To find the vector u3 using the Gram-Schmidt process, we start with the given vectors u1 = (1, 2, 1) and u2 = (2, 1, -1). The Gram-Schmidt process involves orthogonalizing each vector with respect to the previous vectors in the set.
Step 1: Normalize u1 to obtain the first orthonormal vector v1.
v1 = u1 / ||u1|| = (1, 2, 1) / √(1^2 + 2^2 + 1^2) = (1/√6, 2/√6, 1/√6)
Step 2: Find the projection of u2 onto v1 and subtract it from u2 to obtain a new vector u2' that is orthogonal to v1.
projv1(u2) = (u2 · v1) * v1 = (2/√6, 4/√6, 2/√6)
u2' = u2 - projv1(u2) = (2, 1, -1) - (2/√6, 4/√6, 2/√6) = (2 - 2/√6, 1 - 4/√6, -1 - 2/√6)
Step 3: Normalize u2' to obtain the second orthonormal vector v2.
v2 = u2' / ||u2'|| = ((2 - 2/√6)/√(1 + (2 - 2/√6)^2 + (1 - 4/√6)^2 + (-1 - 2/√6)^2), (1 - 4/√6)/√(1 + (2 - 2/√6)^2 + (1 - 4/√6)^2 + (-1 - 2/√6)^2), (-1 - 2/√6)/√(1 + (2 - 2/√6)^2 + (1 - 4/√6)^2 + (-1 - 2/√6)^2))
Finally, u3 is the remaining vector after orthogonalizing u3' with respect to v1 and v2. Since u3' is orthogonal to v1 and v2, u3 will also be orthogonal to both v1 and v2. Therefore, u3 can be expressed as u3 = (a, b, c), where a, b, and c are constants to be determined.
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HElp please thanks I’ll give Brainly
Answer:
3
Step-by-step explanation:
its 3 just trust me
HELP I NEED HELP ASAP
Answer:
C
Step-by-step explanation:
the first person's grows in a line/ with a slope and the second persons grows with a growth rate (the percent).
Answer:
C
Step-by-step explanation:
and forvthe explination the other person explained pretty well
Describe the transformation that took place if f(x)=x? became f (x) = 0.2(x - 5)2 – 2
write the fraction in ascending order.
from most to least:
i: 1/2, 1/3, 1/7, 1/10
ii: 2/3, 2/5, 2/9, 2/11
iii: 5/6, 3/4, 2/3, 1/2
iv: 4/5, 3/4, 5/8, 1/2
Tyrone has 16 model airplanes on his shelf. He has 4 times as many model airplanes as model trains. How many model trains does Tyrone have?
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Step-by-step explanation:
4m =16
divide both sides by 4
m = 4
he has 4 model trains
Explain how you can use ratios of the side lengths to find the angle measures of the acute angles in a right triangle.
Answer:
The answer is below
Step-by-step explanation:
Triangles are polygons with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angled triangles.
Trigonometric identities are equations that uses trigonometric functions to show the relationship between the angles in a right angle triangle and the sides of the right angled triangle.
If θ be an acute angle in a right angled triangle, hyp. is the hypotenuse side of the angle, opp. is the opposite side to the angle and adj. is the adjacent side to the angle, then:
sinθ = opp. / hyp.v; cosθ = adj. / hyp. ; tanθ = opp. / adj.
The temperature in Minneapolis changed from -7 °F at 6 A.M. to 7°F at noon. How much did the temperature increase?
Answer:
14 degrees F
Step-by-step explanation:
Answer:
Step-by-step explanation:
from -7 degrees F to 0 are 7 degrees change
from 0 to 7 are also 7 degrees,
in total are 14 degrees in change
the difference of two numbers is 8. their sum is 17. find the two numbers?
9514 1404 393
Answer:
4.512.5Step-by-step explanation:
Let s represent the smaller number. Then s+8 is the larger number, and their sum is ...
s + (s+8) = 17
2s = 17 -8 = 9
s = 9/2 = 4.5
s+8 = 4.5 +8 = 12.5
The two numbers are 4.5 and 12.5.
_____
Comment on problems of this type
A method is shown here for solving the problem using one equation in one variable. The general solution can be seen to be ...
two numbers = (sum ± difference)/2
Here, that is ...
two numbers = (17±8)/2 = (25, 9)/2 = (12.5, 4.5)
Yesterday, Jack drove 45 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for miles per
gallon?
Answer: 36.4mpg
Step-by-step explanation:
45.5 : 1.25 = ? : 1
45.5 ÷ 1.25 = 36.4 mpg
Note- It would mean the world to me if you could mark me brainliest!
I am not a professional, I am simply using prior knowledge! That car also gets excellent gas mileage!
12 + x = - 3 ( 4 – x )
Answer:
x=12
Step-by-step explanation:
12+x=-12+3x
-2x=-24
x=12
Answer:
x=12
Step-by-step explanation:
12+x=-3(4-x)
12+x=-12+3x
2x=24
x=12
Could you please help me? Thank you!
Answer:
steak
Step-by-step explanation:
you can touch the steak
you can eat the steak
you can smell the steak
you can hear the steak sizzle
you watch the steak as it cooks
what is the answer to 2 (r-4)+5(r+2
Answer:
7r + 2
Step-by-step explanation:
I hope this helps have a great day
3) -4b – 9b + 3b ????????????????????????????
Answer: =-10b
Step-by-step explanation:
Let's simplify step-by-step.
−4b−9b+3b
=−4b+−9b+3b
Combine Like Terms:
=−4b+−9b+3b
=(−4b+−9b+3b)
=−10b
Answer:
=−10b
Answer:
-10b
Step-by-step explanation:
-4b-9b+3b
-13b+3b
-10b
Mark can type 20 words a minute.
How many words can be typed in 7.5 minutes?
Answer: if im correct it should be 9,000 words because you have to multiply 7.5 by 60 because you have to convert it to seconds and then you multiply 20 by 450 ( 7.5 * 60 = 450 ) and then you would have 20 * 450 = 9,000
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
20 x 7.5= 150Are the ratios 16:8 and 4:2 equivalent?
help ?? ;;
um i cant find the answer to this question so any answer that makes sense would help !!
Answer: It's the top left because the line passes through 10 on the y axis.
identify the similar triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation.
The triangle KLM and triangle JKM are congruent triangle
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Triangles that are identical in size and shape are said to be congruent triangles. Inferred from this is that the matching sides and angles are equal. Without checking each of the triangles' sides and angles, we may determine whether two triangles are congruent.
Given a triangle LKJ
We have to find similar triangles in the diagram so the corresponding sides and angles have the same orientation.
By the figure given we can write following things:
LK/LJ = MK/JK
LK/JK = MK/MJ
So the triangle KLM ≅ triangle JKM ≅ triangle JLK
Hence the triangle KLM and triangle JKM are congruent triangle
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can earn 5 coins
Which of the following situations are equal to 5? Select all that apply.
A) 25% of 20
B) 10% of 50
C) 10% of 40
D) 50% of 10
E) 50% of 8
Answer:
B) 10% of 50
Step-by-step explanation:
B) 10% of 50hjxhsujwsdvnidfohiefhiedhefbeefuebfeufbeufrbfrgfeufgeudgegdeudgegdej
correct options arere A,B,D
What is UW? For brainliest
Answer:
UW = 5
Step-by-step explanation:
use the altitude rule and set up a proportion:
4/UW = UW/6.25
cross-multiply:
UW² = 25
UW = [tex]\sqrt{25}[/tex]
UW = 5
Square root of 9 + square root of 64?
Answer:
11...................
Answer:
11
Step-by-step explanation:
the sqare root of something is a number x its self ex.
3x3=9 so the sqare root of 9 is 3
and 8x8=64 so the sqare root of 64 is 8
so the simplified equation is 8+3=11
what is 1.4504 rounded to the neareast cent
Answer:
$1.45
When writing about money, you use the two places after the decimal. In the third place, the number is 0 which rounds down.
PLSS HELPPP
FIRST PERSON TO ANSWER GETS BRAINLIEST!!!
Answer:
top angle: 38bottom left: 77bottom right: 65Step-by-step explanation:
Lucy wasn't allowed to have any pets so she collected stuffed animals instead. She had 36 animals total. 3/12 of them were bears and 4/6 of them were dogs. What fraction of the animals were either dogs or bears?
pls help me!!!!!
Look at triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 2, and C at ordered pair 4, 2.
What is the length of side AB of the triangle?
3
5
Square root of 6
Square root of 13
Answer:
pleasss mark me as brainliest answer the answer is on the pic just tap it
Answer:
6 unit squares
Step-by-step explanation:
count the square inside the shape and beside it
help me out pls (math so imp)
Step-by-step explanation:
use the formula to calculate area of triangle.
What is the surface area?
Answer:
i think its 79
Step-by-step explanation:sorry if im wrong because if i am then i did incorrect math
Answer:
152 yards
Step-by-step explanation:
If you look at the rectangular side, the length is 8, and the width is 5.
The area of this side is 40 yd!
Since this is a 3D shape, there are two of that side.
40 times 2 = 80
Next, the triangle side!
The area of a triangle is base times height divided by 2.
So, this triangle is:
6 times 4 divided by 2 = 12
The area of one triangle side is 12, but there's two!
12 times 2 = 24
Lastly, there's a bottom. 6 times 8 = 48.
Now add them up!
152 yards
Hope this helps!
please help I will give Brainlyest
If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points)
Group of answer choices
143
314
14 ⋅ 3.
14 ⋅ 14 ⋅ 14
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Question 23 pts
(06.01)
Simplify the expression 43 + 2(3 − 2). (3 points)
Group of answer choices
14
16
66
68
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Question 33 pts
(06.04)
What is the value of 5 + 3x when x = 4? (3 points)
Group of answer choices
12
17
32
86
Flag this Question
Question 410 pts
(06.02)
Match the verbal expression with its algebraic expression. (10 points)
Group of answer choices
x3
[ Choose ]
b ÷ 3
[ Choose ]
3a
[ Choose ]
y − 3
[ Choose ]
z + 3
[ Choose ]
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Question 52 pts
(06.03)
For the expression y + 6 − 3, determine the coefficient for the variable term. (2 points)
Group of answer choices
0
1
3
6
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Question 66 pts
(06.03)
9(5x + 1) ÷ 3y
From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present." (6 points)
p
0 words
Flag this Question
Question 74 pts
(06.04)
4x + 1 over 3 y2
What is the value of the expression above when x = 2 and y = 3? You must show all work and calculations to receive full credit. (4 points)
hellllllp
Answer:
number one :
volume = LxWxH
as it is a cube all lengths are the same substitute the values in V= 14x14x14
exponent are when you multiply a value by itself for example 2x2 can be written as 2²
in this case , the answer would be option 1.14³
every angle of a equilateral triangle is_____.
PLS HELPPPPP!!!!!!! The probability that a student plays Animal Crossing is 8%. What is the probability that a student does not play Animal Crossing?
Answer:
92%
Step-by-step explanation:
100-8=92
Answer:
91%
Step-by-step explanation:
If 8% is 8 out of 100, then the rest would be 91%, out of 100.
pls help !!!!!!!!!!!!!!