complex vector question.A bolt is tightened by applying a force to one end of a wrench.
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The Scalar and Cross Product of Vectors
Given two vectors:
[tex]\begin{gathered} \underline{r_1}=(a,b,c) \\ \underline{r_2}=(d,e,f) \end{gathered}[/tex]The scalar product is defined as:
[tex]\underline{r_1}\cdot\underline{r_2}=ad+be+cf[/tex]The cross product is the result of computing the following determinant:
[tex]\underline{r_1}\times\underline{r_2}=\begin{bmatrix}i & j & {k} \\ {a} & {b} & {c} \\ {d} & {e} & {f}\end{bmatrix}[/tex]Where i, j, and k are the unit vectors in each of the directions x, y, and z, respectively.
This concept will be applied to the following physics problem.
Given a force F= (2, 3, 0) and the distance vector d = (4, 0, 0), the torque is defined by:
[tex]\tau=r\times F[/tex]Calculating:
[tex]\tau=(4,0,0)\times(2,3,0)[/tex][tex]\tau=\begin{bmatrix}{i} & {j} & {k} \\ {4} & {0} & {0} \\ {2} & {3} & {0}\end{bmatrix}[/tex]Calculating the determinant:
[tex]\begin{gathered} \tau=0i+12k+0j-(0k+0j+0i) \\ \tau=0i+0j+12k \end{gathered}[/tex]Expressing in vector form τ = (0, 0, 12) <= should use angle brackets
The magnitude of the torque is:
[tex]\begin{gathered} |\tau|=\sqrt[]{0^2+0^2+12^2} \\ |\tau|=\sqrt[]{144} \\ |\tau|=12 \end{gathered}[/tex]The power P is equal to the scalar product of the torque by the angular velocity w. We are given the angular velocity w = (3, 3, 2), thus:
[tex]\begin{gathered} P=(0,0,12)\cdot(3,3,2) \\ P=0\cdot3+0\cdot3+12\cdot2 \\ P=24 \end{gathered}[/tex]P = 24
Related Questions
18. ALGEBRA Angles Q and R are supplementary. If m angle Q = 4x + 9 and m angle R = 8x + 3, what is the measure of each angle?
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Due to increased mailing costs, the new rate will cost publishers $50 million; this is 12.5% more than they
paid the previous year. How much did it cost publishers last year? Round to the nearest hundreds.
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The amount it will cost the publishers last year is 44.4 million
How to calculate the amount it will cost the publishers?The first step is to write out the parameters
The cost of mailing increased for the last one year
Due to this increase, it will cost the publishers $50 million for this current year
The increase is at the rate of 12.5%
The amount it will cost the publishers last year can be calculated as follows
= 12.5/100
= 0.125 + 1
= 1.125
The next step is to calculate last year cost
last year cost= 50/1.125
= 44.4 million
Hence the publishers spent 44.4 million last year
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answers
The number of students who chose not to take French their freshman year is 147.
According to the question,
We have the following information:
72% of students chose to study French their freshman year.
Now, 72% of students is equal to 378.
Let's take the number of students to be x.
So, we have:
72x/100 = 378
72x = 378*100
x = (378*100)/72
x = 525
Now, we have to find the number of students who chose not to take French their freshman year:
(100%-72%)
28%
Now, we have to find the 28% of total number of students:
(28*525)/100
14700/100
147
Hence, the number of students who chose not to take French their freshman year is 147.
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Sean and Darryl are racing on a track. Sean runs 6 miles per hour and gets a 0.25 mile head start. Darryl runs 0.7 mile per hour faster than Sean. If Darryl and Sean run the same distance, how many hours, x, do they run? 6x + 0.25 = 0.7x 0 6x - 0.25 = 3.7x 0 6x +0.25 = 6.7x D 6x + 0.25 = 4.7x
Answers
The relation between speed, distance and time is express as :
[tex]\text{ Sp}eed\text{ =}\frac{Dis\tan ce}{Time}[/tex]Sean and Darryl are racing on a track.
Sean runs 6 miles per hour and gets a 0.25 mile head start.
Speed of Sean = 6
x is the time taken by Sean
So, Distance = speed x Time
Distance travel by sean = 6x
Since, Sean gets a 0.25 mile head start.
So, total distance travel = 6x + 0.25
Darryl runs 0.7 mile per hour faster than Sean,
Speed of darryl = 0.7 + Speed of sean
Speed of daryl = 0.7 + 6
Speed of darryl = 6.7 miles per hour
x is the time taken by Darryl
So, Distance = Speed x Time
Distance = 6.7x
Distance travel by Darryl = 6.7x
Since distance travel by darryl and sean is equal so,
6x + 0.25 = 6.7x
Answer : C) 6x + 0.25 = 6.7x
If 35% of your candies was 42 candies, how many candies do you have?
Answers
Answer:
120 candles
Step-by-step explanation:
42/35 = x/100 and solve for x
x = 120
Answer:
120
Step-by-step explanation:
35%/100=42/x
find the x and y intercepts of 2x-5y=12 (write all answers as points)
Answers
Here, we want to find the x and y intercepts of the given line
We start by writing the equation of the line in the standard form
The standard form is;
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
We have the equation re-written as;
[tex]\begin{gathered} 5y\text{ = 2x - 12} \\ y\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \end{gathered}[/tex]As we can see, we have the y-intercept at the point y = -12/5
The coordinate form at this point is (0,-12/5)
To find the x-intercept, we simply set y to zero
This is;
[tex]\begin{gathered} 0\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \\ \\ \frac{2}{5}x\text{ = }\frac{12}{5} \\ \\ 2x\text{ = 12} \\ x\text{ = }\frac{12}{2} \\ x\text{ = 6} \end{gathered}[/tex]The x-intercept is thus (6,0)
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. For how many minutes has the water been draining when Tank B contains 75 liters of water?
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We get that the function that models this situation is
[tex]L=80-2.5m[/tex]where L is the liters the tank contains and m is the minutes that has passed. So we get:
[tex]75=80-2.5m\rightarrow m=\frac{-80+75}{-2.5}=2[/tex]so the tank has been drained for 2 minutes
Simplify the expression.
the expression negative six sevenths times k minus 7 plus the expression 5 plus one half times k
negative 19 over 14 times k plus negative 12
negative 5 over 14 times k plus negative 2
negative 5 over 9 times k plus negative 12
5 over 14 times k plus negative 2
Answers
The simplified form of the expression, negative six sevenths times k minus 7 plus the expression 5 plus one half times k is negative 5 over 14 times k plus negative 2.
Hence, the correct option is option (B).
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
negative six sevenths times k minus 7 plus the expression 5 plus one half times k.
The expression can be written in mathematical term,
(-6/7)k - 7 + 5 + 1/2(k)
Simplify the expression,
(-6/7)k + 1/2(k) - 7 + 5
((-12 + 7)/14) k - 2
(-5/14) k - 2.
-(5/14)k + (-2)
The simplified form is, negative 5 over 14 times k plus negative 2.
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Can someone please help me solve this pleaseeee, I’m struggling and depressed
Answers
Step-by-step explanation:
your teacher gave you the formula, the values, even did the tricky part by telling you that 63 months are 5.25 years.
all you need to do is put everything into the formula and calculate.
so, calm down, breathe and just use common sense :
1.
after 2 years (means t = 2) :
2000 × (1.025)^(2×2) = 2000 × (1.025)⁴ =
= 2000 × 1.103812890625 =
= $2,207.62578125 ≈ $2,207.63
as rounding to the nearest cent means rounding to 2 positions after the decimal point.
2.
after 63 months = 5.25 years (t = 5.25)
2000 × (1.025)^(2×5.25) = 2000 × (1.025)^10.5 =
= 2000 × 1.295986825... =
= $2,591.973651... ≈ $2,591.97
3.
$2,000
because, even t = 0 we have
2000 × (1.025)^(2×0) = 2000 × (1.025)⁰ = 2000 × 1 =
= $2,000
Given the following expression: 8x2 + 26x – 15 One of its simplified factors is: NOTE: If an answer is (x + 1), then do not use any spaces in your answer and be sure to include the parentheses. Your answer would look like this: (x+1)
Answers
We have the following:
[tex]8x^2+26x-15[/tex]simplify:
[tex]\begin{gathered} 8x^2-4x+30x-15 \\ 4x(2x-1)+15(2x-1) \\ (2x-1)\cdot(4x+15) \end{gathered}[/tex]The answer are (2x - 1) or (4x + 15)
Orlandis earned 2.5% interest on a bank balance of $80. What is the amount of interest earned?
Answers
Given
Bank balance = $80
Interest rate = 2.5%
Amount of interest earned = 2.5% of $80
Amount of interest earned = 2.5/100 of $80
Amount of interest earned = (2.5*80)/100
Amount of interest earned = 200/100
Amount of interest earned = $2.0
hence the amount of interest rate is $2.0
Hi Please help me with math
Answers
Answer:12
Step-by-step explanation:
The number of people in thousands who own a cell phone is a function of the time in years starting in 1990 where p(t) = 20(1.075)^tGrowth or Decay?What is the initial amount of people who own cell phones?Determine the growth/decay rate.
Answers
Solution
[tex]\begin{gathered} 1)\text{ Answer, This is GROWTH } \\ 2)\text{ The initial amount of people wo own a cell phone is },\text{ means when t = 0} \\ P(t)=20(1.075)^t \\ p(t)\text{ = }20(1.075)^0 \\ p(t)\text{ = 20 }\times\text{ 1} \\ p(t)\text{ = 20} \end{gathered}[/tex][tex]\begin{gathered} 3)\text{ To }\det er\min e\text{ the growth/decay rate, we have} \\ p(t)=20(1.075)^t \\ p(t)=20(1+0.75)^t \\ \text{Answer, growth rate is: 0.75 =0.75\%} \\ \end{gathered}[/tex]Please help! Will give brainliest!
Answers
f’(-1 x 2) =-5
LOTS OF POINTS!!!!! The table of values represents a linear function g(x), where x is the number of weeks that have passed and g(x) is the balance in the bank account. Find the slope of the function.
A.
-500
B.
-1/100
C.
-100
D.
-1/500
Answers
Answer: easy it's A -500
The slope of the function (x) is -500!! :D
Find the length of the minor axis of the ellipse described by the equation:x squared over 12 plus y squared over 13 equals 1
Answers
This equation of the ellipse can be modeled by
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The major axis is the y-axis and minor axis is the x-axis.
So, the length of the minor axis of this ellipse is "2a".
First, let's find "a",
[tex]\begin{gathered} a^2=12 \\ a=\sqrt[]{12} \end{gathered}[/tex]The length of the minor axis is >>>
[tex]\begin{gathered} 2a \\ =2(\sqrt[]{12}) \\ =2\sqrt[]{12} \end{gathered}[/tex]Answer[tex]2\sqrt[]{12}[/tex]Luisa bought 4.4 kilograms of apples. How
many ounces of apples did she buy? Use the
conversion rates 1 kilogram = 2.20 pounds
and 1 pound = 16 ounces. Round to the
nearest ounce.
Answers
Answer:
155
Step-by-step explanation:
4.4(2.2)=9.68
9.68(16)=154.88
State a conclusion that seems reasonable 6+06, 8+0=8, 9 -9, 100-0-100 Conclusion:
Answers
Answer
The most obvious conclusion from this is that
Adding 0 to any number gives that number itself.
This concept is known as the additive identity property of 0.
Hope this Helps!!!
help meeeeeee pleaseee !!!!
Answers
The equation of the line that passes through point (8,-1) and perpendicular to 8y = x - 16 is f(x) = -8x + 63.
What is the equation of line that passes through the given points and is perpendicular to the given line?Given the data in the question;
Equation of line: 8y = x - 16Point: (8,-1)First we determine the slope of the initial line using the slope intercept-form. y = mx + b
8y = x - 16
y = (1/8)x - 2
Compared with the slope intercept form,
Slope m = 1/8
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/1/8 = -8
To find the equation of the perpendicular line, we use the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -8) and point (8,-1).
y - (-1) = (-8)( x - 8 )
y+1 = -8x + 64
y = -8x + 64 - 1
y = -8x + 63
Therefore, the equation of the perpendicular line is y = 8x + 63
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Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answers
Answer:
renting a movie for 2 dollars a day
Step-by-step explanation:
the y does not repeat
A+(b+c)=(a+b)+c what property is this? The options are as follows
Identity property of multiplication
Associative property of multiplication
Identity prop. Of addition
Multiplicative inverse prop.
Additive inverse prop.
Commutative prop of addition
Commutative prop of multiplication
Transitive property
Properties
Answers
Given:
The properties and their notations are given.
To match:
Explanation:
31. It is given that,
[tex]a+0=a[/tex]Since zero is the additive identity.
So, the property is an identity property of addition.
32. It is given that,
[tex]a+b=b+a[/tex]Here, the property is the commutative property of addition.
33. It is given that,
[tex]a\cdot(b\cdot c)=(a\cdot b)\cdot c[/tex]Here, the property is an Associative property of multiplication.
34. It is given that,
[tex]a+(-a)=0[/tex]Since -a is the additive inverse of a.
So, the property is the Inverse property of addition.
35. It is given that,
[tex]a\cdot1=a[/tex]Since 1 is the multiplicative identity.
So, the property is an identity property of multiplication.
36. It is given that,
[tex]a\cdot(b+c)=ab+ac[/tex]Here, the property is a distributive property of addition.
37. It is given that,
[tex]a\cdot b=b\cdot a[/tex]Here, the property is a commutative property of multiplication.
38. It is given that,
[tex]a\cdot\frac{1}{a}=1[/tex]Here, the property is an inverse property of multiplication.
39. It is given that,
[tex]a+(b+c)=(a+b)+c[/tex]Here, the property is an Associative property of addition.
Final answer:
31. E
32. A
33. D
34. AC
35. AB
36.
in a classroom challenge,students had to create a triangular pyramid using various items. Each group then use your measurements to remind the volume . which group found the volume of triangle pyramid with a base area of 16 square in?
Answers
Volume of a triangular pyramid = 1/3 × base area × height
We have been given base area as 16 square in
Volume of a triangular pyramid = 1/3 × 16 × height
We need to check the options for the expression whose result will give a base area of 16 square in.
From the options:
(8×3)/2 = 12
(11×4)/2 = 22
(16 ×18)/2 = 144
(8 × 4)/2 = 16
1/3 and the height is common to all options. The expression in bracket represent the base area.
Hence, the group that found the volume of triangle pyramid with a base area of 16 square in is
[tex]\frac{1}{3}(\frac{8 ×4}{2})\times q\text{ (option D)}[/tex]Polygon KLMN is drawn with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2). Determine the image vertices of N′ if the preimage is rotated 90° counterclockwise. N′(−4, 2) N′(4, −2) N′(−2, −4) N′(2, 4)
Answers
ANSWER
N'(-2 , -4) Option C
EXPLANATION
Given:
A polygon KLMN with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2).
Desired Outcome:
Image vertices of N′ if the preimage is rotated 90° counterclockwise
Answer: The correct answer is C
Step-by-step explanation:
I was correct on the quiz. WOWWWW
Which of the following activities are examples of data gathering?Check all that apply.
Answers
Answer.
D.
Step by step explanation.
It's defined as the procedure of collecting, measuring, and analyzing accurate insights for research using standard validated techniques.
The most critical objective is ensuring that information rich and reliable data is collected dor statistical analysis so that data-driven decisions can be made for research
Find the probability of selecting a 10 or diamond when a card is drawn from a standard deck of cards.
Answers
The probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
The question asks us to find the probability of picking a 10 or diamond from a deck of cards.
A standard deck of cards contains 52 cards in total.
The deck contains 4 "10s"
And the deck also contains 13 diamond cards.
Thus, we can find the probability of drawing a "10" as:
[tex]P(10)=\frac{n\text{umber of 10s}}{total\text{ number of cards in deck}}=\frac{4}{52}[/tex]Similarly, we can find the probability of drawing a diamond as:
[tex]P(\text{diamond)}=\frac{n\text{umber of diamonds}}{total\text{ number of cards in deck}}=\frac{13}{52}[/tex]Now that we have the individual probabilities, we can find the probability of drawing a 10 or a diamond using the OR probability:
[tex]\begin{gathered} P(A\text{ OR B)= P(A) + P(B)} \\ \text{where, A and B are independent events} \end{gathered}[/tex]Therefore, we can solve the question. This is done below:
[tex]\begin{gathered} \text{Probability of selecting a 10 or a diamond P(10 OR Diamond)=} \\ P(10)+P(\text{Diamond)} \\ \\ \text{But P(10)=}\frac{4}{52} \\ P(\text{Diamond)}=\frac{13}{52} \\ \\ \therefore P(10\text{ OR Diamond)=}\frac{4}{52}+\frac{13}{52}=\frac{17}{52} \end{gathered}[/tex]Thus, the probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
Equation: y =
Write an equation of the line that passes through the given point and is parallel to the given I
(-4, 2); y = 1/4x + 1
Answers
The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
The equation of the line parallel to the line is
y = 1/4 x +1
The slope intercept form is
y = mx + b
Where m is the slope of the line and b is the y intercept
By comparing the given equation and slope intercept form of the line
The slope of the line is m = 1/4
Then the point slope form is
[tex](y-y_1)= m(x-x_1)[/tex]
The line is passing through the point (-4,2)
Substitute the values in the equation
(y-2) = 1/4(x-(-4))
y-2 = 1/4(x+4)
y-2 = (1/4)x+1
y = (1/4)x+3
Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
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Question: Between what two conSecutive integers does v145 fall?{ } { }
Answers
We can find the answer to this question by using the known exact square roots of the following numbers:
[tex]\begin{gathered} \sqrt[]{144}=12 \\ \sqrt[]{169}=13 \end{gathered}[/tex]And as you can see, the number 145 is between 144 and 169.
Thus, its square root, must be between the integer values of 12 and 13.
I need it in slope intercept form and it has to be PERPENDICULAR to the equation it gives.
Answers
The equation of the line in slope intercept form perpendicular to 6x - 2y = 12 and has the same y-intercept is y = - 1 / 3 x - 6
How to find equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to 6x - 2y = 12 and have the same y-intercept.
Hence, perpendicular lines follows the rule below:
m₁m₂ = -1
6x - 2y = 12
6x - 12 = 2y
y = 3x - 6
Hence,
3m₂ = -1
m₂ = - 1 / 3
Therefore, the slope of the line is - 1 / 3.
The y-intercept is -6
Therefore,
the equation of the line is y = - 1 / 3 x - 6
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19. Which repon(s) represent students that enjoy wimming and tennis?TennisSwimmingAFHikingA BBDC. (BAND D)D. IA AND C)
Answers
To determine the regions that represent the students that enjoy swimming and tennis, we need to determine the intersection between the Swimming group and the Tennis group. This intersection is represented by the groups B and D. The correct answer is C.
Maleri Designs sells cartons of cloth face masks ($18) and cartons of hand-sanitizer ($9) on eBay. One of their
customers, Mod World, purchased 21 cartons for $297. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F= Face masks.
Answers
Answer:
F=12 C=9
Step-by-step explanation:
$18 12 times is $216 $9 9 times is $81 $216+81=$297