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:
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Answer:
first one is 6.0 and the second is 130
Step-by-step explanation:
how many ants will there be in the ant farm?
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:)
Express 8.4km/min in km/hr
Please answer quickly i have exam tomorrow!!!
Answer:
540km/hr
Step-by-step explanation:
8.4km/min×60min/km
=8.4/60
=540km/hr
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
Answer:
Opposite: Line SQ
Adjacent: Line SR
Hypotenuse: Line RQ
Step-by-step explanation:
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
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?
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.Learn more about scale factor on:
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I will give BRAINLIEST plz help
Answer:
-0.37
-2.86
0.91
0.19
1.46
Step-by-step explanation:
A circle has a diameter of 62 meters. What is the circumference of the circle
Answer:
the circumstance is 194.78
please help, please and ty.
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
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Please solve: 6x - y = -1
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?
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
Answer:
c 15.9 m
Step-by-step explanation:
you are welcome
Find the side length of the triangle 4x+8=3x+12
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!!!
PLS HELP ME
How do you find the radius???
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 measure of angle y, 38,41,19
You need to cut a 16 foot long 2x4 into 3.5ft sections. How many ehole sections will you have
Math help because I forget
Answer:
R.I.P
Step-by-step explanation:
goodluck doing that
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?
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:
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
Answer:
somos
Step-by-step explanation:
somos means us
Ricardo and us
-8 less than a number is no more than 12
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
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.
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
Pls help me asap!! Only answer if u know the correct answer! Thanks! :)
What type of angle is 90 degrees
Answer:
Obtuse or right angle
Step-by-step explanation:
Also you should stop making your question worth so many points
Please help me
20 points
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
30 65 and 75 lcm12 24 36 and 48 lcm6 8 15 and 35 lcm20 25 35 and 70 lcm18 20 24 30 lcm
What is 2+21*13-45+12*67
Answer:
1034
Step-by-step explanation:
Answer:
1034
Step-by-step explanation:
Find the perimeter. Simplify your answer.
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
pls help me with this question ...
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
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
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
Answer:
the answer is 7 + 3 . 5
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)
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
i think the last question today lol
Answer:
the picture is not clear
Step-by-step explanation: