Answers
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
How to determine the magnitude and the direction of a resultantVectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
Resultant[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Magnitude[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex] (2)
Direction[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex] (3)
Where [tex]\theta[/tex] is resultant angle, measured in degrees.
If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:
Resultant[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]
[tex]\vec r = (-54.824, 18.531)[/tex]
Magnitude[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]
[tex]\|\vec r\| \approx 57.871[/tex]
Direction[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]
[tex]\theta \approx 198.676^{\circ}[/tex]
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]
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Related Questions
A cashier samples the transaction of every 10th person who goes through the line at a craft store. Out of 40 people, 32 used a coupon. If 750 people go to this store each day, how many people would you expect to use a coupon?
Answers
2x(5x-2)+(3x-0.5)*2=2x+3+10x-5+2x+3
Find X
(give step by step)
Answers
Answer:
x = 1.348331477 and 0.148331477
Step-by-step explanation:
TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac.x=2×10−(−12)±(−12)2−4×10(−2)Square −12.x=2×10−(−12)±144−4×10(−2)Multiply −4 times 10.x=2×10−(−12)±144−40(−2)Multiply −40 times −2.x=2×10−(−12)±144+80Add 144 to 80.x=2×10−(−12)±224Take the square root of 224.x=2×10−(−12)±414The opposite of −12 is 12.x=2×1012±414Multiply 2 times 10.x=2012±414Now solve the equation x=2012±414 when ± is plus. Add 12 to 414.x=20414+12Divide 12+414 by 20.x=514+3Now solve the equation x=2012±414 when ± is minus. Subtract 414from 12.x=2012−414Divide 12−414 by 20.x=53−14The equation is now solved.
x=514+3x=53−14
The swiss mathematician leonhard euler and the french mathematician rene descartes both discovered a pattern in the numbers of edges, vertices, and faces of polyhedrons. solve problems 810.
Answers
Answer:
I am stuck on this two
Step-by-step explanation:
rectangle, 6 8 14 12
Find the slope of the line that is parallel and perpendicular to the following equation.
y + 4 = -3(x +1)
Answers
Answer:
Parallel: -3
Perpendicular: 1/3
Step-by-step explanation:
First I would convert the equation into slope-intercept form to more easily identify the slope:
[tex]y+4=-3x-3\\ y=-3x-7[/tex]
Slope-intercept form is defined as y=mx+b where m is the slope and b is the y-intercept so we can identify the slope of this line as -3.
When a line is parallel to another line, this means that they have the same slope, therefore the slope of the line parallel to the equation is -3.
Perpendicular lines will have slopes that are negative reciprocals of each other, the negative reciprocal of -3 is 1/3; therefore, the slope of the line perpindicular to the equation is 1/3.
Answer:
parallel slope = -3
perpendicular slope: [tex]\sf \bold{\frac{1}{3} }[/tex]
Explanation:
y + 4 = -3(x +1)y + 4 = -3(x) - 3y = -3(x) - 3 - 4y = -3x - 7comparing with y = m(x) + b [ "m" is the slope, "b" is the y-intercept ]
slope: -3y-intercept: -7Parallel/Tangent slope:
m₁ = m₂ (same)
Perpendicular/Normal slope:
m₁ * m₂ = -1 (negatively reciprocal)
⇒ Here parallel slope:
m = -3⇒ Here perpendicular slope:
-3 * m₂ = -1m₂ = -1/-3m₂ = 1/34 1/3-1 1/4
Estimate the answer by rounding each fraction to the nearest whole number and then subtracting.
A. 5
B. 3
C. 3 1/2
D. 3 1/12
Answers
Answer:
D. 3 1/12
Explanation:
[tex]\rightarrow \sf 4\dfrac{1}{3} -1\dfrac{1}{4}[/tex]
convert into improper fraction
[tex]\rightarrow \sf \dfrac{13}{3} -\dfrac{5}{4}[/tex]
make the denominators same. 12 is the common factor of both 3 and 4
[tex]\rightarrow \sf \dfrac{13(4)}{12} -\dfrac{5(3)}{12}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{52}{12} -\dfrac{15}{12}[/tex]
join both fraction
[tex]\rightarrow \sf \dfrac{52-15}{12}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{37}{12}[/tex]
convert into mixed fraction
[tex]\rightarrow \sf 3\dfrac{1}{12}[/tex]
how to compare 10.5 to 11 and 19
Answers
Answer:
Line up the decimal points. **Answer is Least to greatest: 10.5 , 11, 19**
Step-by-step explanation:
You need to line each number up.
