To solve problem 6, we first need to find the orthogonal projection of y onto u. To do this, we use the formula for the projection of a vector y onto a vector u: proj_y = (y·u)/(u·u) * u. . Plugging in y = -2 and u = [2, 1],
Calculate the dot products: y·u = (-2)(2) + 0(1) = -4 and u·u = (2)(2) + (1)(1) = 5.
Next, we need to compute the distance d from y to the line through u and the origin. To do this, we first find the vector v that connects the point y to the line through u and the origin. We do this by subtracting the projection of y onto u from y: use the formula: d = ||y - proj_y||.
y - proj_y = [-2 - (-8/5), 0 - (-4/5)] = [2/5, 4/5].
Finally, we find the length of v, which is equal to the distance d: d = √[(2/5)^2 + (4/5)^2] = √(20/25) = √(4/5) = 2/√5.
In conclusion, the orthogonal projection of y onto u is [-8/5, -4/5], and the distance from y to the line through u and the origin is 2/√5.
To know more about vector visit:
https://brainly.com/question/13322477
#SPJ11
CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3.
A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4
I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.
Answer:
B. v(t) = sin(t) + cos(t) + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Function NotationCalculus
Antiderivatives - Integrals
Integration Constant C
Solving Integration Equations
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.
[tex]\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt[/tex]
Step 1: Define
a(t) = cos(t) - sin(t)
v(0) = 3
Step 2: Integrate
Set up integral: [tex]\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt[/tex][integral] Rewrite [Integration Property - Subtraction]: [tex]\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt[/tex][Integral] Trig integration: [tex]\displaystyle v(t) = sin(t) - [-cos(t)] + C[/tex][Velocity Integration] Simplify: [tex]\displaystyle v(t) = sin(t) + cos(t) + C[/tex]Step 3: Find Function
We need to solve for the entire function, meaning we need to find constant C.
Substitute in given point [Velocity Integration]: [tex]\displaystyle v(0) = sin(0) + cos(0) + C[/tex][Velocity Integration] Substitute: [tex]\displaystyle 3 = sin(0) + cos(0) + C[/tex][Velocity Integration] Evaluate trig: [tex]\displaystyle 3 = 0 + 1 + C[/tex][Velocity Integration] Add: [tex]\displaystyle 3 = 1 + C[/tex][Velocity Integration] Isolate C [Subtraction Property of Equality]: [tex]\displaystyle 2 = C[/tex][Velocity Integration] Rewrite: [tex]\displaystyle C = 2[/tex][Velocity Function] Substitute in C [Velocity Integration]: [tex]\displaystyle v(t) = sin(t) + cos(t) + 2[/tex]Topic: Calculus
Unit: Basic Integration
Book: College Calculus 10e
What is the slope of the line that connects the points (0.5, 4.5) and (1.5, 2.5)?
Answer:
Slope is -2
Step-by-step explanation:
Question: 2 out of 10
~!¡! Volume !¡!~
(Pleaaase go try to answer the first one- )
Answer:
B) 2,340
Step-by-step explanation:
Two supplementary angles are in the ratio of 5 to 7. Find positive difference of the measure of the two angles. Do the same problem, only do it for complementary angles instead of supplementary angles.
Answer:
30° is the difference if they are supplement
15° is the difference if they are complementary
Step-by-step explanation:
Let 5x = the measure of the smaller angle
and 7x = the measure of the larger angle
If they are supplementary, then 5x + 7x = 180
12x = 180
x = 15
5x = 5(15) = 75 = the measure of the smaller angle
7x = 7(15) = 105 = the measure of the larger angle
105 - 75 = 30 = difference of the measures
Now, if they are complementary, then 5x + 7x = 90
12x = 90
x = 7.5
5x = 7(7.5) = 37.5 = the measure of the smaller angle
7x = 7(7.5) = 52.5 = the measure of the larger angle
52.5 - 37.5 = 15 = difference of the measures
The church's goal for the fundraiser was $18,000. They exceeded their goal by 8%. How much money did they raise?
Answer:
Step-by-step explanation:
18000(1+8/100)
18000(108)/100
19440
A Train crosses a bridge 100 m in 45 sec at a speed of 60 km/h find a time taken by the train to cross a clock tower
Ans is 351/8.
hope it is helpful
Choose the correct description of the graph of the compound
inequality (1 point)
x -3 <-11 or x + 5 2 14,
• A number line with a closed circle on 8, shading to the left, and
an open circle on 9, shading to the right
A number line with an open circle on
8, a closed circle on 9, and
shading in between
O A number line with an open circle on -8, shading to the left, and
a closed circle on 9, shading to the right
A number line with a closed circle on -8, an open circle on 9, and
shading in between
Answer:
A number line with a closed circle on -8, an open circle on 9, and shading in between
I need help with math
Answer:
0,-2 0,-5
2,-3 1,-4
Step-by-step explanation:
what number makes this equation true?
