Consider the line parametrized by r(t) = (3,-1,9) + t(8, 12, -6). Identify the parametrizations equivalent to r(t). r1(t) = (11, 11, 3) + t(8,12,-6) r2(t) = (4,0, 10) +1(8,12,-6) r3(t) = (6,-2, 18) + (8,12,-6) r4(t) = (3,-1,9) + f(-4, -6,3) r5(t) = (8,12,-6) + t(3,-1,9)
r6(t) = (-1, -7,12) + f(4,6,-3)

Answers

Answer 1

Therefore, the parameterizations r1(t), r2(t), r3(t), r4(t), and r5(t) are all equivalent to r(t), while r6(t) is not.

How to find equivalent parameterizations of a given line?

To determine if two parameterizations are equivalent, we need to check if they represent the same line. We can do this by checking if the direction vectors of the lines are parallel and if they pass through the same point.

The line parametrized by r(t) = (3,-1,9) + t(8, 12, -6) has a direction vector of (8,12,-6).

r1(t) = (11, 11, 3) + t(8,12,-6) has the same direction vector and passes through the point (11, 11, 3).

r2(t) = (4,0, 10) +1(8,12,-6) also has the same direction vector and passes through the point (4, 0, 10).

r3(t) = (6,-2, 18) + (8,12,-6) has the same direction vector and passes through the point (6, -2, 18).

r4(t) = (3,-1,9) + f(-4, -6,3) represents the same line, as the direction vector (-4,-6,3) is a scalar multiple of (8,12,-6), and it passes through the point (3,-1,9).

r5(t) = (8,12,-6) + t(3,-1,9) represents the same line, as it has the same direction vector and passes through the point (8,12,-6).

r6(t) = (-1, -7,12) + f(4,6,-3) represents a different line, as it has a different direction vector and does not pass through the point (3,-1,9).

Therefore, the parameterizations r1(t), r2(t), r3(t), r4(t), and r5(t) are all equivalent to r(t), while r6(t) is not.

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Related Questions

On what type scale are the variables in a chi-squared test of independence measured?
a. categorical/nominal
b. ordinal
c. ratio
d. interval

Answers

Categorical/nominal  type scale are the variables in a chi-squared test of independence measured.

In a chi-squared test of independence, the variables are measured on a categorical/nominal scale. This means that the variables represent distinct categories or groups, and there is no inherent order or numerical value associated with the categories.

Categorical/nominal variables are qualitative in nature and represent different attributes or characteristics. Examples of categorical/nominal variables include gender (male or female), marital status (single, married, divorced), and type of car (sedan, SUV, truck). Each category is mutually exclusive and does not have any numerical significance.

In a chi-squared test of independence, these categorical variables are used to examine the relationship between two variables. The test assesses whether there is a statistically significant association between the variables, indicating whether they are independent or dependent on each other.

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Paula's Pizza Parlor uses the following ingredients to make pizza.


Number of Pizzas Sauce (oz) Cheese (oz)
3 15 12
7


At this rate, how much sauce and cheese will Paula use to make 7 pizzas?
Paula will use 19 oz of sauce and 16 oz of cheese to make 7 pizzas.
Paula will use 11 oz of sauce and 8 oz of cheese to make 7 pizzas.
Paula will use 30 oz of sauce and 24 oz of cheese to make 7 pizzas.
Paula will use 35 oz of sauce and 28 oz of cheese to make 7 pizzas.

Answers

At this rate, Paula will use 35 oz of sauce and 28 oz of cheese to make 7 pizzas.

To determine how much sauce and cheese Paula's Pizza Parlor will use to make 7 pizzas, we need to first find the rate at which the ingredients are used. From the given information, we can see that 3 pizzas require 15 oz of sauce and 12 oz of cheese. This means that each pizza requires 5 oz of sauce and 4 oz of cheese.