10.5
11.0
19.0
The reason why 11 and 19 have a decimal point and zero at the end is because you need to do that in order to compare the numbers.
This problem is also a little common sense because 10.5 is the smallest, 19 is the largest while 11 is in the middle.
Which is the equation of a line that has a slope of -5 and a y-intercept of -3? Show me how you arrived at your answer.
a) 2y = -5x - 3
b) -2y = 10x - 6
c) -2y = 10x + 6
d) 2y = 10x - 6
Answers
Answer:
c) -2y = 10x + 6
Step-by-step explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]
The variables stand for:
[tex]y:$ y-coordinate of any point on the line\\$x:$ x-coordinate of any point on the lien\\$m: $ Slope of the line\\$b: $ y-intercept of the line; where the line meets the y-axis[/tex]
Plugging in the given information into the equation:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
Go through the answer choices:
a) 2y = -5x - 3
Divide both sides of the equation by 2
[tex]y=-\frac{5}{2}x-\frac{3}{2}\rightarrow\text{Incorrect!}[/tex]
b) -2y = 10x - 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x-\frac{6}{-2}\\y=-5x-(-3)\\y=-5x+3\rightarrow\text{Incorrect!}[/tex]
c) -2y = 10x + 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x+\frac{6}{-2}\\y=-5x+(-3)\\y=-5x-3\rightarrow\text{Correct!}[/tex]
d) 2y = 10x - 6
Divide both sides of the equation by 2
[tex]y=\frac{10}{2}x-\frac{6}{2}\\y=5x-3\rightarrow\text{Incorrect!}[/tex]
Therefore the answer is c) -2y = 10x + 6
Additional Comments:
We can only divide both sides of the equation by 2 and/or -2 because of the Division Property of Equality. This property states that if we divide one side of the equation by a certain quantity, we must divide the other side by the same quantity so that the equation remains equal.
Solve by factorisation
2x²+3x-20=0
Answers
Answer:
x=5/2 x=-4
Step-by-step explanation:
2x^2+3x-20 = (2x-5)*(x+4)
2x-5 = 0 x=5/2
x+4 = 0 x=-4
Answer: X= -4
Step-by-step explanation:
A solid box with height 60cm, width 10cm and length 10cm needs to be painted.
The paint costs £0.17 per cm2.
How much will it cost to paint the outside of the box?
Answers
Answer:
£442
Step-by-step explanation:
see vid on how to calculate cm² of a box here
Answer:
17cm²
Step-by-step explanation:
area of box =l×w
10cm×10cm=100cm²
0.17×100cm²=17cm²
Times New Roman has tiny lines at the tips of letters, creating an appearance of old-style writing with a fountain pen. Those tiny lines are called _____.
Answers
How many turning points are in the graph of the polynomial function?
2 turning points
3 turning points
4 turning points
5 turning points
Answers
[tex] \mathbb\red{4\:turning\:points} [/tex]
Label the missing angle on this window.
Answers
Answer:
C
Step-by-step explanation:
Since the angles in a triangle add to 180 degrees, the third angle is 180-70-45=65 degrees
What does the value 40 in the equation y=7.5+40 represent in the context of this situation?
Answers
Answer:
40 is an addend in an addition
40 is the y-intercept if the question really is y = 7.5x + 40.
Step-by-step explanation:
40 is just a number in a sum of 2 numbers.
Perhaps you meant
y = 7.5x + 40
If that is the case, then 40 is the y-intercept.
The science club is selling homemade cookies to raise money for a field trip. The club members know that 12 dozen cookies
uses 3 pounds of flour. Use that information solve each part below. Homework Help
a. How much flour is needed for 18 dozen cookies?
b. How many cookies can be made with 10 pounds of flour?
Answers
The flour needed for 18 dozen cookies is 4.5 pounds.
The number of cookies that can be made with 10 pounds of flour is 40 cookies.
How much flour is needed?The first step is to determine the flour needed for 1 dozen cookies.
Flour needed = 3/12
Flour neeeded for 18 dozens = 3/12 x 18 = 4.5 pounds
How much cookies can be made?
