find the cartesian equation of r=3i+paremeter (i+2j)

Answers

Answer 1

The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Now,

Since, The equation is,

⇒ r = 3i + λ (i + 2j)

Where, 'λ' is a parameter.

Hence, The Cartesian equation is find as;

⇒ xi + yj = 3i + λi + 2λj

By compare, we get;

⇒ x = 3 + λ

⇒ y = 2λ

Thus, The Cartesian equation is;

⇒ (x - 3) / 1 = (y - 0)/2 = λ

Therefore, The Cartesian equation will be;

⇒ (x - 3) / 1 = (y - 0)/2

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Related Questions

50 points! Which expression is equivalent to 7(y - 4)? * 1 point
7y - 28
7y - 4
3y
7y - 3
I have to explain also!

Answers

The answer is 7y - 28. You use the distributive property. So you multiply 7 and y and multiply 7 and -4. Therefore the answer is 7y - 28

The function f(x) = 2x3 + 3x2 + 2x – 1 is divided by (x – 1) .

Answers

Step-by-step explanation:

here is your answer hope it helps you plaz mark me as brainlist

NEED ANSWERS ASAP PLEASE HELP!!! THE NUMBERS ARE THE QUESTION #

Answers

Area of the parallelogram is 882 square units

the solution of the inequality is plotted in the last number line

area o the glass window is 144π cm²

the second number line is the correct plot

the water left after the serving is 2 gallons 3 quart 1 pint

How to find the area of the parallelogram

Area of a parallelogram is given by the formula

= base *  height

= 63 * 14

= 882 square units

The solution of the number line is b/2 ≥  4

= b ≥  8

the last option is correct

Area of circle is solved by

= πd² / 4

= π * 24² / 4

= 144π cm²

The inequality 4 > -y

= -4 < y

The second option is correct

total fluid ounces used

= 68 * 4 = 272 ounces

272 ounces = 2.125gallons

5 - 2.125 = 2.825 gallons

2.875 gallons

0.875 gallons = 3.5 quart

2 gallons 3.5quart

0.5 quart = 1 pint

2 gallons 3 quart 1 pint

Water left in the cooler is 2 gallons 3 quart 1 pint

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After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =

Answers

Answer:  -2

Step-by-step explanation:

4y/4 = -8/4

     y = -2

Answer:

Step-by-step explanation:

Answer is -2

help me with this you need to do associative property of addition, identity property of addition, associative property of multiplication, and identity of multiplication also tell what Properties are shown. due tomorrow morning​

Answers

Answer:

12 x 12

Step-by-step explanation:

(12+0)=12

(12 x 1)= 12

PLEASE IT DUE SOON!!! DONT EVEN KNOW WHERE TO START IM SO CONFUSED!!!

QUESTION DOWN BELOW!! ONLY HAVE 20MIN SO PLEASE SOMEONE!!

Answers

A test point which is in the solution set for the linear inequality is: C. (-2, 4).

How to determine the true test point?

In order to determine which ordered pairs is a true solution based on the given linear inequality, we would have to test each of the ordered pairs by substituting their values into the linear inequality as follows;

For ordered pair (-2, -4), we have:

2x - 9y < 0

2(-2) - 9(-4) < 0

-4 + 36 < 0

32 < 0 (False).

For ordered pair (-1, -5), we have:

2x - 9y < 0

2(-1) - 9(-5) < 0

-2 + 45 < 0

43 < 0 (False).

For ordered pair (-2, 4), we have:

2x - 9y < 0

2(-2) - 9(4) < 0

-4 - 36 < 0

-40 < 0 (True).

For ordered pair (-1, -1), we have:

2x - 9y < 0

2(-1) - 9(-1) < 0

-2 + 9 < 0

7 < 0 (False).

