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

summer babysitting. She decided
to put this money in a bank that
earns a 5% simple interest rate.
How many years will it take to
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A) 10 years
B) 12 years
C) 15 years
D) 18 years
E) 20 years​

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Answer: B.12 years

Step-by-step explanation:

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Answer:

944 cubic feet

Step-by-step explanation:

You need to take the area of the figure separately.

[tex]8*10*5=400[/tex]

[tex]17*8*4=544[/tex]

400 + 544 =944


Given the equation in point slope form y-5=1/2(x+1)

Answers

Answer:

The slope of this equation is 11/2. The point is (1/2, 0)

Step-by-step explanation:

I hope this is the right answer, good luck!

Behind you there is a sneeze. You don't know it at the time, but this begins a chain reaction of flu that ripples through the school
It starts with only 20 students but the number infected grows every day at a rate of 10% How many people are infected at day 24.

Answers

Answer:

how bad do u need this answer 1 through 10

mang pedro has 20 kilogram of rice.he will repack it in 1/2 kilograms per bag.how many bags will he need?​

Answers

40, since each kilo of rice fills two bags and he has 20 kilos.

Answer:

20,since each kilo of rice fills two bags so he i'll have 40 bags.

Please help me answer this :)
Explain your answer

Will give brainiest ! Oh

Answers

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because the points are going up by 10 :)

What is the equation for calculating the area of a triangle?

A = 1/4 base · height
B = length · width
C = pi · height
D = 1/2 base · height

Answers

Answer:

A= 1/2 base*height

Step-by-step explanation:

: )

The correct equation for calculating the area of a triangle is D = 1/2 base · height.

The equation for calculating the area of a triangle is D = 1/2 base · height. This formula represents the most commonly used method for finding the area of a triangle.

To use this formula, you multiply the base of the triangle by its corresponding height, and then divide the result by 2.

This is because the area of a triangle is equal to half the product of its base and height.

By dividing by 2, we account for the fact that a triangle is essentially half of a parallelogram.

Therefore, the correct equation for calculating the area of a triangle is D = 1/2 base · height.

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3 1/4 x 6 1/2 x 2=? I need help please!!

Answers

Answer:

42.25

Step-by-step explanation:

Answer:

[tex]\frac{169}{4}[/tex] or 42.25

Step-by-step explanation:

If you turn the fractions into decimals they become easier to multiply.

1)  3.25 x 6.50 = 21.25

2) 21.25 x 2 = 42.25

For a submarine cable, the range of signalling is governed by the function


f(r) = r^2 ln⁡(1/r)

where 0
Find df/dr.

Answers

Answer:

 [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Step-by-step explanation:

Explanation

Given function f(r) = r² log r  ....(i)

Apply derivatives formula

              [tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]

             [tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]

            [tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]

Differentiating equation (i) with respective to 'r' , we get

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]

Final answer:-                

               [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Help please .
Solve for variable

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w=16.5; could you make me the brainiest? Please

Alexandra’s soccer team played 25 games and won 22 of
them. What percent did the team win?

Answers

Answer:

88%

Step-by-step explanation:

25*4=100. this means we have to multiply 22*4, which gets us 88%

Answer:

0.88%

Step-by-step explanation:

25 divided by 22

What is the value of the expression 30 X 5 + 6 X 4


will give brainliest

Answers

Answer:

174

Step-by-step explanation:

Answer:

30 × 5 + 6 × 4= 150 + 24= 174

Step-by-step explanation:

I hope it helps ❤❤

From the figure and statement provided, select the proper TO PROVE Statement.

If two parallel planes are cut by a third plane, the lines of intersection are parallel.

MN= 1AB

AB- BC= AC

M is parallel to

AB= BC

a is parallel to B

Answers

Answer: a is equal to b

Step-by-step explanation:

Answer:

a is parallel to b

Step-by-step explanation:

3x3z−6z for z=5 solve pllllsslssss

Answers

hi luv!!!
i’m doing the problem right now, so in the first part. do you want me multiply 3x with 3z?

Simplify this expression.
[tex]\frac{4^{9} }{4^{3} }[/tex]

Answers

9x9x9x9divide by 4x4x4

Answer:

4⁹ / 4³ = 4⁶ = 4096

Step-by-step explanation:

You can solve this by realising that exponents (the 9 and the 3 in this case), simply tell you how many times to multiply the numbers together.

What you're see there then can also be expressed as:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}[/tex]

Because the numerator and denominator are all multiples of the same number repeatedly, you can simply eliminate the bottom three fours from the top and bottom, giving you:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times (4 \times 4 \times 4)}{(4 \times 4 \times 4)}\\\\= 4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

[tex]4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

A simpler way to look at it is to understand that when the same number is being raised to different bases, and then multiplied or divided, you can simply add or subtract the exponents.  For example, speaking very generically:

[tex]x^a \times x^b = x^{a + b}[/tex]

and

[tex]x^a \div x^b = x^{a - b}[/tex]

In this case then, we can simply say:

[tex]\frac{4^9}{4^3} = 4^{9 - 3} = 4^6[/tex]

So when simplified, the expression is equal to 4⁶, or 4096.