The first step is to determine the number of cookies that can be made with one pound of flour:
12/3 = 4
Number of cookies that can be made iwth 10 pounds of flour = 4 x 10= 40 cookies
To learn more about multiplication, please check: https://brainly.com/question/13814687
what fraction of 1/2 square centimeter is 1/2 centimeter square
Answers
Answer:
1/2
Step-by-step explanation:
The ratio of interest is ...
(1/2 cm)²/(1/2 cm²) = (1/4)/(1/2) = 1/2
One-half centimeter squared is half of 1/2 square centimeter.
WHat is the correct answer?
Answers
Answer:
9 ft.
Step-by-step explanation:
Rectangular Prism’s Volume:
[tex]\displaystyle \large{V=\sf{width*length*height}}[/tex]
Given:
width = 2.1 ft
length = 4 ft
height = j
volume = 75.6 cubic feet
Therefore, apply given information in the formula:
[tex]\displaystyle \large{75.6=2.1*4*j}\\\displaystyle \large{75.6=8.4j}[/tex]
Divide both sides by 8.4 to solve for j.
[tex]\displaystyle \large{\dfrac{75.6}{8.4}=\dfrac{8.4j}{8.4}}\\\displaystyle \large{\dfrac{75.6}{8.4}=j}\\\therefore \displaystyle \large{j=9}[/tex]
Henceforth, the value of j is 9 feet.
Quadrilateral ABCD is reflected over the x-axis to create A′B′C′D′. What are the coordinates of A'?
Question 8 options:
(2, 4)
(-2, 4)
(4, 5)
(6, 12)
Answers
Answer: (2, 4)
Step-by-step explanation: If it is reflected over the x-axis then the coordinates of A is (2, 4)
What is the slope ( it has a slope of -2) (it has a slope of -1) (it has a slope of 2)
Answers
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = ( - 1, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2
Answer:
[tex]slope = -2[/tex]
Step-by-step explanation:
Step 1: Determine two points
We need to take two points off of the equation that is used in thsi graph and we can see that we have (0, 0) and (-1, 2)
Step 2: Determine the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - 0}{-1 - 0}[/tex]
[tex]m = \frac{2}{-1}[/tex]
[tex]m = -2[/tex]
Answer: [tex]slope = -2[/tex]
This year a total of 2,185 seventh and eighth grade students attended the junior high school one thousand forty three students are seventh graders how many students are eighth graders
Answers
Answer:
1142
Step-by-step explanation:
(all)2185-(7th)1043=1142(8th)
Han and Priya want to know the mean height of the 30 students in their dance class. • The mean height for Han’s sample is 59 inches. • The mean height for Priya’s sample is 61 inches.
Answers
Answer:
60 inches
Step-by-step explanation:
Add 59+61 =120 which you divide by 2 for the mean of 60.
Abby has four pieces of ribbon for a project. The lengths of the ribbons are 3.7 cm, 2.9 cm, 2.6 cm, and 3.5 cm. What is the measure of the shortest ribbon?
3.7 cm
2.9 cm
2.6 cm
3.5 cm
Answers
Answer:
2.6 cm is the correct answer
Step-by-step explanation:
Answer:
2.6 cm
Step-by-step explanation:
it is the shortest
p.7 Central Angles and Inscribed Angles
#4 What is the measure, in degrees, of arc JKI ?
4) JKI
80°
K
mJKI =
degrees
Helppp me
Answers
Answer:
280°
Step-by-step explanation:
There are 360° in a circle. you are given an arc that is 80°.
To find the arc JKI, subtract 80 from 360.
360 - 80 = 280°
Find the distance between the points.?
Help 40 points!!!
Answers
Answer:
34
Step-by-step explanation:
Distance - formula
Answer:
34
Step-by-step explanation:
best to use the formula: √(X1-X2)²+(Y1-Y2)²
(If u want to know why, it's determinated by pithagoras' theory.)