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using a slope formula find the slope pf the line theough the points (0,0) and (2,6)

Answers

Step-by-step explanation:

slope formula: (y2-y1)/(x2-x1)

at the point (0,0), it is known that x=0 and y=0.at the point (2,6), it is known that x=2 and y=6.

slope: (6-0)/(2-0) =6/2 =3

"How do we transform System A into System B?
Equation [A1] → Equation [B1]
Equation [A2]→ Equation [B2]
Equation [A1]+Equation [A 2] → Equation [B 2]
Equation [A2]+ Equation [A 1] → Equation [B 1]"

Answers

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform system A into System B ?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step by step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

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Determine the equation of the parabola that opens up, has vertex (7, 7), and a focal
diameter of 16.

Answers

Answer:

Step-by-step explanation:

Question: Determine the equation of the parabola that opens up, has vertex (7,7), and a focal diameter of 16 . This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer: ((x2)−14x+87)/16

Step-by-step explanation:

  focal diameter = 16,

  4a=16;

  a=4.

(h,v)=(7,7-a)

==> (h,v)=(7,3)

the equation of the parabola =  ((x-7)^2)=16(y-3)

                                                => y = ((x^2)-14x+87)/16.

A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?​

Answers

Answer: $5400

Step-by-step explanation:

x =  amount raised so far

13500 - x = amt. still needed

x/3 = (13500 - x)/2

2x = 3(13500 - x)

2x = 40500 - 3x

5x = 40500

x = 40500/5 = 8100 (amt. raised so far)

13500 - 8100 = 5400 (amt. still needed)

The vertex angle of an isosceles triangle measures
15 degrees more than one of its base angles. How
many degrees are there in a base angle of the
triangle?

Answers

The required three angle is 55 , 55 and 70

What is an angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Let each of the base angle of isosceles triangle = x

Vertex angle = (x+15)

Sum of the angle = 180

x + x + (x + 15) = 180

3x + 15 = 180

3x = 180 - 15

x = 165 / 3

x = 55

Each base angel = 55

Vertex angle = x + 15

                      = 55 + 15

                      = 70

Required three angles = 55 , 55 and 70

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Apply the distributive property to simplify the expression


8(12x – 20)

Answers

I believe the answer must be 96x-160

Because we have to multiply 8x12 which is 96. and there is x next to it. so keep the x as it is.

and next to it is minus ( - ) sign so keep it as it is.

now we have to multiply 8x20 which is 160.

so if we write it together it will be:

so if we write it together it will be:96x - 160.

Thank you

If f(1)=7, f(5)=-3, f(11)=-9, g(7)=11, g(-3)=6 and g(-9)=1, then find g(f(11))

Answers

Answer:

1

Step-by-step explanation:

g(f(11))

It says in the problem that f(11) = -9

So:

g(-9)

It says again in the problem that g(-9) = 1

So the answer is 1

.............................

Answers

The answer is 1,200

First you need to add . + . to get 1.5M and then you need to subtract the rest ( 1.5M - one million four hundred ninety-eight thousand eight hundred )

So then you get 1,200

Hope this helped!

10 less than the product of 8 and b

Answers

Step-by-step explanation:

8b-10

hope it helps. please mark brainliest

Answer:  The correct answer is (8*b) - 10

Step-by-step explanation:

When translating word problems into equations, the term "product" denotes multiplication, and "less than" denotes subtraction.

This wording "10 less than the product of 8 and b" tells us to multiply 8 and b, then subtract 10:

(8*b) - 10

What is the equation of the line that passes through the point (2,-6) and has a slope of -3?

Answers

Answer is y = -3x

Step by step

We can use point slope form to solve

y - y1 = m (x - x1)
Substitute your x and y and slope

y - -6 = -3 (x - 2)
Distribute

y + 6 = -3x + 6
Subtract 6 from both sides


y +6 -6 = -3x + 6 - 6
Combine

y = -3x is your answer

HELP PLEASE I NEED IT

Answers

Answer:=

Step-by-step explanation:

Find the Maclaurin series of the following functions. Step by Step Please

Answers

The Maclaurin series of xcos(-x) up to n = 3 is

[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

The function is given in the question as

m(x) = xcos(-x)

Taylor (Maclaurin) series of xcos(x) up to n=5

A Maclaurin series is given by  f(x),

[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]

[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]

We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

f⁽⁰⁾(x) = f(x) = xcos(x)

Evaluate the function at the point: f(0)=0

1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)

1st derivative at the given point: (f(0))′=1

2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)

Evaluate the 2nd derivative at the given point: (f(0))′′=0

3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)

Evaluate the 3rd derivative at the given point: (f(0))′′′=−3

Now, use the calculated values to get a polynomial:

[tex]m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....[/tex]

[tex]m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

Thus, the Maclaurin series of xcos(-x) up to n = 3 is

[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

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Find the smallest length that can be divided exactly into equal sections of length 5m,8m and 12m

Answers

As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.

