Find the unit tangent vector at the given value of t for the following parameterized curves.

r(t)= ⟨7–√e^t,3e^t,3e^t⟩

, for 0≤t≤1
; t=ln 2

Answers

Answer 1

Answer:

[tex]T(ln2)[/tex][tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]

Step-by-step explanation:

Given : [tex]r(t)=<7-\sqrt{e^t}, 3e^t,3e^t > .........(i)[/tex]

We first have to differentiate of equation [tex](i)[/tex]

[tex]r'(t) = < \frac{\sqrt{e^t} }{2} , 3e^t,3e^t> ..........(ii)[/tex]

Now to get a unit tangent vector at the given value of [tex]t[/tex], we put [tex]t = ln2[/tex] in equation [tex](ii)[/tex]

[tex]r'(ln2) = < \frac{\sqrt{e^{ln2}} }{2} , 3e^{ln2},3e^{ln2}>[/tex]

            [tex]= <\frac{1}{\sqrt{2} } ,6,6>[/tex]        [∵[tex]e^{lna}=a[/tex]]

Now to get a unit tangent vector , we will divide our vector [tex]r'(ln2)[/tex] by its magnitude. So let's first find the magnitude.

[tex]|r'(ln2)|=\sqrt{(\frac{1}{\sqrt{2} } )^2 +6^2+6^2}[/tex]

             [tex]= \sqrt{\frac{1}{2}+36+36 }[/tex]

             [tex]= \sqrt{\frac{145}{2} }[/tex]

Now we can find the our unit tangents vector.

      [tex]T(ln2)=\frac{r'(ln2)}{|r'(ln2)|}[/tex]

                  [tex]= \frac{<\frac{1}{\sqrt{2}} ,6,6> }{\sqrt{\frac{145}{2}} }[/tex]

                  [tex]= <\frac{\frac{1}{\sqrt{2} } }{\sqrt{\frac{145}{2}} } ,\frac{6}{{\sqrt{\frac{145}{2}} }}, \frac{6}{{\sqrt{\frac{145}{2}} }} >[/tex]

                   [tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]

Hence, [tex]T(ln2)[/tex] [tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]


Related Questions

Evaluate the expression P(6,1)

Answers

Answer:

p(6,3)=120

Step-by-step explanation:

In the pic is how to do it

The value of the permutation expression P(6, 1) will be 6.

What are permutation and combination?

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Evaluate the expression P(6, 1).

We know that the formula for the permutation is given as,

ⁿPₓ = n! / (n - x)!

From the above, the value of n is 6 and the value of x is 1. Then we have

⁶P₁ = 6! / (6 - 1)!

⁶P₁ = 6! / 5!

⁶P₁ = 6 x 5! / 5!

⁶P₁ = 6

The value of the permutation expression P(6, 1) will be 6.

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

#SPJ5

Someone please help me

Answers

Answer:

 1. X:    0, -3

 2. Y:   1, -1

 3. Z:    4, -4

 4. M:   -4, 1

 5. N:    -2, 2

 6. P:    2, 4

 7. Q:    2, 0

 8. R:   -3, -1

Answer:

1. (0,-3)

2. (1,-1)

3. (4,-4)

4. (-4,1)

5. (-2,2)

6. (2,4)

7. (2,0)

8. (-3,-1)

9-17: first photo

18a: second photo

18b. A pentagon.  When you connect the points, the shape has 5 sides

Step-by-step explanation:

Is the given value a solution of the inequality?

Answers

Answer:

I don't think so

Step-by-step explanation:

if the s has to be more than or equal to then s would have to equal 8 or more

What is 1 infinity plus 1 infinity equal.​

Answers

Answer:

infinity

Step-by-step explanation:

lol

Infinity your welcome :)

GUYS PLS HELP 25 POINTS + BRAINLIEST IF CORRECT ANSWER

Answers

Answer:

B) 50º

Step-by-step explanation:

first we need to find angle MPL. to do this we do 180 - 70 - 60 = 50º. angle KPN is the smae as angle MPL. so angle KPN is 50º.

Answer:

C

Step-by-step explanation:

your answer is C because when you solve the answer question you get 60 degrees .What I did to get the answer is that I solve each solution answer and that is how I got 60 degrees

Hope this helps:)

Pls mark brainlist

First try was incorrect
Simplify: 4(-3 - 2x) simplify

Answers

-12-8x is the answer your looking for :)

-12+8x
.........................

