To verify that { ¯ u1, ¯ u2 } forms an orthogonal set, we need to show that their dot product is zero. Let ¯ u1 = and ¯ u2 = . Then, their dot product is:
¯ u1 · ¯ u2 = a1a2 + b1b2 + c1c2
If this dot product is zero, then the vectors are orthogonal. So, we need to solve the equation:
a1a2 + b1b2 + c1c2 = 0
If this equation is true for our given vectors ¯ u1 and ¯ u2, then they form an orthogonal set.
To find the orthogonal projection of ¯ v onto w = span{ ¯ u1, ¯ u2}, we can use the formula:
projw ¯ v = ((¯ v · ¯ u1) / (¯ u1 · ¯ u1)) ¯ u1 + ((¯ v · ¯ u2) / (¯ u2 · ¯ u2)) ¯ u2
where · represents the dot product.
So, we first need to find the dot products of ¯ v with ¯ u1 and ¯ u2, as well as the dot products of ¯ u1 and ¯ u2 with themselves:
¯ v · ¯ u1 = av a1 + bv b1 + cv c1
¯ v · ¯ u2 = av a2 + bv b2 + cv c2
¯ u1 · ¯ u1 = a1 a1 + b1 b1 + c1 c1
¯ u2 · ¯ u2 = a2 a2 + b2 b2 + c2 c2
Then, we plug these values into the formula to get the projection:
projw ¯ v = ((av a1 + bv b1 + cv c1) / (a1 a1 + b1 b1 + c1 c1)) ¯ u1 + ((av a2 + bv b2 + cv c2) / (a2 a2 + b2 b2 + c2 c2)) ¯ u2
This is the orthogonal projection of ¯ v onto w.
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Mariana is painting her new bedroom purple. She has decided to mix her own purple paint. To create the shade of purple she likes best, she must maintain a ratio of 5 ounces red to 6 ounces blue. If she has 21 ounces of blue paint, how much red paint will she need?
Answer:
Red paint needed = x = 17.5 ounces
Step-by-step explanation:
Ratio of red to blue paint = 5 ounces : 6 ounces
If she has 21 ounces of blue paint, how much red paint will she need?
Ratio of red to blue paint = x ounces : 21 ounces
Equate the ratios
5 : 6 = x : 21
5/6 = x/21
Cross multiply
5*21 = 6*x
105 = 6x
x = 105/6
x = 17.5 ounces
Red paint needed = x = 17.5 ounces
HELP PELASE ASAPppppp
Answer:D
Step-by-step explanation:
What is the area of this?
Answer:
Step-by-step explanation:
[tex]A=\frac{hb}{2}\\ \\ A=\frac{14(20)}{2}\\ \\ A=140ft^2[/tex]
Answer:
150 ft
Step-by-step explanation:
You use Pythagoras theorem to work out the base of the triangle.
<3
Help please! Thank youuuuuuuuu
Answer:
3 3/5 meters (B)
Step-by-step explanation:
Since this is perimeter, you must find the "outside".
The top side: 1/4 * 4 = 1
Left side: 1/5 * 4 = 4/5
Bottom: 1
Right side: 4/5
Add them up!
1 + 1 + 4/5 + 4/5
2 8/5
3 3/5
B!
Determine a quadratic equation in standard form that has each pair of roots.
X=5±√2/3
Step-by-step explanation:
you have to add 5 and 2 which is 7 and decide by 3 or estimate
Order the values of the differences from least to greatest. First, write the fractions as decimals. StartFraction 4 Over 5 EndFraction is and Negative 1 and one-half is . Next, plot the numbers on the number line. The greatest number is . Using the students' names, the correct order is .
Complete Question:
Ms. Perez's biology class grew sunflowers to learn about plants. During the first week, the average sunflower grew 3 inches. The table shows the difference from the average for three students.
Order the values of the differences from least to greatest.
Student: Raj. Difference (in.): 4/5
Student: Clara. Difference (in.): -1 1/2
Student: Jacob. Difference (in.): 0.9
Answer:
[tex]-1.5[/tex], [tex]0.8[/tex] and [tex]0.9[/tex]
The greatest is: 0.9
By student names: Clara, Raj and Jacob
Step-by-step explanation:
See comment for complete question
Given
Differences:
[tex]\frac{4}{5}[/tex], [tex]-1\frac{1}{2}[/tex], [tex]0.9[/tex]
Required
Order from least to greatest
We have: [tex]\frac{4}{5}[/tex], [tex]-1\frac{1}{2}[/tex], [tex]0.9[/tex]
First convert fractions to decimal
[tex]\frac{4}{5} = 0.8[/tex]
[tex]-1\frac{1}{2}= -1.5[/tex]
[tex]-\frac{3}{4} = -0.75[/tex]
So, the differences become:
[tex]0.8[/tex], [tex]-1.5[/tex], [tex]0.9[/tex]
Now arrange from least to greatest
[tex]-1.5[/tex], [tex]0.8[/tex] and [tex]0.9[/tex]
From the above representation,
The greatest is: 0.9
By student names, we have:
Clara, Raj and Jacob
This is done by simply replacing the numbers with the student name.