7 x ? = 8 3/4
Answer:
1 1/4 or 1.25
Step-by-step explanation:
7 x ? = 8 3/4
(8 3/4) / 7 = 1 1/4
Rectangle A has a length of 6 and width of 4. Rectangle A prime has a length of 9 and width of 6. Find the scale factor of the dilation shown. 1/2 3/2 2 2/3
Answer: The scale factor of the dilation [tex]=\dfrac32[/tex]
Step-by-step explanation:
[tex]\text{Scale factor}=\dfrac{\text{Side in image}}{\text{Corresponding side in preimage}}[/tex]
Given: Rectangle A has a length of 6 and width of 4.
Rectangle A prime has a length of 9 and width of 6.
Scale factor = [tex]\dfrac{9}{6}\ \ \ or \ \ \dfrac{6}{4}[/tex]
[tex]=\dfrac32[/tex]
Hence, the scale factor of the dilation [tex]=\dfrac32[/tex]
Answer:
3/2
Step-by-step explanation:
Mary ate x pounds of cherries. Leslie ate LaTeX: \frac{6}{9}6 9 more. Write an expression to represent how many pounds of cherries Leslie ate.
Answer:
The expression to represent number of cherries Leslie ate = ( x + [tex]\frac{6}{9}[/tex] ) pound.
Step-by-step explanation:
As given,
Mary ate cherries = x pound
And
Leslie ate [tex]\frac{6}{9}[/tex] more.
⇒Leslie ate cherries = ( x + [tex]\frac{6}{9}[/tex] ) pound.
The sail of a boat is in the shape of a right triangle. Which expression shows the height, in meters, of the sail?
The sail of a boat is a right triangle with an acute angle equal to 35 degrees and the side of the sail which is the hypotenuse to the right triangle is 8 meters long.
cosine 35 degrees over 8
8(tan 35°)
tangent 35 degrees over 8
8(cos 35°)
Answer:
8(cos35)
Step-by-step explanation:
Your welcome.
The expression that models the height is 8 cos35
SOH CAH TOA identityFrom the given information, we have the following
Hypotenuse = 8metersHeight = adjacentUsing the SOH CAH TOA identity
cos theta = adj/hyp
cos 35 = adj/hyp
cos 35 = adj/8
Hyp = 8 cos35
Hence the expression that models the height is 8 cos35
Learn more on SOH CAH TOA here: https://brainly.com/question/22307176
cuánto es 30+30 me lo dices
Answer:
60
Step-by-step explanation:
3+3 es 6, después ponele el 0 al final
For every pound a company spends on advertising, it spends £0.45 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
SO HARDDD
What is the square root of 267.8?
lol
“Stay close to anything that makes you glad you are alive.” – Hafez.
C h a t here Bradyn and Lis, plz. I keep getting logged out when I use the other one :p
Answer:
16.3645959315
Step-by-step explanation:
a. a triangle with one right angle and two congruent sides
Answer:
is an isosceles right triangle, angles 45, 45, & 90 degrees
Step-by-step explanation:
Ms. Potts washed 1/4 of her laundry. Her son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
Answer:
Son washed moreRemaining 9/28 of the laundryStep-by-step explanation:
Make denominators common to see the difference in fractions:
1/4 = 7/283/7 = 12/28Son washed more laundry as 12/28 > 7/28
Together they washed:
7/28 + 12/28 = 19/28 of the laundryRemaining part is:
1 - 19/28 = 28/28 - 19/28 =9/28 of the laundryStep-by-step explanation:
9/28 is your answer......
On average, A person spends $240 every 3 months on their cell phone bill... What would the price be for 1 month be?... How much would this person pay over the course of one year?
Pls help me asap!!
Answer:
$81 for 1 month
$972 for 1 year
Step-by-step explanation:
Answer:
$80 for one month and $960 over the course of one year
Step-by-step explanation:
240 / 3 = 80
12 x 80 = 960
Kevin received 1105 marbles. Kevin would like to give each of his friends some marbles. If Kevin has 12 friends, how many marbles would each person, including Kevin, receive?