What is an LCM example?

The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.

What is the LCM of 4 and 8?

8 is the LCM of 4 and 8. The LCM is the number that can be divided by the provided numbers equally. You can discover the least common multiple of 4 and 8 by looking at the common multiples. 4 is a multiple of 8, 12, 16, 20, 24, etc.

finding prime factors of the given numbers by repeated division method in order to find the LCM;

2 | 5,8,12

5 | 5,4,6

2 | 1,4,6

2 | 1,2,3

3 | 1,1,3

0 | 1,1,1

so we get 2x5x3x2=60

As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.

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The shortest length which can be split into equal segments of length 5 meters, 8 meters, or 12 meters is 120.

What does "section" signify in terms of forms and purposes?

Your form may be divided into sections with the help of sections, as the name suggests. This enables your users to input responses that might be categorized. The fact that sections divide your form into distinct screens is another significant benefit. For instance, a first screen shows section 1. When concealed lines in external views cannot adequately represent a part's inner design, sections are employed. The internal components can be viewed more clearly by imagining cutting through the thing and removing a section of it.

Briefing:

Finding the LCM by repeatedly dividing the supplied integers to get their prime components:

2 | 5,8,12

2 | 5,4,6

2 | 5,2,3

3 | 5,1,3

5 | 5,1,1

1 | 1,1,1

So we get 2*2*2*3*5*1 = 120

The lowest length that could be divided into precisely equal segments in lengths 5 m, 8 m, and 12 m is 120, which equals the LCM of 5, 8, & 12.

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An airplane cruises 1 kilometer in
1
12
of a minute. What is its cruising speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
kilometers per minute

Answers

Answer: It is 12 kilometers per minute

Step-by-step explanation:

in the problem that you'll need to simplify your answer and write it as a proper fraction, mixed number, or whole number so I can confirm this is 100% correct.

Step-by-step explanation:

5. Find the value of x. Round the length to the nearest tenth. 18 yd 309 2?. ​

Answers

By Trigonometric formula - Tan(∅) =  [tex]\frac{opposite}{adjacent}[/tex] , we got that answer - x= 10.4 yard (On rounding to tenth place)

what are trigonometric equations?

An equation containing one or more trigonometric ratios of unknown angles is known as a trigonometric equation. In terms of angles, it is written as ratios of the sine, cosine, tangent, secant, and cotangent angles. A trigonometric equation is, for instance, cos2 x + 5 sin x = 0.

For angle 30 degrees adjacent side is 18 yard and opposite side is x.

=>  Tan(∅) =  [tex]\frac{opposite}{adjacent}[/tex]

=>  Tan(30) = [tex]\frac{x}{18}[/tex]

=>  x=Tan 30 (18)

=>  x= 10.39

=>  x= 10.4 yard (On rounding to tenth place)

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2 = x
3 26
How do i solve this equation

Answers

Answer:

do the butterfly method if you don't know how to do that comment and I'll show you a screenshot

You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase. How much is due the first month?

Answers

$25 due the first month

Solve for x. Leave your answer in simplest radical form.

Answers

Answer:

√122

Step-by-step explanation:

first we have to find the missing side with x on the 5 and 9 triangle by using the theorem


a^2+b^2=c^2

9^2+5^2=c^2

81+25=c^2

106=c^2

√106=c


and now we can use this as a side to find x

4^2+√106^2=x^2

16+106=x^2

122=x^2

√122=x

Hopes this helps please mark brainliest

Find the probability of rolling a sum greater than 7 given that you rolled an odd number first.