See attachment for number line
Answer:
4/5 is 0.8 , -1 1/2 is -1.5 , The greatest number is 1.3 , mia, raj, clara, jacob
Step-by-step explanation:
Simplify.
[tex]\frac{8\sqrt{6mn} + 6\sqrt{8mn} }{2\sqrt{2mn} }[/tex]
Which expression is equivalent to 5x² + 4x - 2?
a- (5x-1)(x+2)
b- (5x+1)(x-2)
c- (5x+1)(x+2)
d- none of these
Answer:
D because non of them work lol
Step-by-step explanation:
Hope this Helped
What is 2/3 divided by 6/12? REDUCE ANSWER TO SIMPLEST FORM.
Answer:
1 1/3Step-by-step explanation:
To divide fractions, multiply by the reciprocal.
So we have:
2/3 x 12/6 = 24/18 = 4/3 = 1 1/3
How far is the star away from
the earth in AU?
Answer:
6623 AU
Step-by-step explanation:
I assume the angle measure 0.000302 is in radians.
Draw a segment from the Sun to the Star.
Use the upper small triangle.
The angle at the Star measures 0.000151 radians.
The opposite leg measures 1 AU.
We need the hypotenuse which is the distance from the Star to Earth.
sin A = opp/hyp
sin 0.000151 rad = 1/x
x sin 0.000151 rad = 1
x = 1/(sin 0.000151 rad)
x = 6623
Answer: 6623 AU
The ratio of dimes to quarters in a money bag is 12.2. If there are 8 quarters. How many dimes are there?
Answer:
98
Step-by-step explanation:
Given: The ratio of dimes to quarters in a money bag is 12.2
Also, there are 8 quarters.
To find: Number of dimes
Solution:
Number of dimes : Number of quarters = 12.2
Number of dimes : 8 = 12.2
Therefore,
Number of dimes = 12.2 × 8 = 97.6 ≈ 98
OMG, GUYSS please helppp this is due in like.. 10 mins.. will give brainliest, please also add an explanation... THANKYOU I LOVE YOU!!!!
House builders unload a large crate of bricks onto the bed of a truck. The bottom of the crate measures 1.0 m by 2.0 m, and the crate weighs 38 000 N. What pressure does the crate exert on the bed of the truck?
Answer:
19,000 pa.
Step-by-step explanation:
I hope this helps
(3a+2.5b)^2=9a^2+6.25b^2+*
Please help before Thursday
Step-by-step explanation:
We have (x + y)² = (x + y)(x + y) = x² + 2xy + y².
Let x be 3a and y be 2.5b.
Therefore (3a + 2.5b)²
= (3a)² + 2(3a)(2.5b) + (2.5b)²
= 9a² + 15ab + 6.25b².
Hence the '*' sign should be replaced with 15ab.
Answer:
Given that, ( 3a + 2.5b )² = 9a² + 6.25b² + *
We know that, ( x + y )² = x² + y² + 2xy
According to the above problem, we get
( 3a + 2.5b )² = (3a)² + (2.5b)² + (2×3a×2.5b)
( 3a + 2.5b )² = 9a² + 6.25b² + 15ab
Therefore,
The sign " * " should be 15ab.
15ab is the right answer.[
1
What is the distance between the points (-4, -8) and (10,-8)?
Need help
Answer:
2
Step-by-step explanation:
√(-8-8)^2 +(10+4)^2=
✓-32+28
✓4
=2
Other equipment totaled 33000. You earn a commission of 20% on every sale you make. If you put 35% of your earnings on this particular sale into a savings account what is the amount invested
9514 1404 393
Answer:
2310
Step-by-step explanation:
Assuming "this particular sale" totals 33000 in its entirety, the commission is ...
20% × 33000 = 6600
The amount of that going to the savings account is ...
35% × 6600 = 2310
The amount invested is 2310.
✓3 correct to 5 decimal places
Answer:
1,73205
Step-by-step explanation:
First, count out the five decimal places, and then look at the sixth place:
[tex]\sqrt{3}[/tex] ≈ 1,73205 | 0807...
