Suppose u and v are orthogonal vectors with ||u|| =5 ||u||= 1/2 ||v||, find ||u+v||.
help pleas I will give you 15 points
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
Solve the following complex equation
18+22i=3x-2yi
Answers
Answer:
[tex]this \: a \: complex \: equation \: so \: compare \\ \: real \: term \: and \: imaginary \: term \\ so \\ 18 = 3x \: \: and \: 22i = - 2yi \\ x = \frac{18}{3} \: \: \: \: and \: y = \frac{22i}{ - 2i} \\ x = 6 \: \: \: y = - 11 \\ then \: 6 \times 3 - - 2 \times 11i \\ = 18 + 22i \\ thank \: you[/tex]
What was Veronica's speed if she drove 475 miles in 6 1/4 hours?
Answers
Answer: 76 mph
Step-by-step explanation: speed is distance divided by time so 475 : 6.25 = 76 (mph)
Answer:
76 mph
Step-by-step explanation:
To find the answer, you would divide the miles she drove: 475 by the amount of time it took to get there: 6 1/4 hours. Convert the fraction to a decimal: 1/4= .25 so your problem would look like this...
475 / 6.25 = 76
what is the sum for the 20th row and the 50th row
Answers
Answer:
Step-by-step explanation:
lkj
Write a function C(t) to represent the cost of
renting a canoe for t hours. The rental charge
is $25 plus $2 for every 20 minutes of rental.
Find C(1.5) and describe its meaning.
Answers
Answer:
C(t)=25+2t
C(1.5)=25+2(1.5)=28
$28 for 1.5 minutes rent
A function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t and the cost for 1.5 minutes will be $28.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given that the rental charge is $25 plus $2 for every 20 minutes of rental.
The function formed for the given data will be:-
C(t)=25+2t
At 1.5 minutes the rent will be calculated as below:-
C(1.5)=25+2(1.5)=28
Therefore, the function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t, and the cost for 1.5 minutes will be $28.
To know more about the function follow
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work out the value of v°
Answers
Answer:
v+91=180(being co-interior angle)
v=180-91
v=89,
Answer:
Step-by-step explanation:
v°+120°+91°+(180°-155°)=360°
v°+236°=360°
v°=360°-236°
v°=124°
A company that makes barber scissors has found that the sales volume for barber scissors is directly proportional to the size of the sales force and inversely proportional to the price of the scissors. If 19440 pairs were sold in 2003, when there were 54 salespeople and the price was $20 a pair, what is the sales forecast for the upcoming year with 50 salespeople and a price of $18 a pair?
Answers
Answer:
20,000 pairs of barber scissors.
Step-by-step explanation:
The sales volume V for barber scissors is directly proportional to the size S of the sales force and inversely proportional to the price P of the scissors.
In other words, we can write that:
[tex]\displaystyle V = \frac{kS}{P}[/tex]
Where k is the constant of proportionality.
19,440 pairs were sold in 2013, when there was 54 salespeople and the price was $20 a pair. Hence, V = 19440 when S = 54 and P = 20. Substitute and determine the value of k:
[tex]\displaystyle \begin{aligned} (19440) &= \frac{k(54)}{(20)} \\ \\ 19440 &= \frac{27}{10}k \\ \\ k &=\frac{10}{27}(19440) = 7200 \end{aligned}[/tex]
Hence, our equation is:
[tex]\displaystyle V = \frac{7200S}{P}[/tex]
We want to determine the sales forecast with 50 salespeople and a price of $18 a pair. Hence, S = 50 and P = 18:
[tex]\displaystyle \begin{aligned} V&= \frac{7200(50)}{(18)} \\ \\ &= 20000\end{aligned}[/tex]
In conclusion, 20,000 pairs of barber scissors can be expected to be sold.
The algebraic expression for The quotient of 86 and x
Answers
Answer: 86 ÷ x or 86 / x
Step-by-step explanation:
A quotient is a number that results when one number is divided by another.
Therefore, in order to get the quotient, numbers or terms should process division which the final answer would be quotient.
In the process, [÷ ] or [/] the division signs shall be applied.
The quotient of 86 and x represents 86 divided by x, which the final result would be [tex]\boxed {86/x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
I believe the answer you are looking for is simply just 86÷x or 86/x.
Write an expression that represents the perimeter of the rectangle
below. Write your answer in STANDARD FORM
5x + 2
2.x
Answers
[tex]\\ \sf\longmapsto Area=Length(Breadth)
[tex]\\ \sf\longmapsto Area=(5x+2)2x[/tex]
[tex]\\ \sf\longmapsto Area=10x^2+4x[/tex]
Preparing a glucose solution In a certain medical test
designed to measure carbohydrate tolerance, an adult
drinks 7 ounces of a 30% glucose solution. When the test is
administered to a child, the glucose concentration must be
decreased to 20%. How much 30% glucose solution and
how much water should be used to prepare 7 ounces of
20% glucose solution?
Answers
3.5 ounces hope this helps
Emma jogs 2 miles along the beach in 1/3 of an hour. If she travels at a constant rate, how far will she jog in an hour?
Answers
Answer:
6
Step-by-step explanation:
you do 2 times 3 because you 2 miles is only 1/3 and you want do get the answer for an hour so 2/3 is 6
Answer:
6 miles
Step-by-step explanation:
If emma jogs at a constant rate she will travel 6 miles in 1 hour.
1/3 of an hour times 3 equals 1 hour and the 2 miles every 1/3 times 3 will be 6
hope it helps
Which property is 5+ a = a + 5 ?
Select one:
O a. Commutative Property of Addition
O b. Identity Property of Addition
O c. Commutative Property of Multiplication
O d. Inverse Property of Addition
Answers
Answer:
[tex]commutative \: property \: of \: addition \\ thank \: you[/tex]
The quotient of 31 and the product of a number and - 8?
Answers
Answer:
[tex]\frac{31}{-8n}[/tex]
Step-by-step explanation:
Overall, the expression is a quotient, and you're dividing 31 by whatever the product is of -8 and an unknown number (a variable). The product of -8 and a number means you multiply them together
help me senpai...ahhhhh...plz.... someone
Answers
Answer:
The answer is 3/3 or 1
Step-by-step explanation:
I. If pqr = 1, then 1*1*1 = 1 , so p = 1, q = 1 and r = 1
When [tex]1^{-1}[/tex] = 1
[tex]\frac{1}{1 + 1 + 1}[/tex] + [tex]\frac{1}{1 + 1 + 1}[/tex] + [tex]\frac{1}{1 + 1 + 1}[/tex]
= [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{3}{3}[/tex]
= 1
Hope that help :D
m−4=2m what does m= Please help
Answers
Answer:
-4
Step-by-step explanation:
you would subtract m from both sides to get -4=m
why are there three zeros in the product of 6 times 103
Answers
Answer:
There’s not
Step-by-step explanation:
It’s 618
In 2004 a certain oil company spent sh 1740000 on crude oil import .This was a 20%increase 0ver the money on crude oil import in 2003.
a) How much did the company spend on crude oil import in 2003.
b)What was the difference in the money spent on crude oil import in the two years?
Answers
Answer:
a = 1,450,000
b = 290,000
Step-by-step explanation:
A: 1,740,000 = x*1.20
1,740,000/1.2 = x1.20/1.20
1,450,000 = x
B: 1,740,000 - 1,450,000 = 290,000
John sold a car for 60,000 dollars and made a profit of 20%.what is the cost price of the car
Answers
Answer:
72,000
Step-by-step explanation:
20% of 60,000 = 12,000
60,000 + 12,000 = 72,000
Chow,...!
the degree of the polynomial -5 + 3x^6 + 2x^5 + 6x^3 is
Answers
Answer:
6
Step-by-step explanation:
As the highest power of x in the expression is 6, the degree is 6
Answer:
3x6+2x5+6x3−5
Standard Form
Step-by-step explanation:
HAVE A BLESS DAY :D
how do I solve -2a = -24
Answers
Answer:
12
Step-by-step explanation:
you would divide -2 on both sides to isolate the variable a leaving you with 12
Answer:
12
Step-by-step explanation:
-2a= -24
or, a= -24/-2
:. a= 12
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y = 3/4m + 2
Step-by-step explanation:
Distance from point 1 to point 2 is up 3, over 4
Point 1 intercepts (0, 2).
