Determine the projection of vector w onto vector u. u=9i-6j, v=-3i-2j, w=19i+15j
Answers
Answer:
\(proj_uw=6.2i-4.2j\)
Step-by-step explanation:
The projection of a vector \(v\) onto a vector \(u\) is defined as the projection of the vector \(v\) on the line that contains the vector \(u\). It can be calculated using the following formula:
\(proj_uv=\frac{u\cdot v}{||u||^2} u\)
Where:
\(u\cdot v\)
Is the dot product between \(u\) and \(v\) which is given by:
\(u\cdot v= $$\sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$$\)
and:
\(||u||\)
Is the magnitude of vector which can be calculated as follows:
\(||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}\)
In this sense, the projection of vector w onto vector u is:
\(proj_uw=\frac{u\cdot w}{||u||^2} u\)
Where the dot product between \(u\) and \(w\) is:
\(u\cdot w =(9*19)+(-6*15)=171-90=81\)
And the magnitude of \(u\) is:
\(||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}\)
Thus:
\(proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.15\rangle\approx6.2i-4.2j\)
Answer:
A on edge
Step-by-step explanation:
Got it right on quiz (:
Related Questions
please help me .......
Answers
Please Help-Explain the first person gets brainliest!!!! URGENNTT!!
Answers
Answer:
a= 6∧7
b= 13
Step-by-step explanation:
first you count how many 6s there are and thats the power
and then for b you find the √169 which basically means 13 x 13
Answer:
a= 6∧7
b= 13
Step-by-step explanation:
A quantity with an initial value of 7200 decays exponentially at a rate of 0.3% every
day. What is the value of the quantity after 10 weeks, to the nearest hundredth?
Answers
Answer:5834.36 You're welcome
Answer:5834.36
Step-by-step explanation:
Mike and his friends bought cheese waters for $4 per packet and chocolate wafers for $3 per packet at a camival. They spent a total of $36 to buy a total of 10 packets of waters of the two varieties
Part A: Write a system of equations that can be solved to find the number of packets of cheese wafers and the number of packets of chocolate wafers that Mike and his friends bought at the camival Define the variables used in the
equations (4 points)
Part B: How many packets of chocolate wafers and cheese wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer
Answers
The system of equations is:
x + y = 10
4x + 3y = 36
The solution is x = 6 and y = 4.
How to write the system of equations?A)
Let's define the variables:
x = number of cheese wafers.y = number of chocolate wafers.We can write the system of equations:
x + y = 10
4x + 3y = 36
Isolate x on the first equation to get:
x = 10 - y
Replace that in the other one:
4*(10 - y) + 3y = 36
40 - 4y + 3y = 36
40 - y = 36
40 - 36 = y
4 = y
And thus, the value of x is:
x = 10 - y = 10 - 4 = 6
They bought 6 cheese wafers and 4 chocolate ones.
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Write the vector (3,9) as a linear combination of the unit vectors i and j.
Answers
The vector (3,9) as a linear combination of the unit vectors i and j is 3 * i + 9 * j
To write the vector (3, 9) as a linear combination of the unit vectors i and j, we need to find the coefficients that multiply the unit vectors to obtain the components of the given vector.
The unit vectors i and j represent the directions of the x-axis and y-axis, respectively. The vector (3, 9) can be expressed as:
(3, 9) = a * i + b * j
where a and b are the coefficients we need to find.
Since the unit vector i corresponds to the x-axis, the coefficient a represents the component of the vector (3, 9) in the x-direction. Similarly, the coefficient b represents the component of the vector (3, 9) in the y-direction.
To find the coefficients, we can equate the corresponding components:
3 = a
9 = b
Therefore, the vector (3, 9) can be written as:
(3, 9) = 3 * i + 9 * j
In this representation, the coefficient 3 indicates that the vector (3, 9) has a magnitude of 3 in the x-direction (i.e., parallel to the x-axis), and the coefficient 9 indicates that it has a magnitude of 9 in the y-direction (i.e., parallel to the y-axis).
