Consider vectors u = ⟨2, 1⟩ and v = ⟨4, –1⟩ with the angle between them equal to 40°. What are the scalar projections uv and vu?
a) uv = 1.33 and vu = 1.33
b) uv = 1.33 and vu = 3.16
c) uv = 1.71 and vu = 1.33
d) uv = 1.71 and vu = 3.16
Answers
Answer:
D. uv = 1.71 and vu = 3.16
Step-by-step explanation:
The scalar projections are uv = 1.71 and vu = 3.16
The correct option is (D)
What is meant by scalar projection?The definition of scalar projection is the length of the vector projection.
Given: u = ⟨2, 1⟩, = ⟨4, –1⟩, and θ = 40°
Proj u_v = |u| cosθ
= 2.25 * cos 40
= 2.25 * 0.7660
=1.72
and, Proj v_u = |v| cosθ
= 4.123 * cos 40
= 4.123 * 0.7660
= 3.16
Learn more about this concept here:
https://brainly.com/question/19938443
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Related Questions
what is an equivalent fraction to 3/8 ? Find a common denominator for the pair of fractions. Then, write equivalent fractions with the common denominator. 3/8 and 9/28
Answers
Answer:
6 1/6
Step-by-step explanation:
A fraction that is equivalent to 3/8 is 6 1/6
According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event F) is 0.2805. The probability that the driver is 24 years old or less (event A) is 0.1759. The probability that the driver is female and is 24 years old or less is 0.0424. Answer parts (a) through (d) below.
(a) Find the probability of FUA. P (FUA)Round to four decimal places as needed.)
(b) Find the probability of F'UA. P(FUA) (Round to four decimal places as needed.)
(c) Find the probability of FnA'
Answers
Question d:
(D) Find the probability of F'nA'
Answer:
0.4140
0.7619
0.2381
0.9576
Step-by-step explanation:
Given that :
Female in fatal accident P(F) = 0.2805
Driver is 24 years or less P(A) = 0.1759
Driver is female and 24 years or less P(FnA) = 0.0424
A.) Find the probability of FUA.
P(FUA) = P(F) + P(A) - P(FnA)
= 0.2805 + 0.1759 - 0.0424
= 0.4140
(b) Find the probability of F'UA.
P(F'UA) = 1 - P(F) + P(FnA)
= 1 - 0.2805 + 0.0424
= 0.7619
C.) P(FnA') = 1 - P(F'UA)
= 1 - 0.7619
= 0.2381
(d) Find the probability of F'nA'
P(F'nA') = (FnA)' = 1 - (FnA)
= 1 - 0.0424
= 0.9576
Help me please and thank you
Answers
Possibly B but i'm not sure..
I need help with this plz percent equations the question is blank % of 35 = 21
Answers
Answer:
60%
Step-by-step explanation:
HELPPP FASTTT PLEASE
Answers
Answer:
(3,-2)
Step-by-step explanation:
I used a graphing calculator to get the solution, attached is what I got with the graphing calculator.
hope this helps.
Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not.
Answers
Answer:
The equation of a linear function is:
[tex]y = 2x+4[/tex]Step-by-step explanation:
Given the table
x y
-10 -16
-3 -2
1 6
2 8
Determining the slope between the points (-10, -16), (-3, -2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)[/tex]
[tex]m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (-3, -2), (1, 6)
[tex]m=\frac{6-\left(-2\right)}{1-\left(-3\right)}[/tex]
[tex]m=2[/tex]
Determining the slope between the points (1, 6),(2, 8)
[tex]m=\frac{8-6}{2-1}[/tex]
[tex]m = 2[/tex]
As the slope between the points is the same. Thus, the table represents the linear function.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 2 and any point let say (1, 6)
[tex]y - 6 = 2(x-1)[/tex]
[tex]y-6 = 2x-2[/tex]
[tex]y = 2x-2+6[/tex]
[tex]y = 2x+4[/tex]
Therefore, the equation of a linear function is:
[tex]y = 2x+4[/tex]Given the function f(x)= x^4 - 4x^3 -2, determine the absolute minimum value of ff on the closed interval [-2, 4].
Answers
Answer:
Absolute Minimum: (3,−29)
Step-by-step explanation:
A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
Answers
HELPPP ASAP WILL MARK BRAINILEST
Answers
Andy is correct! Andy has the function 4, his leading coefficient is negative, and his functions contains zeros. Hope this helps!
2.) Jennifer bought a shirt at Forever 21 for $21.50 after a 3% sales tax. What was the original price of the shirt?
Pls answer and expplain how you got it
Answers
Answer:
$20.87
Step-by-step explanation:
Divide 1.03 into 21.50
can someone help me please !!!!!!
Answers
Answer: From top to bottom of the chart: -13, -6, 1, 8, 15
Step-by-step explanation:
You can solve the equation by putting the numbers in the graph (under the letter x) into the equation. Meaning when it says "-2", you can write 7(-2)+1, or 7 times negative 2 minus one, which equals -13. Do the same thing with the rest :]
(26+5)•2-15
Please show with step
Answers
31•2-15
62-15
47
That’s step by step
Answer:
47
Step-by-step explanation:
(26+5) • 2-15
Follow Pemdas
P.E.M.D.A.S
Parenthesis first
31•2-15
Multiplication next
62-15
47
3 facts about "What is a Hurricane"?