To find the total amount of sauce and cheese needed for 7 pizzas, we can simply multiply the amount needed for one pizza by 7. This gives us a total of 35 oz of sauce and 28 oz of cheese needed to make 7 pizzas.

It is important to accurately calculate the amount of ingredients needed for a given amount of pizzas to ensure that there is enough to satisfy demand without wasting excess ingredients. This can help businesses like Paula's Pizza Parlor manage their inventory and expenses efficiently.

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plez help!!!

Find the slope

plez help!!! Find the slope

Answers

Answer:

I believe the slope is 1/4

Step-by-step explanation:

hope this help

Mark me brainlest please

only for smart people!! can anyone find the areas of these for me? Please im struggling

only for smart people!! can anyone find the areas of these for me? Please im struggling

Answers

the first one is 10, second 21, third 36, fourth 10, fifth 480, sixth 60, seventh 1,188, and eighth 14

Answer:

10, 21, 36, 12, 24, 5, 33, 14

Will give Brainly please

Will give Brainly please

Answers

The value of the mean excluding the outlier is 130. 5

What is an outlier?

An outlier can be defined as a data point that differs significantly or greatly from other observations.

It occurs as a result of;

variability in the measurement indication of novel dataexperimental error

From the information given, we have that;

121, 89, 410, 203, 55, 230, 182, 148, 135, 233, 11, 219, 108, 192

Since, the outlier is 410

The mean is given as;

= 121 + 89+ 203+ 55 + 230+182 + 148 + 135 + 233+ 11+ 219 + 108 + 192/13

Add the values

= 1696/13

= 130. 5

Hence, the value is 130. 5

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Sasha likes to run on a track that is 58 of a mile. If she runs 7 laps. How many miles did she run? 758 678 548 438

Answers

Answer:

4 miles

Step-by-step explanation:

4 miles because if if if 58 of mile which is just a half mile basically and she does 7 laps

7 x 0.58=4.06 which is 4 miles

Have a good day :}

what is the value of (5.3x10^4)(4.2x10^3)l

Answers

Answer:

scientific notation = 2.226 * 10^8

Standard form = 222600000

As it is 22.26 * 10^7

Step-by-step explanation:

(5.3x10^4)(4.2x10^3)

Since all the numbers are being multiplied by each other, one can use the associative property to change the order in which they are multiplied.

5.3 x 10^4 x 4.2 x 10^3

= 5.3 * 4.2 * 10^4 * 10^3

= 22.26 * 10^7

Either convert back to scientific notation, standard form or keep as it is.

scientific notation = 2.226 * 10^8

Standard form = 222600000

As it is 22.26 * 10^7

Suppose y varies directly as x. If y = 30 when x = 8, find y when x = 4.

Answers

She she even r Rene Berne r she herb e she e d

Step 2: What factor is used to convert feet per minute into
miles per minute?

Answers

Answer:The conversion factor is 1/88; so 1 foot per minute = 0.011363636342023 miles per hour.

Step-by-step explanation:

Using the quadratic formula to solve x- + 20 = 2x, what are the values of x?

Answers

Answer:

they is no answer because x-+20 is not applicable to math

Answer:

x = -20

Step-by-step explanation:

because there is no quadratic equation there

What is 9m + 6 = 87
please help im desperate fwhe

Answers

Answer:

m=9

Step-by-step explanation:

9m=81

Answer:

9

Step-by-step explanation:

First you have to get the variable by its self (m). So you will get rid of 6 and since it’s positive you will do negative 6 to cancel it out. But what you do to one side you do to the other, so you will do 87 - 6 and get 81. Now it’s 9m = 81. So then since 9 is next to m that implies multiplcation so you do the opposite of multiplication and dived 9 by both sides. And when you do that you get 9.

which question can be answered by solving the inequality 7x<50

which question can be answered by solving the inequality 7x&lt;50

Answers

Answer:a

Step-by-step explanation:

Answer:

ANSWER:A

Step-by-step explanation:

a doctor visits her patients during morning rounds. in how many ways can the doctor visit 4 patients during the morning rounds?