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If x= 4, find 2(x + 6)._____
Answers
Answer:
20
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify.
x = 4
2(x + 6)
Step 2: Evaluate
Substitute in x: 2(4 + 6)(Parenthesis) Add: 2(10)Multiply: 20Answer:
20
Step-by-step explanation:
X=4
2(4+6)
2x4=8
2x6=12
12+8=20
For every 7 push-ups Dulce can do, Sara can do 6. If Ducle did 28 push-ups during gym class, how many push-ups did sara do?
Answers
The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.
How to solve ratio?Number of push ups Dulce can do : number of push ups Sara can do
Let
number of push ups Sara does = x
7 : 6 = 28 : x
7/6 = 28/x
cross product
7 × x = 28 × 6
7x = 168
divide both sides by 7
x = 168/7
x = 24
Therefore, Sara does 24 push ups during the gym class.
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how many strings with seven or more characters can be formed from the letters in evergreen
Answers
There are 4,782,905 strings with seven or more characters that can be formed from the letters in "evergreen".
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
The word "evergreen" has 9 letters. To find the number of strings with seven or more characters that can be formed from these letters, we need to count the total number of possible strings of length 7 or more, and then subtract the number of strings of length 6 or fewer.
The total number of possible strings of length 7 or more can be found by summing the number of strings of length 7, 8, 9, and so on. For each length, we can use the formula for counting the number of permutations with repetition:
\(n^r\)
where n is the number of distinct elements (in this case, 9 letters) and r is the length of the string. So the number of strings of length 7 or more is:
\(9^7 + 9^8 + 9^9 + ...\)
To subtract the number of strings of length 6 or fewer, we can sum the number of strings of length 1, 2, 3, 4, 5, or 6, and use the same formula:
\(9^1 + 9^2 + 9^3 + 9^4 + 9^5 + 9^6\)
Finally, we can subtract this sum from the first sum to get the total number of strings with seven or more characters:
\(9^7 + 9^8 + 9^9 + ... - (9^1 + 9^2 + 9^3 + 9^4 + 9^5 + 9^6)\)
This expression can be simplified using the formula for an infinite geometric series:
a/(1-r)
where a is the first term and r is the common ratio. In this case, a = 9⁷ and r = 1/9. So we get:
\(9^7/(1-1/9) - 9^1/(1-1/9)\)
= 4782969 - 9¹ * 8/9
= 4782969 - 64
= 4782905
Therefore, there are 4,782,905 strings with seven or more characters that can be formed from the letters in "evergreen".
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84/96 in the simplest form
Answers
Answer:
7/8
Step-by-step explanation:
So I have 174 assignments, if I complete 4 assignments a week, how many days till I finish my work?
Answers
If you have 174 assignments and complete 4 assignments per week, it would take you 43 weeks to finish your work. That is roughly 294 days, given that there are approximately 7 days in a week.
If this is the actual amount of work you need to complete, I applaud you mate. Good luck.
Hope this helps! Have a good day. :)what structure is indicated by: 10a, 15t, 3g, 7c?
Answers
The structure indicated by: 10a, 15t, 3g, 7c? is a structure related to the composition of a DNA or RNA sequence.
The given information "10a, 15t, 3g, 7c" suggests a pattern or structure related to the composition of a DNA or RNA sequence.
In molecular biology, DNA and RNA are made up of nucleotides, which consist of a nitrogenous base (adenine, thymine/uracil, guanine, or cytosine) and a sugar-phosphate backbone.
Based on the provided data, it appears that the numbers preceding each letter indicate the count or frequency of that particular nucleotide in the sequence.
Therefore, the structure indicated by "10a, 15t, 3g, 7c" implies the composition of a DNA or RNA sequence with the following nucleotide counts:
10 adenine (A) nucleotides (abbreviated as 10a)
15 thymine (T) nucleotides (abbreviated as 15t)
3 guanine (G) nucleotides (abbreviated as 3g)
7 cytosine (C) nucleotides (abbreviated as 7c)
Together, these nucleotides make up a portion of the DNA or RNA sequence, indicating the presence and quantity of each base in that particular section.
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The cost of a fishing pole was $57 last week. This week, the cost fell to $48 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
HELPPPP PLSSSS
Answers
Answer:
15.8%
Step-by-step explanation:
To find the percentage decrease, you can use the formula:
(original cost - new cost) ÷ original cost × 100 = percentage decrease
Plugging in the given numbers:
(57 - 48) ÷ 57 × 100 = 15.8%.
