Suppose u and v are orthogonal vectors with ||u|| =5 ||u||= 1/2 ||v||, find ||u+v||.
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Answers
Answer: 5*sqrt(5)
This is the same as sqrt(125).
It approximates to roughly 11.1803
=========================================================
Explanation:
Vector u is 5 units long as indicated by the notation ||u|| = 5. Some math books would say |u| = 5, and it's the same thing. The double bars are probably more fitting because it helps emphasize we're looking for the length of a vector and we're not using absolute value bars.
The second equation ||u|| = (1/2)*||v|| can be rewritten into ||v|| = 2*||u|| telling us that vector v is twice as long compared to vector u. Since vector u is 5 units long, that must mean vector v is 10 units long.
vector u = 5 units longvector v = 10 units longThe two vectors are orthogonal, i.e. they are perpendicular. The vector u+v represents the diagonal of the rectangle as shown below in the attached image. Vector u is horizontal, v is vertical, and u+v is the diagonal. Technically we don't know where vector u is pointed along a compass (it may or may not be pointing directly east), but I find it's easier to have it set up like this. The answer will be the same regardless of where vector u is pointed. Rotations don't affect vector lengths.
We can see that vector u+v effectively breaks down component-wise into the horizontal component u and vertical component v (think of them as x and y components respectively).
Furthermore, note how there are two right triangles that form when we draw in the diagonal of the rectangle.
To find the length of vector u+v, we apply the pythagorean theorem.
a^2+b^2 = c^2
( ||u|| )^2 + ( ||v|| )^2 = ( ||u+v|| )^2
( 5 )^2 + ( 10 )^2 = x^2
25 + 100 = x^2
125 = x^2
x^2 = 125
x = sqrt(125)
x = sqrt(25*5)
x = sqrt(25)*sqrt(5)
x = 5*sqrt(5) is the length of vector u+v
In other words, ||u+v|| = 5*sqrt(5)
Keep in mind that this trick using the pythagorean theorem only works when vectors u and v are orthogonal. The process to find ||u+v|| for non-orthogonal vectors u,v is a bit more complicated.
Related Questions
I need help dont just add both numbers ill give extra hundrend after you answer
Answers
Answer:
28
Step-by-step explanation:
According to the question,
2 helmets and 1 football cost $80, while 1 helmet and 2 football cost $76
Let x represent cost of football and let y equal cost of helmet.
Write the system of equations,
[tex]x +2 y = 80[/tex]
[tex]2x + y = 76[/tex]
Eliminate the x variable by multiplying the top equation by -2
[tex] - 2x - 4y = - 160[/tex]
[tex]2x + y = 76[/tex]
Add both equations.
[tex] - 3y = - 84[/tex]
[tex]y = 28[/tex]
So one helmet cost $28
How do you simplify a fraction with a denominator of a variable like this
6x/x
Answers
Step-by-step explanation:
The x's will simply cancel each other out and you will be left with a 6
hope it makes sense
:)
find x step by step
Answers
Answer:
[tex] \frac{4 + (x + 1)}{x + 1} = \frac{16}{12} \\ \\ \frac{5 + x}{x + 1} = \frac{16}{12} \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11[/tex]
Answer:
x = 11 cm
Step-by-step explanation:
Segments DE and BC are parallel (that's what the arrows tell you), so there are two similar triangles formed.
[tex]\triangle{ADE} \sim \triangle{ABC}[/tex]
Corresponding sides are in proportion, so
[tex]\frac{AD}{AB}=\frac{12}{16}[/tex]
The length of AB is (x + 1) + 4 = x + 5, and 12/16 simplifies to 3/4, so
[tex]\frac{x+1}{x+5}=\frac{3}{4}[/tex]
"Cross multiply" to get
[tex]4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11[/tex]
can someone please help me with this?
Answers
Answer:
These are the missing numbers
Sec1
A. 12, 29/2, 17 (arithmetic)
C. 3/16, 3/32, 3/64 (geometric)
D. 17, 33, 65 (neither)
Sec2
A. 8, 48 (growth)
B. 16, 32 (growth)
C. 1, 2 (rate)
Step-by-step explanation:
Section 1
A. add by 2.5 or 5/2
C. multiply by 1/2
D. double the value-added
Section2
A & B. multiply by 2
C. add 1/2
What is the area of a triangle if height is 4cm find the base also plsss help me please
Answers
Answer:
This is the formula u can use but the parameters are not complete
Step-by-step explanation:
b=2 A/h
Answer:
8 cm^2.
Step-by-step explanation:
Area = 1/2 * base * height
= 1/2 * 4 * 4
= 8.
NẾU BẠN BÌNH CÓ 34 QUẢ TÁO, BẠN AN LẤY ĐI TỔNG CỘNG 23 QUẢ. HỎI AN CÓ BAO NHIÊU QUẢ TÁO
Answers
Answer:
Bạn An có 23 quả táo
Step-by-step explanation:
Vì AN lấy đi 23 quả táo nên số táo vẫn bằng như thế
hey please help i’ll give brain
Answers
Hi ;-)
[tex]3\cdot\boxed9=9\cdot3[/tex]
Answer:
3 × 9 = 9 × 3
Step-by-step explanation:
Is 15.7 an integer ,whole number,natural number
Answers
Explanation:
A marathon is a 26-mile race. An athlete is running a marathon that eventually finishes at a local high school. After x minutes, the distance the athlete is from the school is given by y(in miles), where x+10y=260
If the runner ran for 40min from the start line, what is the remaining distance between the runner and the school?
Answers
Step-by-step explanation:
by deleted user on here.
