Given u = −8i − 3j and v = −12i − 7j, what is projvu?
−4.845i − 1.819j
−7.275i − 4.244j
−7.886i − 2.957j
−11.828i − 6.900j
Answers
Answer:
(b) -7.275i -4.244j
Step-by-step explanation:
The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.
__
The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.
[tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]
Related Questions
What are the coordinates of point F?
Answers
Answer:
C. 4, -2 1/2
Step-by-step explanation:
(x,y)
its kinda easy
Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (8 points) Part B: Find (a - b) (x). Show your work. (8 points) Part C: Find (a - b)(x). Show your work. (9 points) Part D: Find a(b(x)]. Show your work. (10 points)
Answers
a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]
b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]
I am 6 foot and 4 inches what is my height in metres?12 inches=to 1 foot and 1 foot=to 30 cm
Answers
Answer:
1.9 m
Step-by-step explanation:
1 ft = 30 cm (approximately)
12 in. = 1 ft
100 cm = 1 m
Find the height in ft:
4 in. / 12 in/ft = 1/3 ft
6 ft 4 in. = 6 ft + 1/3 ft = 6 1/3 ft
Convert ft to cm:
6 1/3 ft × 30 cm/ft = 190 cm
Convert cm to m:
190 cm × 1 m / 100 cm = 1.9 m
What is the sum of the first 40 positive odd integers?
Answers
Answer:
1600
Step-by-step explanation:
[tex]\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600[/tex]
Determine the cardinality of each set.
(a) {5, 1, 4, {6, 7, 8, ...}}
(b) {ø}
(c) {{{6, 7}}}
Answers
The cardinality of a set refers to the number of elements in the set. It is found by counting the elements in the set.
What is cardinality of a set?The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.
a) There are 6 elements in this set hence the cardinality is 6.
b) There is only one element in the set hence its cardinality is 1.
c) There are two elements in the set hence the cardinality is 2.
Learn more about cardinality of a set:https://brainly.com/question/19257002
#SPJ1
What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?
Answers
The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
How to determine the equation of the directrix?The parabola equation is given as:
[tex]\frac 14(y + 3) = (x -2)^2[/tex]
A parabola is represented as:
[tex]4p(y - k) =(x -h)^2[/tex]
By comparing both equations, we have:
4p = 1/4 ==> p = 1/16
-k= 3 ==> k = -3
The directrix is represented as:
y = k - p
So, we have:
[tex]y = -3 - \frac 1{16}[/tex]
Take the LCM
[tex]y = \frac {-16 * 3- 1}{16}[/tex]
Evaluate
[tex]y = \frac {-49}{16}[/tex]
Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
Read more about parabola at:
https://brainly.com/question/1480401
#SPJ1
what percentage of 2m is 40cm
Answers
Answer:
20%
Step-by-step explanation:
the units of measure must be the same, so
2m = 2 × 100 cm = 200 cm
then
[tex]\frac{40}{200}[/tex] × 100%
= 0.2 × 100%
= 20%
Answer:
20%
Step-by-step explanation:
2 m = 200 cm We are required to find: what percentage of 2m is 40cm.Required percentage [tex]=\frac{40}{200}\times 100[/tex]Required percentage [tex]=\frac{4000}{200}[/tex]Required percentage [tex]=20%[/tex]Is anyone able to solve this equation? It’s urgent
Answers
Answer:
1500
Step-by-step explanation:
You can find the complete solution in the given attachment
Pls help. Answer the question in the picture. I will give 5 stars, a thanks, and brainliest!