So, the percentage decrease is 15.8%.
Select the correct answer. Which statement is false? А. The inequality sign always opens up to the larger number. O B. The greater number in an inequality is always above the other number on the vertical number line. O C. The smaller number in an inequality is always located to the left of the other number on the horizontal number line. O D. The inequality sign always opens up to the smaller number.
Answers
Answer: D.) The inequality sign always opens up to the smaller number
Answer:
im going to go with D
aircraft a has 136 more seats than aircraft b. if their total number of seats is 606, find the number of seats for each aircraft
Answers
Aircraft a has 371 seats and Aircraft b has 235 seats.
What is a linear equation?A linear equation is an algebraic equation that has highest degree of 1.
The total number of seats in both aircraft is 606.
Assuming aircraft b has x number of sheets.
∴ Aircraft a has (x + 136) number of sheets.
From the question itself we can form a numerical expression which is
x + (x + 136) = 606.
2x + 136 = 606.
2x = 606 - 136.
2x = 470.
x = 470/2.
x = 235.
So, Aircraft b has 235 seats and Aircraft a has ( 235 + 136) = 371 seats.
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Iggy wants to purchase a six-cylinder sports car that costs $15,690. The dealer is offering either a $3,500 instant rebate or 20%-off discount. Which incentive should Iggy use to pay the lowest price for the car?
Step 1: Find the price after rebate.
$12,190
$12,490
$13,190
$12,552
Answers
What is the image point of (-6,-9)(−6,−9) after a translation left 1 unit and down 5 units?
Answers
Answer:
(-7,-4)
Step-by-step explanation:
-6-1=-7
-9-(-5)=-4
Questions 13 - 14 are Squares, use the properties of squares to help you solve.
13. VU=_______
SU=_______
TV=_______
SW=_______
14. m∠EFG=________
m∠GDH=________
m∠FEG=________
m∠DHG=________
Answers
In a square, all angles are 90 degrees, so m∠EFG = m∠FEG = m∠GDH = m∠DHG = 90 degrees.
Here are the solutions to Questions 13 and 14:13.
Since the given figure is a square, all the sides of it are equal and all the angles are 90 degrees.
VU = ST = TV = SW = Side length of the square.
So, VU = ST = TV = SW = 6 inches (Given)14.
Since the given figure is a square, all the angles of it are 90 degrees.
m∠EFG = m∠FEG = 90 degrees (As the angle is formed between a side of the square and the diagonal)
m∠GDH = m∠DHG = 90 degrees (As the angle is formed between a side of the square and the diagonal)So, m∠EFG = m∠FEG
= m∠GDH = m∠DHG = 90 degrees.
To solve questions 13-14, we use the properties of squares.
If a figure is a square, then all the sides are equal, and all the angles are 90 degrees.
The first part of question 13 is to find the sides of the square.
We are given that VU= ST = TV = SW.
Therefore, the side length of the square is 6 inches.
We can use any of the four sides to find the side length. If all sides of the square are given, we could use any of them to find the side length.
The second part of question 13 requires us to find VU, SU, TV, and SW
We have found in the first part that all these sides are equal to 6 inches.
Therefore, VU= SU= TV= SW= 6 inches.
To solve question 14,
we need to find the angles m∠EFG, m∠GDH, m∠FEG, and m∠DHG.
These angles are formed between the side of the square and the diagonal.
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A closed half-plane is the solution of a linear inequality that comes close to the boundary line.
O True
O False
Answers
Answer:false
Step-by-step explanation:
Please help in math!!
Answers
Answer: C
Step-by-step explanation:
Less than or more than without "or equal" means that the dot is not shaded, otherwise it is.
So the answer is C
a business has gross sales of $200,000, sales returns of $1,000, cost of goods sold of $39,000, operating expenses of $40,000, and taxes of 35% what was the net profit
Answers
The net profit is given as follows:
$130,000.
How to obtain the net profit?The total earnings of the company are given as follows:
$200,000 + $1,000 + $39,000 = $240,000.
The expenses are of:
$40,000.
Hence the profit is given as follows:
$240,000 - $40,000 = $200,000.
(subtraction of earnings by expenses).