The length of a room is 7.25 feet longer than the width, x, of the room. Which expression represents the perimeter of the room?

Answers

Answer:

P = 14.5+4x

Step-by-step explanation:

Let the width of the room is x.

Length = 7.25 feet longer than the width = 7.25 +x

We need to find an expression the represents the perimeter of the room.

Perimeter = sum of all sides

P = 2(l+b)

l is length and b is width

P = 2(7.25 +x+x)

=2(7.25 +2x)

=14.5+4x

Hence, the required expression for the perimeter is 14.5+4x.

x2 - 2x + 1 = 0? Please answer fast I need it now

Answers

Answer:

1

Step-by-step explanation:

x2 - x2 = 0

+1 = 1

If each of the numbers in the following data set were multiplied by 17, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
A. 986
B. 1207
C. 476
D. 612

Answers

Answer:

B

Step-by-step explanation:

Elena and Noah used different methods to compute 0.23 x 1.5. Both calculations were correct. Analyze the 2 methods.

Answers

Answer:

i have this same question. im sorry but i don't get it either. sorry..

Step-by-step explanation:

A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying

Answers

Answer:

You end up paying 22% of the original price.

Step-by-step explanation:

The statement indicates that a store has clearance items that have been marked down by 60% and this means that you have to pay 40% of the price as:

100%-60%=40%

Now, the statement says that the are advertising an additional 45% off clearance items which means that you will have a 45% discount on the 40% of the original price. So, you have to calculate 45% of 40 and subtract that from 40 to find the percentage that you will end up paying:

40*45%=18

40-18=22

According to this, the answer is that you end up paying 22% of the original price.

20 to the power of 3 divided by 2​

Answers

Answer:

4000

Step-by-step explanation:

20 to the power of 3 is 8000 and 8000/2 is 4000

20^3 = 8000 / 2 = 4000

What is the solution to the system? x + y = 4 x+y=1​

Answers

Given :

x + y = 4x + y = 1

To Find :

The value of x and y.

Answer :

x + y = 4 ....[Equation (i)]x + y = 1......[Equation (ii)]

Adding eqⁿ (ii) and eqⁿ (i) we get :

→ x + y + x - y = 4 + 1

→ 2x = 5

→ x = 5/2

x = 2.5

Now, put the value of x = 5/2 in eqⁿ (i) we get :

→ x + y = 4

→ 5/2 + y = 4

→ y = 4 - 5/2

y = 1.5

Rani bought 9 similar notebooks. She gave the cashier $10 and received change of $5.05. What was the cost of 1 notebook?

Answers

55 cents. (10-5.05)/9

Answer: the anwer is 0.55

Step-by-step explanation: if he received 5.05$ change that wasnt the cost. to find real cost subtract 5.05 from ten then divide 4.95 by 9 which equels 0.55

pls give brainest award

Find the value of N
9 : 10 = 54 : N

Answers

Answer:

I think Value of N is 60

Step-by-step explanation:

because 9 ×6 =54

therefore, 10×6=60

hope its correct and hope ti helps..

Can somebody help me thank you.

Answers

The second one (7x6)-6= 36 you multiply 7 and 6 to find the total batteries and them minus 6 for the batteries used in the flash light

3 There are 5 times as many boys as girls in a school.
Together the school has 810 pupils.
How many boys are there?

Answers

Answer:

Number of boys = 675

Step-by-step explanation:

Given that:

There are 5 times as many boys as girls in a school.

Number of pupils in school = 810

Let,

x be the number of girls

y be the number of boys

According to given statement;

x+y=810      Eqn 1

y = 5x         Eqn 2

Putting y=5x in the Eqn 1

x+5x=810

6x=810

Dividing both sides by 6

[tex]\frac{6x}{6}=\frac{810}{6}\\x=135[/tex]

Putting x=135 in Eqn 2

y = 5(135)

y = 675

Hence,

Number of boys = 675

6.5(6.24-1.69)=?
pls help

Answers

Answer:

29.575

Step-by-step explanation:

6.5(6.24-1.69)= 6.5(4.55) = 29.575

Answer:

[tex]6.5(6.24 - 1.69) \\ = 6.5 \times 4.55 \\ = 29.575[/tex]

29.575 is the right answer.