*20 points*
Answers
Answer:
1/5x + 2
Step-by-step explanation:
hope this helps
describe in detail how you would create a number line with the following points:3, 2.25, the oppisite of 4 and- (-1 1/2). please be sure to describe on which tick marks each point is plotted and how many tick marks are between each iteger. it may help for you to draw this number line by hand on a sheet of paper pls answer NO WRONG ANSWERES
Answers
Answer:
here man that's the answer
what is the answer to this
Answers
Step-by-step explanation:
[tex]m {}^{2} + 5 \\ = 9 {}^{2} + 5 \: \: \: \: \: \: \\ = 9 \times 9 + 5 \\ = 81 + 5 \: \: \: \: \: \: \: \\ = 86 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
hope it will be helpful
Answer:
86
Step-by-step explanation:
Evaluate the expression:Plugin the value of m, in the expression
m² + 5 = 9² + 5
= 81 + 5
= 86
Erica earned a total of $67,250 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college?
Answers
Step-by-step explanation:
x = earnings from the store
y = earnings from the college
x + y = 67,250
x = 3y + 1,250
now we use the identity of the second equation in the first equation :
(3y + 1,250) + y = 67,250
4y = 66,000
y = $16,500
x = 3y + 1,250 = 3×16,500 + 1,250 = 49,500 + 1,250 =
= $50,750
7x^2+3y^2+12x+2y-6=0 Help me find the value of a,b,c and the discriminant number
Answers
Answer:
b o a h d
Step-by-step explanation:
1*5 3%9 46% &45 that is the answer
how to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3
Answers
PLS HELP ASAP!… WILL MARK BRAINLIEST
Which of the following are exterior angles? Check all that apply.
Answers
The exterior angles in the given triangle are angles 4 and 5.
What are the exterior angles?
The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.
To learn more about angles, please check: https://brainly.com/question/2766460
#SPJ1
Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
a. $2,416
b. $3,840
c. $2,088
d. $1,740
I couldn't find the answer to this question when I really needed it, so I did the work myself and got D as the answer. I ended up getting it right because you divide 29,000 by 12, then multiply the answer (2416) by 28%, which gives you the answer, D, 1740. Hope that helped!
Answers
Answer:
d. $1,740
Step-by-step explanation:
The annual after-tax salary is found by subtracting the tax from the salary. The tax is found by multiplying the tax rate by the salary. The monthly after-tax income is 1/12 of the annual after-tax income.
__
stepsannual tax = 0.28 × $29,000 = $8,120
annual take-home pay = $29,000 -8,120 = $20,880
monthly take-home pay = annual pay / months per year
= $20,880 / 12 = $1,740 . . . . net monthly income
_____
Additional comment
The net pay will be (1 - 0.28) = 0.72 times the nominal salary. The monthly pay will be 1/12 of the annual pay. These combined factors give a monthly net pay of (0.72)(1/12) = 0.06 times the annual pay.
0.06 × $29000 = 6×$290 = $1740
A rectangle measures 12 m by 14 m. If the width is decreased by 3 m and the length is increased by 4 m, how much would the area change?
Answers
Answer:
6 m²
Step-by-step explanation:
Original area :
12 × 14 = 168 m²
New area :
(12-3) × (14+4) =
9 × 18 = 162 m²
168 - 162 = 6
Area would change by 6 m²
2a - (a + 3) I need Answers
Answers
Answer:
a-3
Step-by-step explanation:
[tex]2a-(a+3)\\= 2a - a - 3\\= a - 3[/tex]
Answer:
a-3
Step-by-step explanation:
2a - (a+3)
removing bracket
2a -a-3
a-3
final answer
a-3I need help with 7 and 4 and 9 also 10
I will give the most higher points I got
Answers
*When multiplying with a whole number u can turn it into a fraction by putting a one under it
So 3/1 times 3/5 = 9/5
*just multiply straight across
4. 2/1 times 1/4 = 2/4 = THEN SIMPLIFY = 1/2
9. 3/4 times 3/1 (cups)
*multiply straight across
9/4 = 2 1/4 (cups of sugar)
So she uses less than 3 cups to make all 3 loaves
* 10. Sorry I can’t tell if it says 5/6 on both of them
If it says 5/6 on both of them then the answer is obvious and she worked more than that over the course of 2 days
* 10. It must be a 5/9 on the second one
So if so
5/6 times 2/1 (days)
10/6 then we need to multiply the 6 denominator (bottom of the fraction) with something to = 9 denominator
9 divided by 6 = 1.5
10/6 times 1.5 for both the numerator (top) and denominator (bottom)
= 15/9 (simplified 1 6/9)
This one she exercised more than 5/9
At time t=0 a woman tosses an apple straight up into the air. At time t= 0.5, it begins to fall back to her hand. She catches the apple at t=1.0. Treat motion upward a positive. which of the follwong graphs could represent the motion of the apple?