Considering the taxes, the net profit is 100 - 35 = 65% of $200,000, hence:
0.65 x 200,000 = $130,000.
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the radius of a circle is 4 inches
r=4
Answers
Answer:
Step-by-step explanation:
A soccer club has 560 members. So far, 78
of the members have helped clean up their practice park.
What percent of the members have helped clean up the park?
How many members have helped clean up the park?
Answers
The percentage of members who have contributed to park cleanup will be 87.5%.
There will be 490 members who have helped clean up the park.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
As per the question, So far, 7/8 of the soccer club's 560 members have helped clean up their practice park.
The percentage of members that helped clean up the park will be calculated as :
= 7/8 × 100
= 87.5%
The members that have helped clean up the park will be calculated as :
= 7/8 × 560
Apply the multiplication operation, and we get
= 490 members
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Solve for x.. 5x+18=45
Answers
Answer: x=5.4
Step-by-step explanation:
5x+18=45
-18 on both sides
45-18=27
5x=27
divide 5 on both sides
x=5.4
Answer: x=5.4
Step-by-step explanation:
5x=27
x=5.4
A small cup holds 75% as much as a large cup. If the small cup holds 36 units, how much does the large cup hold?
Answers
Answer:
48
Step-by-step explanation:
75/100 = 36/x
x = 48
Factor completely. (x^2 – 4)(x^2 + 6x + 9)
Answers
This is the same as (x-2)(x+2)(x+3)^2. The order of the factors doesn't matter.
===============================================
Explanation:
x^2-4 factors to (x-2)(x+2) after using the difference of squares rule
x^2+6x+9 factors to (x+3)(x+3) after using the perfect square trinomial factoring rule
So overall, the original expression factors to (x-2)(x+2)(x+3)(x+3)
We can condense this into (x-2)(x+2)(x+3)^2 since (x+3)(x+3) is the same as (x+3)^2
-------------------
Side notes:
Difference of squares rule is a^2 - b^2 = (a-b)(a+b)The perfect square trinomial factoring rule is a^2+2ab+b^2 = (a+b)^2can you help me with this please 2+6f–2+10f
Answers
You just combine the like terms (2,-2) and (6f+10f) and get the answer.
H28−−√ was simplified and the final answer is 87√. What was the value of H in the original question?
Answers
Solution
To solve this problem, we only need to equate and solve for H
\(\begin{gathered} H\sqrt{28}=8\sqrt{7} \\ divide\text{ both sides by }\sqrt{28} \\ H=\frac{8\sqrt{7}}{\sqrt{28}} \\ \\ H=\frac{8\sqrt{7}}{2\sqrt{7}} \\ \\ H=4 \end{gathered}\)
help i have to do this in likee 7 days
Answers
Therefore 16 people could go
What are the 3 linear functions?.
Answers
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
ILL GIVE BRAINLIEST!!!
Let S be a set of 8 points in the plane. Call a circle abundant if it passes through at least 4 points of S.
(a) Show that there can be at most 14 abundant circles.
(b) Can there be 14 abundant circles? If not, what is the maximum number possible?
Answers
(a) To show that there can be at most 14 abundant circles, we can use the combination formula.
(b) There cannot be 14 abundant circles.
To see why, consider that each circle contains 4 points. If there were 14 abundant circles, then there would be a total of 14 * 4 = 56 points involved.
Since a circle abundant if it passes through at least 4 points of S, we can select any 4 points from the set S to form a circle. The number of ways to choose 4 points out of 8 is given by the combination formula:
C(8, 4) = 8! / (4!(8-4)!) = 70
Therefore, there can be at most 70 abundant circles.
However, this count includes some cases where multiple circles pass through the same 4 points. To eliminate these duplicates, we can consider the maximum number of unique sets of 4 points that can form abundant circles.
(b) There cannot be 14 abundant circles.
To see why, consider that each circle contains 4 points. If there were 14 abundant circles, then there would be a total of 14 * 4 = 56 points involved. However, we are given that the set S has only 8 points. Therefore, it is not possible to have 14 abundant circles.
The maximum number of abundant circles can be determined by considering the maximum number of unique sets of 4 points. Since there are C(8, 4) = 70 unique sets of 4 points, the maximum number of abundant circles is 70.
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