Consider the line L(t)=⟨5+t,1+5t⟩. Then:
Choose perpendicular, parallel or neither. (PS. Answers below may not be true.)

Consider The Line L(t)=5+t,1+5t. Then:Choose Perpendicular, Parallel Or Neither. (PS. Answers Below May

Answers

Answer 1

If L(t) = ⟨5 + t, 1 + 5t⟩, then the tangent vector to L(t) is

dL/dt = ⟨1, 5⟩

Any line parallel to L(t) will have the same tangent vector, up to some scalar factor (that is, if the tangent vector is a multiple of ⟨1, 5⟩).

Any line r(t) with tangent vector T(t) = dr/dt that is perpendicular to L(t) will satisfy

T(t) • ⟨1, 5⟩ = 0

• r(t) = ⟨-5, -2t, 1 - 10t⟩ is parallel to L(t) because its tangent vector is

T(t) = ⟨-2, -10⟩ = -2 ⟨1, 5⟩

• r(t) = ⟨1 + 1.5t, 3 + 7.5t⟩ is parallel to L(t) because

T(t) = ⟨1.5, 7.5⟩ = 1.5 ⟨1, 5⟩

• r(t) = ⟨-2 - t, 2 - 2t⟩ is neither parallel nor perpendicular to L(t) because

T(t) = ⟨-1, -2⟩ ≠ k ⟨1, 5⟩

for any real k (in other words, there is no k such that -1 = k and -2 = 5k), and

⟨-1, -2⟩ • ⟨1, 5⟩ = -1 - 10 = -11 ≠ 0

• r(t) = ⟨3 + 15t, -3t⟩ is perpendicular to L(t) because

T(t) = ⟨15, -3⟩

and

⟨15, -3⟩ • ⟨1, 5⟩ = 15 - 15 = 0


Related Questions

15 more than 2 times a number is equal to -14. Find the number.
please help asap and thank you in advance!

Answers

Answer:

The number is - 14.5

Step-by-step explanation:

Let the number be x.

ATQ, 15+2x=-14, x=-29/2=-14.5

15+ 2x= -14. That is the answer

The Sugar Sweet Company needs to transport sugar to market. The graph below shows the transporting cost (in dollars) versus the weight of the sugar being transported (in tons).
slope of line

Answers

Answer:

where is graph. Hope you understand mr

Step-by-step explanation:

Please mark me brainliest thanks

Find the greatest common factor of these two expressions.
14w5y8x2 and 7w6x2

Answers

Answer:

[tex]7w^{5}x^{2}[/tex]

Step-by-step explanation:

We can start by looking at each variable and and constant separately. In the first one, the constant part is 14 and in the second its 7. We can notice that the GCF of these two is 7. Next we have the part with w. The first one is w^5 while the second is w^6. We can notice that we can factor w^5 out of both, so it is the GCF. We can notice that only the first one has a y, so we can ignore it since it is not in common with both expressions. Lastly, we have x: the first has x^2 and the second has x^2 as well. They are the same, so the GCF would just be x^2.

Now, we can multiply the results together to get the GCF of the whole expressions:

7 * w^5 * x^2 = [tex]7w^{5}x^{2}[/tex]

Driving 70 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 3 hours to get to her destination with the jet traveling at a speed of 400 mph. How many miles does Alicia travel to get to her destination?

Answers

Answer:

Total distance covered= 910 miles

Step-by-step explanation:

Distance = speed x time

Distance covered from home to airport = 70 x 3= 210 miles

Distance covered from airport to destination= 350 x 2= 700 miles

Add them together to get the final answer.

If the statement is true, type true in the space provided. If it is false, replace the underlined
word(s) with the word(s) that will make the statement true.
* The associative (associative is underlined) property is used on the following expression: 2 + 3 = 3 + 2.

Answers

False, It is the commutative property.

Find the slope of the line containing the points (5, 3) and (-7, 2).

Answers

The slope is 1/12 or 0.083
The slope would be 1/12

1. Use the circle shown to answer each question a. Name the circle b. Identify a radius of the circle c. Identify a diameter of the circle d. Identify a different diameter of the circle. ​

Answers

i think the answe is sixteen

find the measure of the angle indicated

Answers

Answer:

Step-by-step explanation:

59°

A bag contains 4 white and 2 black balls of the same size and weight and two balls are selected at random without replacement,what are the possible outcomes ?

Answers

Answer:

Step-by-step explanation:

Total balls in bag = 4+2

= 6 balls

Total white balls = 4

Total black balls = 2

The possible outcomes are

Black and Black or White and White or White and Black or Black and White.