Please help me with this question

Answers

Answer:

11/4

29/6

32/5

Step-by-step explanation:

Answer: 11/4, 29/6, 32/5

Step-by-step explanation:

This is going to help trust me

using the numbers 3, 5, and 8, can you write nine proper fractions and nine improper fractions? You may use each number only once within a fraction. ​

Answers

Answer:

First, we can write a fraction as a/b

Where a is the numerator, and b is the denominator.

A proper fraction is a fraction where the numerator is smaller than the denominator.

Using only the given numbers (only once per fraction), some examples of proper fractions are:

3/5

3/8

5/8

3/85

3/58

5/83

5/38

8/35

8/53

You can see that in all of them the denominator is larger than the numerator.

The improper fractions are those where the numerator is equal or larger than the denominator.

The 9 examples using the given numbers are:

5/3

8/5

8/3

35/8

38/5

53/8

58/3

83/5

85/3

2 cities are 18 inches apart on a map and 30 miles apart in real life whats the scale factor used on the map.

Answers

Answer:

you're scale is 1.6666667

Step-by-step explanation:

because if you do 30 decided by 18 it gives u 1.6666667

There are 23 students in a sixth-grade class. Nine students play hockey.
What is the ratio of students who do not play hockey to the total amount of
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O 9 to 23
O 14 to 23
O 14 to 9
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Answers

Answer:

14:23

Step-by-step explanation:

14:23

Answer:

its 14-23

Step-by-step explanation:

SOMEONE PLEASE PLEASE HELP ME ON THIS!!

Answers

X=22

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[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:

35

Step-by-step explanation:

A. 50 degrees
B. 130 degrees
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D.22 units
E. 13 units

Answers

Answer: all i can do hope this helps a bit 2. 130 degrees

5. 13 units

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Answers

Answer:

-19.9y-5.3

Step-by-step explanation:

Hi I got -19.9y-5.3 hope it’s right

-2(7-15)
What is the value of
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4
O 4
0 -2
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O 4

Answers

The answer to your question is 4

For the given fact below, which subsequent true/false statement is true?

Answers

Answer:

Step-by-step explanation:

Mel passed the math class.

Mel failed the math class.

Mel likes math.

Mel took math this semester.

Question 15

10 Points

Indicate the most appropriate if-then statement that the English sentence represents:

People 25 years or older do not pay an additional car rental fee.

If a person is 25 years old or older, then the person does not pay an additional car rental fee.

If a person is 25 years old or younger, then the person does not pay an additional car rental fee.

If a person does not need to pay an additional car rental fee, then the person is 25 years old or older.

Unknown

Question 16

10 Points

Given: If X, then Y. If Y, then Z.

Y is true. So:

X is unknown, Z is unknown

X is unknown, Z is true

X is false, Z is true

X is true, Z is true

Question 17

10 Points

Using everyday knowledge, which of the following statements is an if-then statement whose reverse is also correct?

If the TV is unplugged, then the TV will not turn on.

If the light bulb was recently on, then the light bulb is hot.

If an ambulance has emergency lights on, then cars on the road pull over.

If the wind is blowing, then the weather is chilly.

Question 18

10 Points

Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.

Statement 1: If Bo is Mel’s sibling, then Mel is Bo’s sibling.

/ Statement 2: If the sprinklers are on, then the grass is wet.

Forward-only / Forward-only

Forward-only / Forward and reverse

Forward and reverse / Forward-only

Forward and reverse / Forward and reverse

Question 19

10 Points

Given: If A AND B, then C. Given: The if-then statement's reverse is also correct. Given A is false, B is false. What is C?

True

False

Both true and false

Unknown

Question 20

10 Points

What pages will be favored for the given search? Search terms: Michael OR Jordan

Pages about Michael Jordan

Pages about Michael, plus pages about OR, plus pages about Jordan

Pages about Michael, plus pages about Jordan

Pages about Michael, plus pages about Jordan, plus pages about both

Question 21

10 Points

The rules for a soccer player receiving a yellow card are as follows:

IF a player

delays-restart

OR (dissents-by-word OR dissents-by-action)

OR ((enters OR re-enters OR leaves) AND NOT (had-permission))

OR ((corner-kick OR free-kick OR throw-in) AND fails-respect-distance)

OR commits-persistence-offences

THEN the player should receive a yellow card

A player leaves the field with permission. Later, the player re-enters the field without permission. The player:

Should receive a yellow card

Should not receive a yellow card

Should receive a yellow card only if the player also delays the restart

Should receive a yellow card only if committing all the other 4 offenses too

Question 22

10 Points

What percentage of people partake in physical activity and abstain from smoking, but do not eat fruit and vegetables?

1%

5%

10%

14%

Question 23

10 Points

Given the true/false statements are true (facts), select the best logical induction made from those statements:

Mo likes oranges. Jai likes oranges. Ben likes oranges.

People don't like apples

People only like oranges

People like oranges

People like fruit

Question 24

10 Points

Given a function described as the table below, what is y when x is 2?

0

1

2

4

Question 25

10 Points

Given a function described as the graph below, what is y when x is 3?