=>√(30-0)²+(16-0)²=√900+256=√1156=34
Transform the solid black function to match the dotted function.
y= Voc
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LO
9
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8
N
6
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4
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-18 9 8
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3
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X
5
7
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N
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-6
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Answers
Transforming the solid line to the dotted line would change the equation of the functions
The equation of the dotted line is: [tex]f(x) = -\sqrt{x - 6} + 3[/tex]
How to transform the function?The equation of the solid line is given as:
y = √x
The solid line undergoes the following transformation to match the dotted line
Reflection across the x-axisTranslate 6 units rightTranslate 3 units upThe rule of the above sequence of transformations is:
(x,y) -> (x - 6, -y + 3)
Using the above transformation rule, the equation of the dotted line is:
[tex]f(x) = -\sqrt{x - 6} + 3[/tex]
Read more about function transformation at:
https://brainly.com/question/17586310
What's the area for ABC?
Answers
Answer:
14
Step-by-step explanation:
7(length) times 4(height) equals 28
28/2= 14
any help would be appreciated.
Answers
Answer:
10.4
Step-by-step explanation:
cosine rule=[tex]a^{2}=b^{2} +c^{2} -2bc*cosa[/tex]
[tex](2\sqrt{3}) ^{2}=(x+2)^{2} +x^{2} -2(x+2)x*cos60\\12=x^{2} +4x+4+x^{2} -2x^{2} -4x*\frac{1}{2}\\2x-8=0\\x=4\\Area=\frac{1}{2}absinc\\ = \frac{1}{2}*6*4*sin60\\\\ =6\sqrt{3}\\=10.4(3 sig.fig)[/tex]
A figure was flipped over the y-axis and then
enlarged three times the original size. Which
transformations were use
a.) reflection over y-axis b.) translation
C.) dilation
d. rotation
Answers
Answer:
Below.
Step-by-step explanation:
a) reflection over y-axis.
b) dilation.
A line passes through the point (-8,5) and has a slope of -3/4 .
Write an equation in slope-intercept form for this line.
Answers
Answer:
Step-by-step explanation:
Formula
The basic formula is
y = mx + b
m = the slope
b = the y intercept
What you know so far
y = mx + b.
You know that the slope = -3/4
y = - 3/4 x + b
y intercept
The point is used to find the y intercept.
x = - 8
y = 5
Subtitute these two values into the equation above.
5 = -3/4 * (-8) + b Multiply the factors on the right
5 = 6 + b Subtract 6 from both sides
5 - 6 = b Combine
-1 = b
Answer: y = -(3/4) x - 1
Answer:
[tex]\Longrightarrow:\boxed{\sf{y=-\dfrac{3}{4}x-1}}[/tex]
Step-by-step explanation:
Use the slope-intercept form.
Slope-intercept form:
[tex]\Longrightarrow: \sf{y=mx+b}[/tex]
The m represents the slope.The b represents the y-intercept.X= (-8)
Y= 5
[tex]\sf{5=-\dfrac{3}{4}*(-8)+b}[/tex]
5=6+b
Subtract the sign.
5-6=b
Solve.
Isolate the term of b from one side of the equation.
Subtract the numbers from left to right.
⇒ 5-6=-1
⇒ -1=b
Change the equation.
⇒ b=-1
So, therefore, the y-intercept is -1.
[tex]\Longrightarrow: \boxed{\sf{y=-\dfrac{3}{4}x-1}}[/tex]
Therefore, the correct answer is y=-3/4x-1.I hope this helps! Let me know if you have any questions.
A sequence can be generated by using a,n = a,n (-1) + 2, where a,1 = 6 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
A.) 6, 12, 24, 48, 96
B.) 2, 8, 14, 20, 26
C.) 2, 12, 72, 432, 2592
D.) 6, 8, 10, 12, 14
Answers
Ursula is starting a new national network of science fiction book clubs. The establishment and expansion of the network is as follows. The original network began with eight people in each club and four clubs in each of two states. Every month, the number of people in each club increases by two and the number of clubs in each state grows by one. The number of states where the groups exist also increases by one every month. The total number of people in the network of book clubs is represented by the expression below, where x is the number of months since the clubs were established.
Answers
Using derivatives, it is found that the correct option is given by:
A. The expression 2x² + 20x + 32 represents the average rate of increase in the total number of clubs in the network across all states.
What is the meaning of the derivative of a function?It is the rate of change of the function over a period of time.
In this problem, the total number of people in the book club after x months is given by:
f(x) = 2x³ + 20x² + 64x + 64
The derivative is given by:
f'(x) = 4x² + 40x + 64 = 2(2x² + 20x² + 32).
It represents the average rate of change across all states, hence option A is correct.
More can be learned about derivatives at https://brainly.com/question/2256078
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