. Assembly line layouts rarely facilitate progressive assembly through use of material handing systems or devices Assembly lines are best suited for products with multiple parts produced in small volumes. Most would consider it desirable for a department store to put the candy department next to the toy department. Interworkcenter flow charts involve a relationship chart showing the degree of importance of locating workstations near to each other.
Answers
The correct statements are:An activity relationship diagram reveals qualitative factors that may be crucial to the workstation placement decision.
Assembly line layouts rarely facilitate progressive assembly through the use of material handling systems or devices.
Most would consider it desirable for a department store to put the candy department next to the toy department.
The incorrect statements are:
Systemic layout planning is most appropriate when the numerical flow of items between workstations is not known. (Systematic layout planning is more appropriate in this case.)
Assembly lines are best suited for products with multiple parts produced in small volumes. (Assembly lines are typically suited for products with high volumes and repetitive processes.)
Interworkcenter flow charts involve a relationship chart showing the degree of importance of locating workstations near each other. (Interworkcenter flow charts typically show the physical flow of materials or information between workstations.)
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add (5y - 1) + (-2y + 4) =
Answers
Answer:
3(y+1)!
Step-by-step explanation:
Solve for a. 25° 55° a a = [? ]° 30°
Answers
We can determine that the necessary angle ∠a is 15° using the provided secant line.
A secant crosses a circle at precisely two points in a case of a circle.
Mathematicians refer to a line that cuts through the points P and Q of any arbitrary curve whose equation is y=f as a secant, from the Latin term secant, which means to cut (x).
So, we know that:
c = 55° and b = 25°
And, the formula is:
∠a = c - b/2
Now, substitute values as follows:
∠a = c - b/2
∠a = 55 - 25/2
∠a = 30/2
∠a = 15°
Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.
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Complete question:
![Solve for a. 25 55 a a = [? ] 30](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/1VY3TSQZoWBtfyFkWo0BSd2dPVh9czLw.jpeg)
O
O
-100
What is the probability of flipping tails on the coin and spinning a 2 on the spinner?
8
Tails
414
4
3
(T.1)
(T.2)
(T.3)
(T.4)
Answers
Answer:
a 50% chance of getting tails
but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc
does it have
when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answers
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
Garden a rectangular garden is 12 feet across and 16 feet long. it is surrounded by a border of mulch that is a uniform width x. the maximum area for the garden, plus border, is 285square feet
Answers
The polynomial equation representing the situation is 4x² + 56x = 93 .
In the question ,
it is given that
the length of the rectangular garden is = 16 feet
the width of the rectangular garden is = 12 feet
we have to surround the border by mulch ,
the width of the border with mulch is = x
So the new length with mulch = 16 + x + x = 16 + 2x
and the new width with mulch is = 12 + x + x = 12 + 2x
also given that the area of garden plus border is = 285 square feet
we know that the area is = length × width
On substituting the values length and breadth , we get
285 = (16 + 2x)×(12 + 2x)
285 = 192 + 32x + 24x + 4x²
4x² + 56x + 192 = 285
4x² + 56x = 285 - 192
4x² + 56x = 93
Therefore , The polynomial equation representing the situation is 4x² + 56x = 93 .
The given question is incomplete , the complete question is
Garden a rectangular garden is 12 feet across and 16 feet long. it is surrounded by a border of mulch that is a uniform width x. the maximum area for the garden, plus border, is 285square feet . Write a polynomial equation to represent the situation ?
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When we find the domain of a rational function given in symbolic form, we find first where it is undefined.- How do we find where a rational function is undefined?- How do we find the actual domain once we know where it is undefined?- State the actual domain of () = (+5)/(x-3)
Answers
- A rational function is undefined when the number causes the denominator equal to zero.
- The domain will be all real numbers except those numbers that cause the denominator to equal zero.
f(x) = (x+5) / x-3
x-3= 0
x=3
Domain: all real numbers except x=3
FIND PERIMETER HELP PLS
Answers
A recipe for two dozen cookies calls for 2 3/4 cups of sugar. How much sugar is needed to make one dozen cookies?
Answers
Answer: 1 3/8
Step-by-step explanation:
Answer:
it is 1 3/8 or 0.375
Step-by-step explanation:
answered
Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with three children will have the given composition. (Enter your answer to four decimal places.) At least one girl
Answers
Answer:
0.875 or 87.5%
Step-by-step explanation:
For each child, there is an equal 1 in 2 probability of having a girl or a boy.
The probability of having at least one girl out of three children includes the probability of having 1, 2 or 3 girls. It can also be written as 100% minus the probability of having all boys, therefore:
\(P(G\geq 1)=1-P(B=3)\\P(G\geq 1)=1-(\frac{1}{2}*\frac{1}{2}*\frac{1}{2})\\ P(G\geq 1)=0.875\)
The probability of having at least one girl is 0.875 or 87.5%.
To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted _______ because a treatment _____ applied to the sales representatives. This is the best statistical study for this situation because the sales director is trying to establish _______.
1. ) An experiment
An observational
A survey
2. ) was
was not
3. ) causality
correlation
Answers
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A triangle has sides with lengths of 13 centimeters, 84 centimeters, and 85 centimeters. Is it a right triangle?
Answers
If a^2 + b^2 = c^2, then it’s a right triangle! If it’s less than c^2, it’s obtuse and if it’s greater than c^, it’s acute.
How do I solve for y in this equation? 3xy-28=15x
Answers
Answer:
x = 28/(3y -15)
Step-by-step explanation:
Put the x-terms on the same side of the equal sign and everything else on the other side. Divide by the coefficient of x.
3xy -28 = 15x . . . . . . given
-28 = 15x -3xy . . . . . subtract 3xy
-28 = x(15 -3y) . . . . . factor out x
-28/(15 -3y) = x . . . . . . divide by the coefficient of x
We prefer to have a positive sign where possible, so we can multiply this by -1/-1 to get ...
x = 28/(3y -15)
Please help if you want BRIANLEIST!!:)) Ty!! :D
Answers
Answer:
1/8 (D)
Step-by-step explanation: