Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):
[tex]u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle[/tex]
Secondly, we add them:
[tex]u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle[/tex]
Thirdly, find the magnitude of the new vector:
[tex]||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871[/tex]
And finally, find the direction of the new vector:
[tex]\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ[/tex]
Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°
Thus, B is the best answer
Problem 2
To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:
[tex]\langle1-7,6-(-1)\rangle=\langle-6,7\rangle[/tex]
Thus, A is the correct answer
Problem 3
Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:
[tex]-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle[/tex]
Thus, C is the correct answer
Problem 4 (top one in 4th image)
Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, [tex]-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle[/tex], which means our magnitude is -60 and our direction remains 30°.
Thus, B is the correct answer
Problem 5 (fake #6, bottom one in 4th image)
Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:
[tex]u=-3i+8j=\langle-3,8\rangle[/tex]
Thus, B is the correct answer
Problem 6 (real one, 5th image)
Recall:
Two vectors are said to be orthogonal if their dot product is 0 and are perpendicular to each other (form a 90° angle)Two vectors are said to be parallel if the angle between the vectors is 0° or 180° i.e. cosθ=-1Knowing these facts, let us compute the dot product:
[tex]u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455[/tex]
Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B
To check if the vectors are parallel, find the angle between them:
[tex]\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ[/tex]
So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.
Thus, D is the correct answer
Related Questions
is 25 fl oz greater than, less than, or equal to 1 pint?
Answer needs to be RIGHT, to be brainliest
Answers
Answer:
greater than
Step-by-step explanation:
there is 16 fl oz in a pint so 25>16
Which expression does sine of the quantity pi plus theta end quantity plus cosine of the quantity pi over 2 minus theta end quantity simplify to?
sin θ + cos θ
2cos θ
0
1
(Equation in photo below)
Answers
Answer:
(c) 0
Step-by-step explanation:
Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.
__
We can start with the identity ...
cos(x) = sin(x +π/2)
Substituting the argument of the cosine function in the given expression, we have ...
cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)
__
The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...
sin(π +θ) = -sin(θ)
The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...
cos(π/2 -θ) = -sin(θ -π) = sin(θ)
Then the sum of terms is ...
sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0
The sum of the two terms is identically zero.
Stacy’s goal is to run at an average speed of 1 mile per 10 minutes. What is the number of laps that she must run in 1/2 hour to reach her goal?
Answers
Answer:
3 miles (3 laps)
Step-by-step explanation:
Assuming 1 lap is a mile, and 1/2 hour has 30 minutes, 1 mile per 10 minutes gives us 3 miles.
Mark stands at the intersection in observes if cars go left right or straight. After watching for a while, he recorded that 10 cars went straight for cars went left and six cars went right. Estimate the probability that the next car goes left then place the probability on the scale below. help me pls. I have way more packets and I need them done by tmr
Answers
Answer:
0.2
Step-by-step explanation:
Total number of cars: 10 + 4 + 6 = 20
Number of cars that turned left: 4
p(left) = 4/20 = 0.2
To place 0.2 on the scale, divide the segment from 0 to 1/2 into 5 equal parts, and place 0.2 on rthe second from the left.
Between which two consecutive whole number is V67 located? NEED HELP PLEASE
Answers
Answer:
betweennnnnnn 8 and 9!!! :)
find the area of a trapezoid
Answers
Answer:
see explanation
Step-by-step explanation:
the area (A) of a trpezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
b₁, b₂ are the parallel bases and h the perpendicular height between them
(1)
b₁ = 12, b₂ = 8 , h = 5
A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 8) = 2.5 × 20 = 50 cm²
(2)
b₁ = 6 , b₂ = 4 , h = 3
A = [tex]\frac{1}{2}[/tex] × 3 × (6 + 4) = 1.5 × 10 = 15 cm²
(3)
b₁ = 7 , b₂ = 4 , h = 4
A = [tex]\frac{1}{2}[/tex] × 4 × (7 + 4) = 2 × 11 = 22 cm²
Answer:
see explanation
Step-by-step explanation:
the area (A) of a trpezoid is calculated as
A = \frac{1}{2}21 h (b₁ + b₂ )
b₁, b₂ are the parallel bases and h the perpendicular height between them
(1)
b₁ = 12, b₂ = 8 , h = 5
A = \frac{1}{2}21 × 5 × (12 + 8) = 2.5 × 20 = 50 cm²
(2)
Help. I will give points
Answers
Answer:
arc sr
Step-by-step explanation:
i can't see the options for the question so lol
im gonna say its sr arc
When K is positive the parabola ____
Answers
Answer:
when the parabola form updward than k is positiveIf the converse of a conditional statement is false, then what other statement must be false?
Answers
Answer:
The statement is false
During which time period was the ANNUAL rate of increase of the speed the GREATEST?
A) from year 1 to year 2
B) from year 1 to year 3
C) from year 1 to year 4
D) from year 1 to year 5
Answers
Answer:
A) year 1 to year 2
Step-by-step explanation:
The increases in speed are found by subtracting the speed from the year before.
1 to 2: 46 -38 = 8
2 to 3: 52 -46 = 6
3 to 4: 57 -52 = 5
4 to 5: 61 -57 = 4
The greatest increase was from year 1 to year 2.
Emily walked 5 2/6 miles in the morning and another 3 3/5 miles in the afternoon What was the total distance she walked?
Answers
Answer:
The correct answer would be 8 14/15 miles.
Step-by-step explanation:
You have to get the fractions 5 2/6 and 3 3/5 to a common denominator (30) getting you the fractions 10/30 and 18/30. 10/30+18/30 is 28/30 which can simplify to 14/15. 5+3 = 8 getting you the answer of 8 14/15
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.
On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).
Which graph represents g(x)?
On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Answers
it goes through the point (2, 10), has a vertex at (5, 1) and goes through the point (8, 10)
Nicole makes $8 per hour working at a daycare center. How much money would Nicole make in 2 1/2 hours?
Answers
Answer:
$20
Step-by-step explanation:
take 8 and multiply it by 2 and you get 16
then take half of 8 which is 4 and add it on
16+4=20
Which confidence level would produce the widest interval when estimating
the mean of a population based on the mean and standard deviation of a
sample of that population?
A. 31%
B. 57%
O C. 69%
D. 42%
Answers
Answer:
C 69
Step-by-step explanation:
The correct option for Which confidence level would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population is C. 69%
What is the population in simple words?
A population is the number of living people that live together in the same place. A city's population is the number of people living in that city. These people are called inhabitants or residents. The population includes all individuals that live in that certain area.
Conclusion: It can be a group of people, objects, events corporations, and so forth. you use populations to attract conclusions. determine 1: population. An example of a population would be the complete scholar body at a faculty. it'd consist of all of the college students who examine in that university at the time of statistics collection.
Learn more about the population here https://brainly.com/question/25630111
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find the value of 6y - 1 given that 17y - 8 = 9
Answers
Answer:
5
Step-by-step explanation:
if 17y-8=9, then you could say that 17y=17, by adding 8 to both sides.
So, y=1
Then, plug that value into the new equation 6y-1.
You recieve 6(1)-1
Therefore, the value of the new equation is 5
Determine whether the statement is true or false.
When an event is almost certain to happen, its complement will be an unusual event.
Answers
Simplify the expression. 5^–3 • 7^0
a)–15
b)0
c)125
d)1/125
Answers
= 5^-3 × 7⁰
= 1/5³ × 1. ( a^-m = 1/a^m ), ( a⁰ = 1 )
= 1/125 × 1
= 1/125 ANSWER
Find the value of :
Answers
Answer:
i) 66
ii) 536
Step-by-step explanation:
Check attachement(s) for solution.
Attachment - 1: Solution (i)Attachment - 2: Solution (ii)If the function f(x) is change to g(x) what transformation has occurred?
(5 Points)
f (x) = 3x - 7 and g (x) = 3x + 3
The graph of g is a vertical strecth.
The graph of g is 3 units above f
• The graph of g is 10 units above f
Answers
Answer:
Step-by-step explanation:
If the function f(x) is change to g(x) what transformation has occurred?
(5 Points)
f (x) = 3x - 7 and g (x) = 3x + 3
The graph of g is a vertical strecth.
The graph of g is 3 units above f
• The graph of g is 10 units above f
The pendulum of a clock swings through an angle of 2.5 radians as its tip
travels through an arc of 50 centimeters. Find the length of the pendulum, in
centimeters.
Answers
r = 50/2.5 = 20 cm
------------------------
Clock pendulums swing 8 degrees or less, which is an included angle of ~0.28 radians
An employee wants to invest $50,000 in a pension plan. One investment offers 4% compounded quarterly. Another offers 3.75% compounded continuously.
(a) Which investment will earn more interest in 4 yr?
(b) How much more will the better plan earn?
Answers
Using compound interest and continuous compouding, it is found that:
a) The investment at 4% compounded quarterly will earn more interest in 4 years.
b) The better plan will earn $537 more.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, the parameters are: P = 50000, r = 0.04, n = 4, t = 4, hence the amount will be of:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(4) = 50000\left(1 + \frac{0.04}{4}\right)^{4 \times 4}[/tex]
A(4) = $58,629.
What is the continuous compounding formula?It is given by:
[tex]A(t) = Pe^{rt}[/tex]
In this problem, this option has r = 0.0375, hence:
[tex]A(4) = 50000e^{0.0375 \times 4} = 58092[/tex]
Then:
Item a:
The investment at 4% compounded quarterly will earn more interest in 4 years.
Item b:
58629 - 58092 = $537.