Probability of black and black = 2/6

= 1/3

Probability of white and white = 4/6

= 2/3

Probability of Black and white or White and black

= 1/3×2/3

= 2/9

please click thanks and mark brainliest if you like :)

possible outcomes will be white and black, white and white, black and white or black and black

Simplify the following expression:

Answers

Step-by-step explanation:

[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]

the cost of 1 kg tomato is RS . 75.Find the cost of 14 kg​

Answers

Answer:

Cost of 1kg tomato=rs.75

Cost of 14kg tomato=(75×14)

rs.1050

6. Find x and y plz help ​

Answers

Answer:

x=6 square root 3 y=9

Step-by-step explanation:

x= 3 square root 3 * 2

y=3 square root 3 times square root 3

You have 3 quarts of brown stock. you need 3 cups to make one serving of braised short ribs How many can you make

Answers

Answer:

4

Step-by-step explanation:

there are 3 cups in a quart

since there are 3 quarts i.e 4*3=12

since you need 3 cups to make a serving

12/3 =4 servings can be made

Find the value of X.

Answers

Answer:

[tex]the \: two \: angles \: are \: equal \: so \: this \\ \: triangle \: is \: issosceless \\ then3x - 6 = 12 \\ 3x = 18 \\ x = \frac{18}{3} \\ x = 6 \\ thank \: you[/tex]

An educator wants to see how the number of absences for a student in her class affects the student’s final grade. The data obtained from a sample are shown.

Number of absences

26

29

32

34

36

37

Final grade

48

68

66

69

76

67

Answers

The Question is solved with a simple linear equation and is explained as follows:

Simple linear equation is :

Y = 86.784 - 2.67x

The educator wants to see the relationship between no of absences and final grades of the student.

No. of absence of student is independent variable while final grade is dependent variable.

The final grades of the student are dependent on the no. of absence they do.

b = Sxy / Sxx

b =  { 2312 [ 37 * 422 ] / 6 } / 337 - 37^2 / 6 = -2.67

a = -2.67 * 37/6 = 86.784

Learn more at https://brainly.com/question/24319270

Find the eigenvalues of the matrix:

[-43 0 80]
[40 -3 80]
[24 0 45]

Answers

Answer:

-3

1 + 4 sqrt( 241 )

1 - 4 sqrt( 241 )

Step-by-step explanation:

We need minus lambda on the entries down the diagonal. I'm going to use m instead of the letter for lambda.

[-43-m 0 80]

[40 -3-m 80]

[24 0 45-m]

Now let's find the determinant

(-43-m)[(-3-m)(45-m)-0(80)]

-0[40(45-m)-80(24)]

+80[40(0)-(-3-m)(24)]

Let's simplify:

(-43-m)[(-3-m)(45-m)]

-0

+80[-(-3-m)(24)]

Continuing:

(-43-m)[(-3-m)(45-m)]

+80[-(-3-m)(24)]

I'm going to factor (-3-m) from both terms:

(-3-m)[(-43-m)(45-m)-80(24)]

Multiply the pair of binomials in the brackets and the other pair of numbers;

(-3-m)[-1935-2m+m^2-1920]

Simplify and reorder expression in brackets:

(-3-m)[m^2-2m-3855]

Set equal to 0 to find the eigenvalues

-3-m=0 gives us m=-3 as one eigenvalue

The other is a quadratic and looks scary because of the big numbers.

I guess I will use quadratic formula and a calculator.

(2 +/- sqrt( (-2)^2 - 4(1)(-3855) )/(2×1)

(2 +/- sqrt( 15424 )/(2)

(2 +/- sqrt( 64 )sqrt( 241 )/(2)

(2 +/- 8 sqrt( 241 )/(2)

1 +/- 4 sqrt( 241 )

Ginny writes down a secret number on her palm. She says that it is a three-digit even number. The units digit is 1 more than the hundreds digit. The tens digit is twice the sum of the units digit and the hundreds digit.

Answers

Answer:

Hello,

Answer 162

Step-by-step explanation:

Let say n the searched number.

[tex]n=\overline{abc}\\a>0\\c=a+1\\b=2*(a+c)\\\\.T.\ means\ True.\\\\\\\begin{array}{c|c|c|c}a&c&b&ok\\1&2&6&.T.\\3&4&14&.F.\\5&6&22&.F.\\7&8&30&.F.\end{array}\\\\\\\boxed{Answer\ n=162}\\[/tex]

1. Find the 4th term for the sequence with formula tn= n² + 1

Answers

Answer:

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

If x + 1 =3, then x=

Answers

Answer:

x = 2

Step-by-step explanation:

x + 1 = 3

transpose

x = 3-1

x= 2

what is factorization of the trinomial below? -x2+2x+48

Answers

Answer:

-(x+6) (x-8)

Step-by-step explanation:

-(x^2-2x-48)

two values the multiply to get 48 and the difference of those two numbers gives you -2.

6,-8

6 x -8 =-48

6-8=-2

In this case we factored out the negative so leave it outside

-(x+6) (x-8)

Answer:

-1(x-8)(x+6) is the answer just took the test

Step-by-step explanation:

The perimeter of a park is 300 feet the length of the park is 50 feet longer than the width. Find the length

Answers

Answer:

55.41 feet

Step-by-step explanation:

Let the width be x.

ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet

Jamal traveled a distance of 520 miles in 9 hours. Part of the time, his rate of speed was 55 mph. The rest of the time his rate of speed was 60 mph. How long did Jamal travel at each rate?

Answers

Answer:

jamal traveled 5 hours at 55mph and 4 hours at 60mph

Step-by-step explanation:

time x will be time jamal travels 55 mph (in hours)

time y will be time jamal travels 60 mph (in hours)

distanced traveled 520 miles

distance = time*speed

520= x*55+y*60

520=55x+60y

jamal traveled for 9 hours

9 hours is composed to the two times x and y

9=x+y

then

x=9-y

substitute into 520=55x+60y

520=55(9-y)+60y

520=495-55y+60y

520=495+5y

25=5y

y=5

x+y=9

x+5=9

x=4

time x is time jamal travels 55 mph (in hours)

time y is time jamal travels 60 mph (in hours)

jamal traveled 5 hours at 55mph and 4 hours at 60mph

what is the area and perimeter of the figure below?

Answers

Answer:

the perimeter is : 40

the area is: 10,000

A box is filled with 14 green cards, 2 yellow cards, and 2 red cards. A card is chosen at random from the box. What is the probability that it is a green or a red card?
Write your answer as a fraction in simplest form.

Answers

Answer:

Probability of getting a green card = 14/18 = 7/9

Probability of getting a red card = 2/18 = 1/9

Step-by-step explanation:

Answer from Gauth math

Tom and Jerry had a race. Tom started at 0200 running at 4.5km per hour. Jerry started
later at 6:30am running at 6.5km per hour. After five hours, who was ahead, and by how
much (answer in kilometres)

Answers

Answer:

Tom, 10.25

Step-by-step explanation:

Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km

Distance covered by Jerry=6.5*(5)=32.5km

Tom is ahead from Jerry by 10.25km

Help
Plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

angle G

sin inverse (21/29) = 46.4

GH

c^2 - b^2 = a^2

29^2 - 21^2 = a^2

a = √(29^2 - 21^2)

GH = 20

therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20

Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?

Answers

Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel's unit walking rate in miles per hour and in hours per miles? 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.

15 points PLEASE ANSWER

Answers

Answer:

D. (25π - 50) sq m

Step-by-step explanation:

Since ABCD is a square with the area of 100, we know that the dimensions are 10 by 10. With that, we can find that triangle ABC = 50 sq m because of (h*l)/2. Since A is the center of the circle that contains arc BD, we know that 10 is the radius of the quarter-circle ABC. Using (πr^2)/4 to get the area of the quarter-circle, we get that the quarter-circle ABC = 25π sq m. But the original triangle ABC in the quarter-circle is not shaded. Therefore, we subtract 50 from 25π, which leads to (25π - 50) sq m.

I hope this helped! :D

Which phrase describes the linear relationship between the x and y values shown in the table?

x l y
8 l 2
9 l 3
10 l 4

A. y is 6 times x
B. x is 6 times y
C. y is 6 less than x
D. y is 6 more than x

Answers

9514 1404 393

Answer:

  C. y is 6 less than x

Step-by-step explanation:

It is not hard to check.

  A. 6 times x is 6×8 = 48, not 2

  B. 6 times y is 6×2 = 12, not 8

  C. 6 less than 8 is 2; 6 less than 9 is 3

  D. 6 more than 8 is 14, not 2

__

The relation described in C matches the table.

2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?​

Answers

Answer:

luke won

Step-by-step explanation:

he is 2 meters ahead of azam witch is in 2dn place

Maggie is the winner. She was the most ahead
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