Answers

The no. of ways in which the doctor visits her patients during morning rounds = 5!

That means we can only find the number of ways if we n+1 factorial the number of rounds. In this case, the factorial is 1x2x3x4x5= 120

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n! Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

In addition to highlighting the connections between variables, it also enables the isolation and individual analysis of the impacts of changing a single variable. The primary drawback is how challenging it is to explore with more than two parameters or several levels.

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Which of the following shows - 49 simplified and written as a complex number?

Which of the following shows - 49 simplified and written as a complex number?

Answers

Answer:

0+7i

Step-by-step explanation:

Answer:

0+7i

Step-by-step explanation:

can someone help please?

can someone help please?

Answers

x=54 is the final answer

Answer:

x = 54

Step-by-step explanation:

In this line, I am going to assume lines l and m are parallel.

Each flat surface is half of a circle, therefore it has 180 degrees. We are given one side and told to find the other.

180 - 116 = 64.

The other angle's total value must be 64.

Now, to solve for x, subtract 10 from 64 [inverse operations].

64-10=54

The value of x in this equation is 54 degrees.

Find the surface area of a cone with a radius of 7 cm and a height of 27 cm

Answers

Your answer: A≈767.33cm²

Answer: 767.33cm²

Step-by-step explanation:

A=πr(r+h2+r2)=π·7·(7+272+72)≈767.32948cm²

Amy has a rectangular garden that is 23 feet wide. If the length of the garden is 12 feet, what is the length of its diagonal, in feet? Round to the nearest tenth​

Answers

Answer:

25.9 feet

Step-by-step explanation:

If you split a rectangle into 2 pieces with a diagonal, each piece will be a right triangle

Therefore we can use the pythagorean theorem to solve this problem

The two legs of the right triangle will be 23 and 12

The formula is a^2 +b^2=c^2

c^2 is the diagonal squared ( the hypotenuse)

So:

12^2+23^2=c^2

144+529=c^2

673=c^2

To find just c we need to find the square root of 673, rounded to the nearest tenth

\(\sqrt{673}=25.9\)

(the equation is rounded)

So the diagonal is 25.9

solve for each variable in the equation 8(3m - 2) - 7m =0

Answers

Answer:

m=16/17

Step-by-step explanation:

8(3m-2)-7m=0

24m-16-7m=0

17m-16=0

17m=16

m=16/17

Answer:

\(\frac{16}{17}\)

Step-by-step explanation:

1. Distribute 8:

8(3m) + 8(-2)

24m - 16 - 7m = 0

2. Combine like terms:

17m - 16 = 0

3. Add 16 to both sides of the equation:

17m = 16

4. Divide both sides of the equation by 17:

m = \(\frac{16}{17}\)

hope this helps :)

the radius of a circle is increasing at a certain instant the rate of increase in the area of the circle is numericallt equa to twice the rate of increase in its circumference. what is the raduis of teh circle at that instant

Answers

So the radius of the circle at that instant is 1.

Let's call the radius of the circle at that instant "r."

The formula for the area of a circle is A = pi * r^2 and the formula for the circumference of a circle is C = 2 * pi * r.

If the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference, we can set up the following equation:

2 * (2 * pi * r) = (pi * r^2)

Solving this equation for r, we find that the radius of the circle at that instant is r = 1.

So the radius of the circle at that instant is 1.

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Twenty thousand, two and twelve hundredths written in Numeric Form ?

Answers

Answer:

202.12

Step-by-step explanation:

EASY i hope this helps

have a great day

god bless

Pls mark me brainliest

Bacteria colonies can triple in size every 4 days. If you start with 150 bacteria microorganisms, how large would the colony be after 16 days? First, complete the equation: Future Amount = 150(1+[?]​

Bacteria colonies can triple in size every 4 days. If you start with 150 bacteria microorganisms, how

Answers

Answer:

But notice that the colony tripled 4 times in 16 days, or it tripled 16 / 4 = 4 times.