What is
12а + 7x - За – 2х

Answers

Answer:

=12a-3a+7x-2x

=9a+5x

This is the answer.

Hope it helps you..

Answer

=12a+7x-3a-2x

=9a+7x-2x

=9a+5x

Explanation

This is the ans. hope you like it....

I have 6 fish. 3 of them drowned. How many fish do I have left?

Answers

Answer:

6

Step-by-step explanation:

because fish don't drown

the art students are using clay. Each student needs 9/10

Answers

Answer:

ok mam yes mam going to do my clay

Need help please ???????

Answers

Answer:

5pm

Step-by-step explanation:

5 x 4= 20 miles

4 x 5= 20 miles

What are the names of these polygons?

Answers

Answer:

1)Quidrilateral

2)Pentagon

What is the length of side EF in the triangle? Please give a step by step explanation, I'm having lots of trouble finding the solution. Thank you!

Answers

Answer:

EF = 8.8 cm

Step-by-step explanation:

In the given right angled ΔDEF, DE is the hypotenuse while EF and DF are adjacent sides. So that applying the Pythagoras theorem, we have;

[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]

[tex]/DE/^{2}[/tex] = [tex]/EF/^{2}[/tex] + [tex]/DF/^{2}[/tex]

[tex]/16.2/^{2}[/tex] = [tex]/EF/^{2}[/tex] + [tex]/13.6/^{2}[/tex]

262.44 = [tex]/EF/^{2}[/tex] + 184.96

[tex]/EF/^{2}[/tex] = 262.44 - 184.96

          = 77.48

EF = [tex]\sqrt{77.48}[/tex]

     = 8.8023

EF = 8.8 cm

The length of side EF is 8.8 cm.

Jug A holds 1800ml Jug B hold 3/10 more. How much does jug B hold?​

Answers

Answer:

Jug B can hold 2340 ml.

Step-by-step explanation:

Given

The amount in Jug A = 1800ml

To determine

How much does jug B hold?​

Give that the Jug B holds 3/10 more, i.e.

[tex]\frac{3}{10}\times \:1800=540[/tex]

Thus,

The total amount in Jug B = 540+1800

                                           = 2340 ml

Therefore, Jug B can hold 2340 ml.

Answer:

get into it

Step-by-step explana   tion:

 

Mrs. Poster's class is divided into three groups of students. Each group has 3 girls and 2 boys, Which expression could she use to find the total number of students in the class?
O 3+(2+3)
(3 X 2) + 3
O 3x (2+3)
(32)

Answers

Answer:

3 X (2+3)

Step-by-step explanation:

If we have five students (3 girls and 2 boys), and three groups, we can use the expression 3 X (2+3), which concludes three groups times five students (in each group), which will give us our total of 15 students.

A pizzeria charges $2 per slice of pizza, plus an additional $0.75 per topping. If
Erica has at most $12.50 to spend on her pizza, how
many toppings could she get
on ONE slice of pizza? Write an inequality expression that represents the
situation and solve! Explain your reasoning (no work, no points)! You can
copy/paste the following symbols as needed: 2s<>
Your answer

Answers

Answer:

Maximum amount of toppings is 14 inequality is t <=14

Step-by-step explanation:

let t be the amount of toppings on the pizza

0.75t + 2 <= 12.50

0.75t <= 10.50

t <= 14

it would be 14. 2 minus 12.50 is 10.50 which divided by .75 is 14

Hello! :)
Please help me solve this + explain your answer :)

I will indeed give you Brainlst <3

Answers

Answer: the triangles are congruent

Step-by-step explanation: if u add up all the angles u get 180 so all angles are congruent

What is 1/2 percentage of a whole number (show work if u can) HELP IM DUM

Answers

Answer:

50%?

Step-by-step explanation:

What is the area of the figure to the nearest hundredth 14m and 4 m

Answers

First you have to find the area of the rectangle which is 14 cm by 4 cm = 56 cm and then find the area of the semicircle which is 1/2(radius by pi): 0.5(4 by 3.14)= 12.56cm
56 cm+ 12.56 cm =68.560 cm to the nearest hundredth is 68.56 cm
Hope it helps☺️

Answer: I believe its 56

Step-by-step explanation:

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