A vector is in standard position, with its terminal point in the second quadrant and an x-coordinate of –5. The vector has a magnitude of StartRoot 61 EndRoot.Complete the statements describing the vector. The y-coordinate of the vector to the nearest tenth is . The direction angle to the nearest whole number is °.

Answers

Answer 1

a.

The y-coordinate of the vector with its terminal point in the second quadrant is 6.

The magnitude of the vector, r = √(x² + y²) where x = x-coorcinate of vector = -5 and y = y-coordinate of vector.

Since r = √61 and r = √(x² + y²)

Making y subject of the formula, we have

y = √(r² - x²)  

Substituting the values of the variables into the equation, we have

y = √((√61)² - (-5)²)  

y = √(61 - 25)  

y = ±√36

y = ±6

Since r is in the second quadrant, its y-coordinate is positive.

So, y = 6

So, the y-coordinate of the vector with its terminal point in the second quadrant is 6.

b.

The direction angle of the vector with its terminal point in the second quadrant is 130°

The direction angle of the vector is gotten from tanФ = y/x

Subsstituting x and y into the equation, we have

tanФ = y/x

tanФ = 6/-5

tanФ = -1.2

tan(180° - Ф) = 1.2

Taking inverse tan of both sides, we have

180° - Ф = tan⁻¹(1.2)

180° - Ф = 50.2°

Ф = 180° - 50.2°

Ф = 129.8°

Ф ≅ 130° to the neares whole number

The direction angle of the vector with its terminal point in the second quadrant is 130°.

Learn more about vectors here:

https://brainly.com/question/18478651

Answer 2

Answer:

first one is 6.0 and the second is 130

Step-by-step explanation:


Related Questions

Question 12 Objective: Given an acute angle of a right triangle, label the hypotenuse, opposite, and adjacent sides. What side is opposite to angle R? What side is adjacent to angle R? R S​

Answers

Answer:

Opposite: Line SQ

Adjacent: Line SR

Hypotenuse: Line RQ

Step-by-step explanation:

Pls help me asap!! Only answer if u know the correct answer! Thanks! :)

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The answer is 168 feet tall!

I hope this helps, please tell me of you want a step by step, I can give one. :)

Find the perimeter. Simplify your answer.

Answers

Answer:

perimeter=32t units

Step-by-step explanation:

let:

a=8t-2

b=8t+2

perimeter=2(a+b)

Subtitute values of a and b:

=2(8t-2+8t+2)

=2(16t)

=32t units

The answer is 32t units

A circle has a diameter of 62 meters. What is the circumference of the circle

Answers

Answer:

the circumstance is 194.78

A xerox machine makes scale copies of the pages in your math book. If the copy comes out the exact same size as the original,what do you think the scale factor is?

Answers

If the copy made by Xerox's machine is same size as the original, the scale factor will be 1.

Recall:

The scale factor = dimension of new copy / dimension of original copy.

Let's assume that one of the dimension of the original copy is 4 inches.

If the new copy is of exact same size as the original copy, therefore the new copy will still have a dimension of 4 inches.

Thus:

Scale factor = 4/4 = 1

Therefore, if the copy made by Xerox's machine is same size as the original, the scale factor will be 1.

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You need to cut a 16 foot long 2x4 into 3.5ft sections. How many ehole sections will you have

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You would have to use a calculator this isn’t easy good luck 568

Please solve: 6x - y = -1

Answers

Answer:

y=6x-1

Step-by-step explanation:

6x - y = -1

-y = -1 -6x

y = 6x+1

Answer:

y = 6x + 1

Step-by-step explanation:

hope it helps

should I show steps?

Which expression can be placed on the right side of the equals sign to form an equation? 6+24= 7+3⋅5 4⋅103+96 3⋅10+2 7²

hurry please im timed whoever gets the correct answer ill give brainliest

Answers

Answer:

the answer is 7 + 3 . 5

Step-by-step explanation:

i think the last question today lol

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Answer:

the picture is not clear

Step-by-step explanation:

30 65 and 75 lcm12 24 36 and 48 lcm6 8 15 and 35 lcm20 25 35 and 70 lcm18 20 24 30 lcm

Answers

Doin it for points sorry

Express 8.4km/min in km/hr

Please answer quickly i have exam tomorrow!!!

Answers

Answer:

540km/hr

Step-by-step explanation:

8.4km/min×60min/km

=8.4/60

=540km/hr

PLEASE HELP I NEED HELP

Which verb of ser do I use?

Example: son, sois, somos, es, eres, soy

Ricardo y yo _____.

I WILL GIVE BRAINLIEST

Answers

Answer: Ricardo y yo somos

Answer:

somos

Step-by-step explanation:

somos means us

Ricardo and us

please help, please and ty.

Answers

Answer:

l.y=4

m.y=-2x+4

n.1x-1

p.x=-4

Step-by-step explanation:

The equations of the lines given in the graph will be,

y = x - 1

y = -2x +4

y = 4

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

For line one the points are:-

( 3,2 ) and ( 1,0)

Slope = ( 0 -2 ) / ( 0 - 3 )

Slope = 1

The equation will be,

y = x + c

0 = 1 + c

c = -1

For line two the points are:-

(0,4) and (2,0),

Slope = ( 0 - 4 ) / ( 2 - 0 )

Slope = -2

The y-intercept will be,

y = mx +c

y = -2x + c

c= 4

The equation can be written as:-

y = -2x +4

The equation of the line parallel to x-axis is,

y = 4

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ2

-8 less than a number is no more than 12

Answers

Answer:

-8 < x ≤ 12

Step-by-step

-8 less than a number would give you

-8 <

a number no more than 12 would give you

x ≤ 12

giving x because we dont know what the number is-

so your full anser would be-

-8 < x ≤ 12

I will give BRAINLIEST plz help

Answers

Answer:

-0.37

-2.86

0.91

0.19

1.46

Step-by-step explanation:

What type of angle is 90 degrees

Answers

Answer:

Obtuse or right angle

Step-by-step explanation:

Also you should stop making your question worth so many points

A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and glue worth $190 per barrel. It must use the same number of barrels of $150 and S190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced

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Answers

Answer:

1034

Step-by-step explanation:

Answer:

1034

Step-by-step explanation:

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Answers

Answer:

R.I.P

Step-by-step explanation:

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Answers

Answer:

Collect as many ants as you can with the container you have provided. A excellent approach to do this is to sprinkle some sugar or bread crumbs in a container and position it near the ant nest, where the ants will gather. A reasonable starting point is about 100.

Step-by-step explanation:

Hope it helps:)

find the measure of angle y, 38,41,19

Answers

If this is DMS then the answer is 38.68861111 degrees

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How do you find the radius???

Answers

Answer:

r = 15

Step-by-step explanation:

Using Pythagoras' identity in the right triangle OAB

with OM and OB the radii r of the circle

OA² = OB² + AB²

(r + 10)² = r² + 20² ← expand left side using FOIL

r² + 20r + 100 = r² + 400 ( subtract r² from both sides )

20r + 100 = 400 ( subtract 100 from both sides )

20r = 300 ( divide both sides by 20 )

r = 15

Find the side length of the triangle 4x+8=3x+12

Answers

Answer:

I think it might be 4.

Step-by-step explanation:

:)

I found something that says 6x or something if that helps?

I hope you get it right!!!

The purpose of a budget is to figure out how to use money in a way that best meets your wants and needs. TRUE OR FALSE. Brainly

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The answer is true :)

a 4 foot statue has a shadow of 3 feet.next to the statue is a telephone pole with a shadow of 18 feet.what is the height of the telephone pole

Answers

Answer:

c 15.9 m

Step-by-step explanation:

you are welcome

A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Rashaad measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

Answers

The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.

Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.

Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

          = [tex]\frac{11}{4}[/tex]

Tan θ = 2.75

θ = [tex]Tan^{-1}[/tex] 2.75

  = 70.0169

θ = [tex]70^{o}[/tex]

Considering triangle formed by the tower and the stake to determine the value of l, we have;

Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos [tex]70^{o}[/tex]  = [tex]\frac{23}{l}[/tex]

l = [tex]\frac{23}{Cos 70^{o} }[/tex]

 = [tex]\frac{23}{0.3420}[/tex]

l = 67.2515

l = 67 feet

The length of the guy wire is 67 feet.

For more on trigonometric, check: https://brainly.com/question/6459892

Please help me





20 points

Answers

Answer:

1). Simplify the expression.

Exact Form:

( [tex]\frac{37}{25}[/tex] )

Decimal Form:

1.48

Mixed Number Form:

( [tex]1\frac{12}{25}[/tex] )

2). Simplify the expression.

91.46

3). Simplify the expression.

Exact Form:

[tex]\frac{17}{24}[/tex]

Decimal Form:

0.7083  ( bar notation)

4). Simplify the expression.

81.49

pls help me with this question ...​

Answers

Here is ur perfect answer

Answer:

x = 207

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

([tex]\sqrt{x}[/tex] )² + 7² = 16²

x + 49 = 256 ( subtract 49 from both sides )

x = 207

True or False: If I am a boy and you are a person, what color is the leaf in the winter time on a pole?

Answers

What? hold up my brain hurts! you made me confused!!

Answer:

There are no leaves in the winter except on evergreens and those are green.

Step-by-step explanation:

A stick 1 meter long casts a shadow 0.6 meters long. A building casts a shadow 25 meters long. How tall is the building (to 2 decimal places)

Answers

Answer:

41.67

Step-by-step explanation:

Using the tangent on the stick with shadow:

tan(θ) = [tex]\frac{1}{0.6}[/tex]

Using the tangent on the building:

tan(θ) = [tex]\frac{h}{25}[/tex]

⇒ h = 25 · tan(θ)

       = 25 · [tex]\frac{1}{0.6}[/tex]

⇒ h = 41.66... ≈ 41.67

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