Answers

Answer:

I think the answer is 1/2. Given the first die was odd, you rolled either a 1,3, or 5. Now on the second roll only a 6,4, or a 2 will give you a sum of 7. Given that is half of the sample space of the second die, it is 1/2?

Step-by-step explanation:

Suppose megan wants to run more sprints and laps. How many of each could she run so that her total sprints and total laps are in the ratio that the coach wanted?

Answers

Answer:

2

Step-by-step explanation:

In a clothing store, 50% of the customers buy a shirt, 30% of the customers
buy a pair of pants, and 15% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
A. 0.20
B. 0.18
C. 0.65
D. 0.80

Answers

Answer:

.20

Step-by-step explanation:

because customers are always right

Please help!!!!
Write an equation in point-slope form that passes through the points (2, 4) and (-3, -6).

Answers

Answer:

uh let's see

Step-by-step explanation:

2,4 and -3,-6

y2-y1/

x2-x1

-6-4

-3-2

-10/-5 = 2

slope is 2

u do the rest I'm tired

rotate (2,-3) 270 degree counterclockwise around (1,-2) then translate (x-2,y+5)

Answers

The image point of the transformation is (-1, 6)

How to determine the image of the transformation?

The coordinate of the point is given as

(2, -3)

The transformations are given as

270 degree counterclockwise around (1,-2) Translation by (x-2,y+5)

The rotation is around the point (1,-2)

So, the point becomes

Point = (2 - 1, -3 + 2)

Evaluate

Point = (1, -1)

The 270 degrees rotation has the algebraic rule of its rotation to be changed from (x, y) to (-y, x) i.e.  (x, y) => (-y, x)

So, we have

(x, y) = (1, 1) after the rotation

The translation is given as

(x - 2, y + 5)

So, we have

(x, y) = (1 - 2, 1 + 5)

Evaluate

(x, y) = (-1, 6)

Hence, the coordinates of the image is (-1, 6)

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order the fraction to least to greatest 2/3 3/7 4/8

Answers

2/3, 4/8, and 3/7. :P
Other Questions
In 1967, a lieutenant in the air force served for six months on active duty in vietnam. In 1998, the veteran was killed in a skiing accident. The veterans surviving spouse wishes to use the veterans life insurance proceeds to make a down payment on a condominium and finance the remainder of the purchase with a va-guaranteed loan. Is the surviving spouse entitled to a va-guaranteed loan? War is cruelty, and you cannot refine it; and those who brought war into our country deserve all the curse and maledictions a people can pour out. I know I had no hand in making this war, and I know I will make more sacrifices to-day than any of you to secure peace. But you cannot have peace and a division of our countryYou might as well appeal against the thunder-storm as against the terrible hardships of war. They are inevitable, and the only way the people of Atlanta can hope once more to live in peace and quiet at home, is to stop the war, which can only be done by admitting that it began in error and is perpetuated in pride.General William Sherman, Letter to the Mayor and Councilmen of Atlanta, 1864How does Sherman attempt to justify his military actions in his March to the Sea?ResponsesA The South deserved the destruction of their lands for making war first.The South deserved the destruction of their lands for making war first.B The South would be allowed to keep their homes if they negotiated a settlement.The South would be allowed to keep their homes if they negotiated a settlement.C The South should be forgiven and welcomed back into the Union.The South should be forgiven and welcomed back into the Union.D The South put up a valiant fight and should be respected.The South put up a valiant fight and should be respected.E The South had no recourse but to continue fighting. what does the mood and the tone of the play indicate to the audience? multiple choice question. when the play as written. the time period of the play. how the play will end. the point of view of the production. 2. 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The level of liquid in the volumeter would fall since atmospheric pressure is greater than the pressure within the test tube. Function g can be thought of as a translated (shifted) version of f(x) = x2.++-7-6-5-4-3-21-2--3--5--6-Write the equation for g(x).9 (x) = [9+22 3 4 5 6 7 suppose you bought a put option with a strike price of $35 for $4. what would be your payoff if the underlying stock is worth $48 at option expiration? (payoff, not profit) Simplify the following expression completely. 3(2x-1)+5(2x-1) Find the difference, and explain how you did it. 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Show your work too! :)