I'm backk!! School has officially started... here we go again
+*♡ FREE QUESTION!! ♡*+
Answers
congrats? Im not sure what to say.
PLEASE HELP FAST
bx = -5
Answers
which of the following equations represents the graph below
Answers
Answer:
Step-by-step explanation:
answer B
since for all real positive r, r^x >0
The unique function who give a negative answer is f(x)=-3* 2^x
4 ÷ 1 1/8 Answer must be in simplest form
Answers
Answer:
4÷ 1 1 /8 = 32 /9 = 3 5 /9
a father has 4,500 naira to distribute among his children how much would a child with 30percent share get. how much would a child with 45percent get
Answers
Answer:
30%=1350
45%=2025
Step-by-step explanation:
30% of 4500 = 0.30 × 4500
=1350
45% of 4500 = 0.45 × 4500
=2025
In how many days could 20 boys do a peice of work which 25 boys can do in 32 days ?
Answers
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will mark brainliest please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
32 dollar
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
$32
Step-by-step explanation:
4 weeks = a month
So add all of the money in the 4 weeks and then estimated
$7.88 + $7.75 + $8.02 + $7.97 = 31.62
Round 31.62 to the nearest whole number
$32
Bananas are $0.59/pound what is the constant of proportionality?
Answers
Answer:
Step-by-step explanation:
y = k x
Total cost = y
number of pounds = x
constant = 0.59
Equation
y = 0.59 x
A car traveling 55.0 miles per hour. Convert this to meters per second.
Answers
Answer:
24.587
Step-by-step explanation:
divide the speed value by 2.237
(x-2)/(x+1)=1/2 . find x
Answers
Answer:
x=5
Step-by-step explanation:
(x-2)/(x+1)=1/2, we use that a/b = c/d is the same as a*d = c*b
2*(x-2) = 1* (x+1), distribute multiplication over subtraction
2x -4 = x +1 , subtract x and add 4 to both sides
2x -x = 1 +4, combine like terms
x = 5
Answer: x = 5
Solve:
Given
(x - 2) / (x + 1) = 1/2
Cross multiply applied
1 (x + 1) = 2 (x - 2)
Expand parentheses and apply the distributive property
x + 1 = 2x - 4
Add 4 on both sides
x + 1 + 4 = 2x - 4 + 4
x + 5 = 2x
Subtract x on both sides
x + 5 - x = 2x - x
x = 5
Check:
Left-hand side = (x - 2) / (x + 1) = (5 - 2) / (5 + 1) = 3/6 = 1/2
Right-hand side = 1/2
1/2 = 1/2
Hope this helps!! :)
Please let me know if you have any questions
a) If 8 workers can complete a piece of work in 18 days, how many workers are required to complete the work in 12 days? b) 20 labourers comnloto the . 1 T
Answers
Answer:
12 workers are required to complete the work in 12 days
Which answer choice correctly shows 450 written as a Roman numeral?
A. CCCCL
B. DMC
C. DCL
D.CDL
Answers
Answer:
D.(CDL)
Step-by-step explanation:
Answer:
CDL
Step-by-step explanation:
C is 100
D is 500
500-100=400
L is 50
400+50=450
Name a pair of adjacent complementary angles
Answers
9514 1404 393
Answer:
∠LJM and ∠MJN
Step-by-step explanation:
Ray JL forms a pair of right angles at J on line KN. Ray JM divides one of those right angles into two adjacent angles with a sum of 90°. Those two angles are adjacent complementary angles. They are ...
∠LJM and ∠MJN
Ted mixed together 3 gal. of Brand A fruit
drink and 6 gal. of Brand B fruit drink
which contains 20% fruit juice. Find the
percent of fruit juice in Brand A if the
mixture contained 25% fruit juice.
Answers
Answer:
The mixture for Brand A fruit is 5%.
How do write nine billion, seven hundred million, forty-five thousand, three hundred six in standard form
Answers
Answer:
9,700,045,306
Step-by-step explanation:
there you go!
Step-by-step explanation:
nine billion, seven hundred million, forty-five thousand, three hundred six
9,700,045,306
simplify the following ；giving your answers in index form
Answers
Answer:
[tex] \frac{ {6}^{10} }{ {6}^{3} } \\ = \frac{ {6}^{3} \times {6}^{7} }{ {6}^{3} } \\ = {6}^{7} \\ thank \: you[/tex]
[tex]f(x) = 2x^{2} +5x-2[/tex]
Answers
Answer:
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 5x - 2[/tex]
[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x) - 2[/tex]
[tex]f(x) = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]
[tex]f(x) + 2 \times \frac{25}{16} = 2( {x}^{2} + \frac{5}{2} x + \frac{25}{16} ) - 2[/tex]
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - 2 - \frac{25}{8} [/tex]
[tex]f(x) = 2(x + \frac{5}{4} {)}^{2} - \frac{41}{5} [/tex]
what is 2 ÷ 3 = as a fraction???
Answers
Answer:
[tex]2 \div 3 \\ \frac{2}{3} [/tex]
Find the measures of unknown angles.
Answers
Answer:
hope this helps you
god bless you
plz help!! will mark brainliest
Answers
Step-by-step explanation:
x + 4 + 3x = 72 Let's agroup all the x
4x + 4 = 72 Subtract 4 on both sides
4x = 68 Divide both sides by 4
x = 17
x + 3 + x – 8 + x = 55 Let's agroup all the x
3x + 3 – 8 = 55 Solve 3 – 8
3x – 5 = 55 Add 5 on both sides
3x = 60 divide both sides by 3
x = 20
How do you make these diagrams??
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Answer:
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