The better plan will earn $537 more.
More can be learned about compound interest at https://brainly.com/question/25781328
Steve drew two circles, one with a radius of 10.0 cm and another
with a diameter of 10.0 cm. Which circle is which
Answers
Answer:
Circle 1 = diameter of 10 cm
Circle 2 = radius of 10 cm
Step-by-step explanation:
The radius is half the diameter.
If both the radius and the diameter are the same length, then the circle with the radius of 10 is larger because 10 times 2 is a 20 cm diameter.
The larger circle is circle #2. If we use the logic from above, the larger circle, #2, has a radius of 10 cm. This leaves us with circle #1 having a diameter of 10 cm.
Circle 1 has a diameter of 10
Circle 2 has a radius of 10
Step-by-step explanation:Diameter and Radius
The diameter is the distance from one point on a circle to the opposite side. Radius is the distance from the center of a circle to a point on the circle. This means that the diameter is twice the size of the radius.
Finding Diameter
One way to find out which circle is which is to find the diameter of both. We know that one of the circles had a diameter of 10. The circle that has a radius of 10 must have a diameter of 20 because 10*2=20. Since the circle with a radius of 10 has a diameter of 20, it must be the larger circle, Circle 2.
Reading the Graph
Additionally, you can read the figure given to you. The radius is from the center of a circle to the outside. The line drawn is 10 meters and goes from the center of circle 2 to the outside of circle 2. Thus, this circle must have a radius of 10.
439,532 written in verbal form
Answers
Answer:four hundred and thirty nine thousand five hundred and thirty two
Step-by-step explanation:
Answer:
four hundred thirty nine thousand, five hundred thirty two
Step-by-step explanation:
Hope this helps :)
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:
A.) 0 < x ≤ 6
B.) 0 < x ≤ 3
C.) 4 ≤ x ≤ 6
D.) x ≤ 6
E.) |x - 5| ≤ 1
F.) |x - 2| ≤ 6
Answers
Answer
4 ≤ x ≤ 6 and |x - 5| ≤ 1
Step-by-step explanation:
I answered the question...i got it right...
Freda bought 700 grams of almonds and 500 grams of cashews. How many kilograms of nuts did Freda buy in all?
Answers
Answer:
1.2kl
Step-by-step explanation:
1000grams=1kilogram
700+500=1200
so 1.2kilograms
Question is attached
Answers
X^2-3x-10
X^2-5x+2x-10
Now group them
X(x-5)+2(x-5)
Again group them
(x-5)+2(x-5) =0
(X+2)(x-5)=0
Hopefully that makes sense to u
Keep the good luck
what is 70-(5x2)+18 with explanation and step please
Answers
Step-by-step explanation:
Please Mark me brainliestAnswer:
78
Step-by-step explanation:
70 - (5 x 2) + 18We should solve according to the order of operations, PEMDAS.
P = ParenthesesE = ExponentsM = MultiplicationD = DivisionA = AdditionS = Subtraction#1) Parentheses
70 - (5 x 2) + 1870 - 10 + 18#2) Subtraction
70 - 10 + 1860 + 18#3) Addition
60 + 18783. Suppose a retail business sale its commodities at a margin of 25% on all items purchased and sold. Moreover the company uses 5% commission as selling expense and Birr 12,000 as a Fixed Cost, then Find the Breakeven revenue for the retail business after developing the equation
Answers
The Breakeven revenue for the retail business is Birr 12,500
What is breakeven?
Breakeven is the point at which the revenue is equals to the cost, hence the profit is zero.
Revenue = Cost
Let x represent the number of items sold, hence:
Revenue = (100% + 25%) of x = 1.25x
Cost = 5% of x + 12000 = 0.05x + 12000
At breakeven:
1.25x = 0.05x + 12000
x = 10000
Hence:
Revenue = 1.25(10000) = Birr 12,500
The Breakeven revenue for the retail business is Birr 12,500
Find out more on breakeven at: https://brainly.com/question/9212451
Find the circumference.
Use 3.14 for π.
r = 2m
C = [?] m
C=πd
Answers
circumference = 12.57m
hope it helps...!!!
Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)
Find the equation using this graph.
Answers
Answer:
the slope is 2
y=2x-1
Step-by-step explanation:
y(2)-y(1)/x(2)-x(1) is the formula for slope
-1-0/0-0.5=-1/0.5=2
however, it is looking for the equation
y=mx+b
(b=y intercept)
m=slope
y=2x-1
Answer:
Step-by-step explanation:
The equation of a line is y = m*x + b
So plug in the numbers...
the slope is the change in y over the change in x or (y - y₁)/(x - x₁)
(-1 - 0)/(0 - 0.5) = 2
so... m = 2
and b is the y-intercept which is -1
therefore the answer is: y = 2x - 1
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
( I have verified my answer on an online calculator)