8 - 4s = s + 13
what is s?
Answers
Answer:
-5s = 5
S= - 1
Step-by-step explanation:
Udndkdjdndjxbdnekdjdndkdjdjd
Because 8-4s=s+13
-8+4s= -8
-4s= s+5
+4s=+4s +5
5 divided by 5 gives you positive 1. Hope this helps
if f(X+4) =3x+4 , then find the value of f(4)
please explain it clearly .
Answers
[tex]\\ \sf\longmapsto f(x+4)=3x+4[/tex]
[tex]\\ \sf\longmapsto f(x)=3x+4-4[/tex]
[tex]\\ \sf\longmapsto f(x)=3x[/tex]
Now
[tex]\\ \sf\longmapsto f(4)[/tex]
[tex]\\ \sf\longmapsto 3(4)[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
Which expression has a value of 13?
(12+6)÷3+3
12+6÷(3+3)
12+(6÷3+3)
(12+6)÷(3+3)
Answers
Answer:
Option b 12+6÷(3+3)
Step-by-step explanation:
12+6÷(3+3)
= 12+6÷6
= 12+1
= 13
You are making spaghetti for dinner. You have the choice of marinara, alfredo, or meat sauce, 4 different shaped noodles, and 2 kinds of cheese. How many different spaghetti dinners can you make?
Answers
Answer:
DCC
Step-by-step explanation:
CDDCDC
Different type of spaghetti dinners is 8
What is combination ?
"The number of possible arrangements in a collection of items where the order does not matter."
For 4 different shaped of noodles = ⁴c₁
⁴c₁ = 4
For two kinds of cheese = ²c₁
²c₁ = 2
Now , multiplying these 4×2 = 8
Hence, 8 type of spaghetti dinners
For more about combination
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Simplify root 20 divided by root 5
Answers
Answer:
2
Step-by-step explanation:
√20 ÷ √5
√20/√5
=> √(20/5)
=> √4
=> 2
help!! this is math.
Answers
Answer:
2,78,31,64,4-2,10-6,54,-97,-38,-8-7,-4-5,-11-1,-16(b) Eric removed 72 fish from his pond over a period of 9 days. He removed the same number of
fish each day, What was the change in the number of fish in the pond each day?
fish
FASTEST WIL BE THE BRAINLIEST
Answers
Answer:
-8
Step-by-step explanation:
72 ÷ 9 = 8
The fish are being taken out, so negative.
I hope this helps!
pls ❤ and mark brainliest pls!
Tìm x để có 1 mệnh đề đúng và 1 mệnh đề sai : x<1/x
Answers
Answer:
x < 0 : 1/2 < 1 ÷ 1/2 ↔ 1/2 < 2 (đúng)
x > 0: 2 < 1/2 (sai)
Step-by-step explanation:
cos a/4= -1/4
cos a= ??
Answers
Answer:
cos a / 4 = -1/4
--->cos a =- 1
Pls help on the top question
Answers
Answer:
-13=5×1+5×4m-2m
-13=5+20m-2m
-13-5=18m
-18=18m
18m=-18
m=18÷18
m=1
Answer:
[tex]\frac{55}{4}[/tex]
Step-by-step explanation:
let the number be n the multiply by - 4 is - 4n and add 5 gives
- 4n + 5 = - 50 ( subtract 5 from both sides )
- 4n = - 55 ( divide both sides by - 4 )
n = [tex]\frac{-55}{-4}[/tex] = [tex]\frac{55}{4}[/tex]
The number is [tex]\frac{55}{4}[/tex] or 13.75 if you prefer