Step-by-step explanation:

150 x 3 x 3 x 3 x 3 = 150 x 34 = 150 x 81 = 12,150.

Hope this helps

Answer:

ha i got nothing

Step-by-step explanation:

he i got nothing

Gravel is being dumped from a conveyor belt at a rate of 30 ft 3ymin, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high

Answers

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

Given the following data: Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min.

Its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

The pile is 10 ft high.

To determine how fast the height of the pile is increasing, we need to differentiate the formula for the volume of a cone with respect to time.

We know that the volume of a cone is given by: \(V = (1/3)πr²h\)

We are given that the base diameter and the height of the cone are always equal, so we can write: r = (d/2)and h = d

where d is the diameter of the base of the cone.

The volume of the cone is given by: V = (1/3)π(d/2)²d

Simplifying, we get:\(V = (1/12)πd³\)

Differentiating both sides with respect to time, we get:

dV/dt = (1/4)πd² (dd/dt)

We are given that dV/dt = 30 ft³/min, and we want to find dd/dt when h = 10 ft.

Substituting V = (1/3)π(10/2)²(10)

= (1/3)π(25)(10)

= (250/3)π and d = 10,

we get:

30 = (1/4)π(10²)(dd/dt)

Simplifying, we get:

dd/dt = 12/π

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

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Dan has £100. Colin takes £y. How much is left

Answers

£100 - £y would be left :D


£100 - £y would be left :D

HELP ASAP DUE IN 5 minutes

HELP ASAP DUE IN 5 minutes

Answers

Answer:

60 cubic units

Step-by-step explanation:

What is the value of the expression?
15x−4y
when x=7 and y=8
show your work below

Answers

Answer:

73

Step-by-step explanation:

Substitute the numbers for x and y and multiply them by the number they're attached to

15(7)-4(8)

105-32

73

A company's prospectus includes:
A) The company's investment options.
B) The company's guaranteed return strategy.
C) The company's revenue and net worth.
D) The company's research

Answers

A company's prospectus includes: A) The company's investment options.

What is a company's prospectus?

Company's prospectus can be defined as the document that entails  detail information of a company investment option that are available for sales to potentials buyers or investors.

Examples of the investment options are:

BondsStocksMutual Funds etc

Therefore the correct option is A.

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A company's prospectus is a formal legal document designed to provide information and full details about an investment offering for sale to the public.


Find the distance between the following pair of points.

A(-3,1), B(7,13)

Answers

Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where \((x_1, y_1)\) is the first coordinate and \((x_2, y_2)\) is the second coordinate.

\(\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}\)

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= \(\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}\)

= \(\sqrt{12^2+(7+3)^2}\)

= \(\sqrt{244}\)

= 15.6 units (3 s.f.)

Additional:

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of the travelers arriving at a small airport, 60% fly on major airlines, 30% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. of those traveling on major airlines, 50% are traveling for business reasons, whereas 60% of those arriving on private planes and 90% of those arriving on other commercially owned planes are traveling for business reasons. suppose that we randomly select one person arriving at this airport. what is the probability that the person

Answers

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Ryan bought 7 kg of tomatoes for $15.40. What was the cost per kilogram?

Answers

Answer:

$2.20 per kilogram

Step-by-step explanation:

Take the total cost and divide by the number of kilograms

15.40/ 7

2.20

$2.20 per kilogram

Answer:

Step-by-step explanation:

I am not sure if this is corect but you need to devide 7 by 15.40

and that is my best estimate

HELP PLEASE


identify the solution to the system of equations

HELP PLEASE identify the solution to the system of equations

Answers

Answer:

solved graphically,

it's just the point where the two lines intersect

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