1

3

6

10

Question 26

10 Points

The figure below shows total costs for three gym memberships. Which is the most accurate statement?

Of the 3 memberships, Monthly is cheapest for under 5 months, while Standard is cheapest for over 10 months.

Platinum is costliest for any duration

Monthly is cheapest for any duration except for 5-10 months

Standard is cheapest for a duration between 5-10 months; other plans are cheaper for shorter or longer durations.  

Question 27

10 Points

The figure shows estimated medical costs versus what a user actually pays for three health insurance plans with different deductibles. For which plan does the user pay the least for estimated medical costs of $4,000?  

$500 deductible plan

$1,000 deductible plan

$2,000 deductible plan

The user pays the same for all three plans.

Question 28

10 Points

What is the value of cell C2?

2

24

50

64

Question 29

10 Points

What formula should be entered in A3 to compute A1 divided by C3?

=A3/A1

=A1/C3  

=A1*C3

=C3/A1

Question 30

10 Points

Based on the vertical bar chart below, in which of the following months were approximately 10% of professional European soccer players born?

January

April  

October

December

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Details & Information

 

Assessment due date

2/2/21, 1:59 AM (EST)

 

Goals & standards

Aligned with 2 goals

 

Attempts

1 attempt left

Grading

Maximum points

300 points

Description

Complete the midterm exam. You have one attempt at the exam. So, be sure you review all previous course

Hence , correct option is Option B i.e. Mel did pass the class.

How to Solve:

The statement says that Mel scored C+ is Chemistry.

We will approach our answer logically by examining each option.

Option A says Mel does not like chemistry. This Cannot be true because maybe Mel likes chemistry but he just has scored less or maybe this C+ is an achievement for Mel.

Option B says that Mel did pass the class. This is possible because a student is considered as not qualified if he/she scores D or below, but Mel has scored C+ which is above the qualifying criteria.

Option C says that Mel did not achieve a passing grade for the class which is false because C+ is a passing grade scored by Mel.

Option D is Mel took math this semester which doesn't makes any sense.

hence, Option B is correct.

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Is this a function?

Answers

No I don’t believe it is

Find two points for each labeled line in the graph below. Then use those two sets of coordinate points to help you find the slope and use whichever method for finding equations that you prefer to find the equation of each line listed. You only need to write the equation of each line for your answer. Remember, you must first put the equations in slope-intercept form. Label your answers m and b to represent the slope and y-intercept.

A:
B:
C:
D:

Answers

Answer:

???

Step-by-step explanation:

wheres y

Answer:

the equation to find slope is (y2-y1)/(x2-x1)

A: (-4,1) (0,3) (for all of these except for the last one, i included the y-intercept as one of the points)

3-1/0-(-4)

2/4

m=1/2

y= 1/2x +3

B: (0,-1) (3,1)

3-0/1-(-1)

m=3/2

y=  3/2x -1

C: (0,-3) ( 6,-1)

-1 -(-3) / 6-0

2/6

m= 1/3

y = 1/3x -3

D: (3,-3) (6,0)

0 -(-3) / 6-3

3/3

1

m= 1

y -y1 = m (x - x1)  (this is point-slope form, plugging in the slope and a point on the line, and then solving it will give you slope-intercept form)

y - 0 = 1(x -6)

y = 1x -6

Step-by-step explanation:

I hope this helped :)

PLEASEE HELP IM BEGGING YOU

Answers

Answer:

1 7/12

Step-by-step explanation:

Its 1 7

/12

Answer:

1 7/12

Step-by-step explanation:

Hope this helps!

Brainiest?

I need help with This one

Answers

Answer:

1 and 2

Step-by-step explanation:

If y was 1: -2 x 1 + 18 = -2 + 18

= 16  This works

If y was 2: -2 x 2 + 18 = -4 + 18

= 14  This works

If y was 3: -2 x 3 + 18 = -6 + 18

= 12  This does not work since -2y + 18 has to be greater than 12.

Your answer would be 1&2 I hope this helps!!!!!!!!!

please help asap!!!!!

Answers

Answer:

angle RQS

Step-by-step explanation:

Can someone please help me Please I'm desperate
Rob is 7 years older than James. Kate is 2 years younger than James. If the sum of their ages is 116, how old are each of the siblings?

Answers

Answer:

James is 37, Rob is 44, and Kate is 35

Step-by-step explanation:

Set up an equation where x is James' age:

Rob's age can be represented by x + 7, since he is 7 years older than James

Kate's age can be represented by x - 2, since she is 2 years younger than James

Add these together in the equation and set it equal to 116:

(x + 7) + (x - 2) + (x) = 116

Add like terms and solve for x:

(x + 7) + (x - 2) + (x) = 116

3x + 5 = 116

3x = 111

x = 37

So, James is 37.

Find Rob's age by adding 7 to this:

37 + 7

= 44

Find Kate's age by subtracting 2:

37 - 2

= 35

So, James is 37, Rob is 44, and Kate is 35

Answer:

Rob = 44

Kate = 35

James = 37

Step-by-step explanation:

Rob = 44     which is 7 years older than James

Kate = 35     which is 2 years younger than James

James = 37

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