The sixth decimal is less than 5, so we round to the smaller side.
find the measure of the angle
PLEASE HELP!!!
I-ready!
Answer:
35,.......,..............
help find value of y please
Answer:
The third option
Step-by-step explanation:
60+y=180
y=120
Answer:
y = 120
Step-by-step explanation:
Having trouble solving this:
Answer:
1/250
Step-by-step explanation:
0.4% in fraction form is 0.004
or 4/1000
4/1000 reduced to it's simplest form is 1/250 (divide numerator and denominator by 4)
solve for x or find x
the answer is x= 4
AB and CD are the same length
8x-1 =31
8x=32
x=4
Which point on the number line has the greatest absolute value? 1.P (-6) 2. Q (-2) 3. R (1) 4. S (5)
Answer:
P(-6)
Step-by-step explanation:
1.P (-6) 2. Q (-2) 3. R (1) 4. S (5)
The absolute value of a number disregards ir removed the negative sign from the number and treats as positive.
The absolute value of the numbers given in the option above :
P(-6) = |6|
Q(-2) = |2|
R(1) = |1|
S(5) = |5|
Hence, the option which has the greatest absolute value when arranged on a number line is |6|
Harry and his family travel 204 miles in 3.4 hours. If they continue at this constant speed, how long will it take them to travel 420 miles?
Answe
7
Step-by-step explanation:
204 dived by 3.5
i did 204 dived by 60 then
420 dived by 60
The time taken by the family to reach is T = 7 hours
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed be represented as S
Now , the value of S is
S = D / T
speed = distance / time = 204 miles / 3.4 hours = 60 miles per hour
where , the distance D = 420 miles
And , T = 420 / 60
T = 7 hours
Hence , the time taken for 420 miles is 7 hours
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The perimeter of the triangular park shown on the right is 15x-2 what is the missing length
Answer:
missing length is 6x - 1
Step-by-step explanation:
To find missing length, add two known sides and subtract from perimeter
(15x - 2) - (4x + 4 + 5x - 5)
(15x - 2) - (9x - 1) = 6x - 1
What is the solution to the system of equations below?
y = two-fifths x minus 3 and x = –10
Answer:
y = 1
Step-by-step explanation:
Substitute -10 for x so the equation would be y=2/5-10-3
that would then be y=4-3
which would equal 1
40 percent of what is 524
Answer:
1310
Step-by-step explanation:
Answer:
7.63
(Hope this helps! Btw, I am the first to answer.)
Julie earns $9 each week as an allowance. If she spends $5 each week for lunch money and saves the rest, which expression shows how much money she will save in x weeks?
Answer:
(x)4
Step-by-step explanation:
(x) is the amount of weeks and 4 is the amount of money that is saved every week.
What is the value of x?
Answer:
jhg hstu35kk4t6ek
3tnk63e6oktelrt
Step-by-step explanation:
4n5kdti3eo5
if Ralf can bike in 45 kilometers in 3 hours,what will be his average rate of biking
A.9 kilometers/h
B.12 km/h
C.15 km/h
D.20 km/h
Answer:
C.15 km/h
Step-by-step explanation:
speed= distance/time
The coordinates of one endpoint of a line segment are (4,-12). The length of the segment is 5 units. Determine four coordinates that could serve as the other endpoint of the given line segment.
Answer:
Step-by-step explanation:
Since we are given the starting position of the line segment and the length we can simply add or subtract the total length of the line segment to the x or y starting position. This would give us all the possible endpoints that are exactly 5 units away from the starting position in every direction. We can either add or subtract because this would give us the left, right, up, and down directions from the starting position. After making these changes we are left with the following four possible endpoints.
(-1 , -12)
(9 , -12)
(4, -17)
(4, -7)
For a school fundraiser, Troy sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50.
What was the cost of a bag popcorn?
A. $10.35
B. $6.00
C. $6.27
D. $6.50
Answer:
Cost of a bag popcorn = $6.5
Step-by-step explanation:
Given:
Number of popcorn bags sold by Troy = 28
Number of candy bar sold by Troy = 40
Number of popcorn bags sold by Jake = 17
Number of candy bar sold by Jake = 20
Amount Troy earn = $282
Amount Jake earn = $160.5
Find:
Cost of a bag popcorn
Computation:
Assume;
Cost of a bag popcorn = a
Cost of a candy bar = b
28a + 40b = 282..........eq1
17a + 20b = 160.5...............eq2
eq2 x 2
34a + 40b = 321.........eq3
eq3 - eq1
6a = 39
a = 6.5
Cost of a bag popcorn = $6.5