Answers
The graph that could represent the motion of the apple is graph B.
What is a graph?A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
What is the solution to the equation |x − 4| = 17?
Answers
[tex]~~~~~~|x-4| = 17\\\\\implies x -4 = 17~~~~ \text{or}~~~~~ x -4 = -17\\\\\implies x = 17+4~~~~\text{or}~~~~~ x = -17+4\\\\\implies x = 21~~~~~~~~~\text{or}~~~~~x = -13[/tex]
the number of keys on the keyring minus 2
Answers
Translating the given phrase into a variable expression is equal to k - 2.
What is a variable expression?A variable expression refers to a mathematical equation which can be used to show the relationship that exist between a numerical quantity and a variable.
Next, we would translate the given phrase into a variable expression as follows:
Let the number of keys on the keyring be k.
Therefore, the variable expression is equal to k - 2.
Read more on expressions here: https://brainly.com/question/12189823
#SPJ1
Complete Question:
Translate the phrase into a variable expression. Use the letter k to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The number of keys on the keyring minus 2?
Please help me with my math
Answers
Find the slope of the line containing the pair of points.
(2, -9) and (12,6)
Answers
Answer:
slope = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 9 ) and (x₂, y₂ ) = (12, 6 )
m = [tex]\frac{6-(-9)}{12-2}[/tex] = [tex]\frac{6+9}{10}[/tex] = [tex]\frac{15}{10}[/tex] = [tex]\frac{3}{2}[/tex]
How do I complete this?
Answers
Answer + Step-by-step explanation:
CE bisects AB
CE ⊥ AB
Then
CE is the perpendicular bisector of AB.
Therefore
CA = CB and DA = DB
…………………………………
we have :
CA = CB
DA = DB
CD is a common side of the two triangles ACD and BCD
Hence , ΔACD ≅ ΔBCD
⇒ ∠CAD ≅ ∠CBD.
An internet cafe charges $3.75 to use a computer and $.45 per minute while accesing the internet. What function rule describes this situation?
Answers
Answer:
y = $3.75(x) + .45$
Step-by-step explanation:
Take the input and subsitute
What is the total number of different 9-letter arrangements that can
be formed using the letters in the word Projector?
Answers
Jessie is painting a cardboard box for a school project and needs to know much paint she needs to cover the box.
6n
10 in.
Answers
Answer:
incomplete question
Step-by-step explanation:
in order to calculate for the surface area of a rectangular box we would need 3 measurements:
length
width
height
you only provided 2
[tex]-3/z+7/4z=5/z-25[/tex]
Answers
Answer:
z = 1/4
Step-by-step explanation:
See attached image
Answer:
z = 5
Step-by-step explanation:
simplify
5/(z-25) first
turning it into
((0 - 3/z) + 7/4z) - 5/(z - 25) = 0
then simplify 7/4z
((0 - 3/z) + 7/4z) - 5/(z-25) = 0
when the fractions denominator is 0 then the numerator must be 0
turning the equation into
-25 * (z - 5) = 0
solve
-25 = 0
something that is not zero cannot equal zero.
z - 5 = 0
5 - 5 = 0
z = 5
hope this helps:)
Which of the following functions is graphed below?
Answers
Answer:
A.
Step-by-step explanation:
the correct answer is A. y=|x-2|+3.
For more details see the attachment.