Answer:
85 for each person including kevin
In AHIJ, h = 38 inches, i = 45 inches and j=61 inches. Find the measure of ZH to the nearest degree.
Answer:
38°
Step-by-step explanation:
Delta math
if the ratio of the length to perimeter is 5:16 what is the area of the rectangle
What's the negative reciprocal of –7
Answer:
0.14285714285
Step-by-step explanation:
This is what I got from the calculator.
Answer:
1/7 (1 over 7)
Step-by-step explanation:
The negative reciprocal of –7 is 1/7 (1 over 7)
An empty rectangular tank measures 60 cm by 50 cm by 56 cm. It is being filled with water flowing from a tap at a rate of 8 liters per minute. How long will it take to fill up the tank? (1 liter = 1000 cm3)
Answer:
21 min
Step-by-step explanation:
V = lwh
V = 60(50)(56) = 168000 cu. cm
8 liters = 8000 cu cm
168000/8000 = 21 min.
A group of friends were working on a student film that had a budget of $900. They used 33% of their budget on equipment. How much money did they spend on equipment?
They used 33/100 of their money on equipment which means if they have a budget of 900 dollars they used...
900*33/100=9*33=297 dollars on equipment.
The amount used on equipment is $297.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Budget = $900
Percentage of the budget used.
= 33%
Now,
The amount of budget used.
= 33% of 900
= 33/100 x 900
= $297
Thus,
The amount used on equipment is $297.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ6
Math problem please help
Answer:
The second one and the last one
Step-by-step explanation:
The third quadrant is of all negitive. The reason it is, is because it is on the left side of the x axis which makes it go lower like subtracting and dividing, then it is on the bottom half of the y axis which again is the same reason
i hope i helped and have a great day!
Answer:
B and D
Step-by-step explanation:
because in the 3rd quadrant both the x and y will be negative
1st quadrant all x and y are positive
2nd quadrant y are positive but x are negative
and in 4th quadrant x are positive and y are negative.
if brainiest is earned its greatly appreciated
Like seriously I gat no idea what the the answer is
Peter and Myra are on their school's activity planning committee. They are polling each
homeroom class to find how many students are in after-school clubs. In Peter's class, 9 out of
the 20 students are in clubs. In Myra's class, 12 out of the 24 students are in clubs. Do the
two classes have the same ratio of students in clubs to total students?
yes
No
Answer: No
Step-by-step explanation: because 12 out of 24 is 1/2 while 9/20 is a bit off of one half therefore no
Here is the assignment : You are "selling" the polynomial. You must convince the buyer you have the Best polynomial on the market by describing as many of its specific characteristics.
(Have fun and be creative, but most importantly, be accurate to avoid bad reviews)
Here is your Polynomial: f(x)=x^3-10x^2+28x-24
Step-by-step explanation:
A polynomial is an expression that can be built from constants and symbols called variables or indeterminates by means of addition, multiplication and exponentiation to a non-negative integer power. Two such expressions that may be transformed, one to the other, by applying the usual properties of commutativity, associativity and distributivity of addition and multiplication, are considered as defining the same polynomial.
A polynomial in a single indeterminate x can always be written (or rewritten) in the form
{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},}a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},
where {\displaystyle a_{0},\ldots ,a_{n}}a_{0},\ldots ,a_{n} are constants and {\displaystyle x}x is the indeterminate.[2][3] The word "indeterminate" means that {\displaystyle x}x represents no particular value, although any value may be substituted for it. The mapping that associates the result of this substitution to the substituted value is a function, called a polynomial function.
This can be expressed more concisely by using summation notation:
{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}
That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms. Each term consists of the product of a number – called the coefficient of the term[a] – and a finite number of indeterminates, raised to nonnegative integer
can someone please help me and if you could explain your answer so I can try to do the others on my own that be awesome :)
Answer:
Step-by-step explanation:
its 6
Graph the image of rectangle STUV after a reflection over the line y= –x
Answer:
U (7,1)
T (10,1)
V (7,9)
S (10,9)
Step-by-step explanation:
The image of the rectangle STUV after a reflection over the line y= –x is attached below.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The coordinates of the points in the graph are S(-9,-10) , T(-1,-110) , U(-1,-7) , V(-9,-7)
We have to graph the image of the rectangle STUV after a reflection over the line y= –x
The points obtained after graphing ate,
U (7,1)
T (10,1)
V (7,9)
S (10,9)
Thus, the image of the rectangle STUV after a reflection over the line y= –x is attached below.
Learn more about the geometric transformation here:
brainly.com/question/16156895
#SPJ2