Answers
Find the total area:
8 cm
16 cm
29 cm
22 cm
Answers
Answer: 81, 664 is the total!
Step-by-step explanation:
Find the x and y intercept of the line below
2x + 5y = 10
Answers
Answer:
x - intercept = 5
y- intercept = 2
Step-by-step explanation:
2x + 5y = 10
Write the equation in [tex]\frac{x}{a}+\frac{y}{b}=1[/tex] form
So, divide the equation by 10
[tex]\frac{2x}{10}+\frac{5y}{10}=\frac{10}{10}\\\\\frac{x}{5}+\frac{y}{2}=1[/tex]
x - intercept = 5
y- intercept = 2
Answer:
(5,0) and (0,2)
Step-by-step explanation:
Basically, all we need to do is enter 0 for both variables. We can do this because the y-value of an x-intercept will always be 0, and the x-value of a y-intercept will always be 0.
So, to find the x-intercept we can set y equal to 0 and then solve for x.
[tex]2x+5(0)=10\\2x=10\\x=5[/tex]
So the x-intercept will be (5,0).
We can do the same thing to find the y-intercept.
[tex]2(0)+5y=10\\5y=10\\y=2[/tex]
The y-intercept is (0,2)
Hope this helps!
Which of these equations represents a line parallel to the line 2x + y = 6?
A) y= 2X+3
B) y -2X=4
C) 2X -y=8
D) y= -2X+1
Answers
Answer:
D) y= -2X+1
Step-by-step explanation:
All of the lines are perpendicular to the line 2x+y=6 except for D) y= -2X+1.
Derive the equation, in the
form y = mx + b, for the line. (Look at the photo.)
Answers
Answer:
y=2x+1
Step-by-step explanation:
y=mx+c
y-intercept is 1
y=mx+1
gradient= rise/run= 2/1= 2
y=2x+1
Find the percent increase. Round to the nearest percent.
From 95 books to 139 books.
The percent increase is __%
(I just need the answer, no need for explanation)
Answers
Answer:
32%
Step-by-step explanation:
at least twenty caters long
Solve correctly and I’ll give brainliest.
Answers
Answer:
7
Step-by-step explanation:
-2 x 6 = -12
-6/1 ÷ -3/1 = 2
-12 - 2 = -14
-14 ÷ -2 = 7
A package of notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.
Answers
Answer:
24
Step-by-step explanation:
Given that:
Number of yellow notepads = 6
Number of Blue notepad = 6
Number of green notepads = 6
Number of pink notepads = 6
Samole space for experiment :
(Number of different distinct notepads * Number of notepads in each)
(4 * 6) = 24
Your aunt and uncle took turns driving on a 580-mile trip that took 10 hours. Your uncle drove at a constant speed of 60 mph and your aunt drove a constant speed of 55 mph. How long did each person drive?
A. Write the two equations.
B Solve the equations and give both answers.
Answers
Answer:
Aunt drove 4 hours
Uncle drove 6 hours.
Step-by-step explanation:
Equations:
580 = 55/x + 60/y
600 = 55x + 60y
Happy Holidays!
Solve the following equation for the
variable (a). -3a = 15
a = 5
a = 12
a = -5
a = 18
Answers
-3/-3a = 15/-3
a = -5
a negative & negative equals positive!
A taxi in myrtle beach charges $2 per mile and $1 per person. If a taxi cab ride for 2 people cost $12, how far did the taxi cab travel ( don’t include units (miles) in the answer)
Answers
Answer:
I belive the answer is 5
Step-by-step explanation:
$12- $2 for ppl= $10
$10÷$2 per mile = 5
Solve the following system by using substitution:
x = -3y - 17
2x + 3y = -7
Answers
Answer:
x=10 and y=−9
Step-by-step explanation:
Answer:
(x,y) = (10,-9)
Step-by-step explanation:
x=-3y-17
2x+3y=-7
2(-3y-17)+3y=-7
y=-9
x=-3(-9)-17
x=10
What is the solution for x in the
system of the following
equations?
3x+4 y= 31
3x-4 y=-1
Answers
Answer:
5
Step-by-step explanation:
In a grocery store, a packet of chips that usually costs $12 is on sale for 30% off. What is the sale price after the discount?
Answers
Answer:
3 dollars 6 cents or 3.6
Step-by-step explanation:
you need to divide the 30 percent by the twelve dollars to get your answer
GEOMETRY-TRIG
Rampy Ronald is fixing to make a jump with his dirt bike across an 80-foot ravine full of lava. The ramp he’s going to hit to make the jump is 15 feet long, forms a 30° with the ground and ends 5 feet from the edge of the ravine. That said, if he hits the ramp at his bike’s full speed of 60mph, he’ll reach a maximum height of 30 feet.
6. From the start of the ramp to when he reaches his maximum height, how far will Rampy Ronald have traveled horizontally?
7. Is Rampy Ronald going to make the jump, or is he fixing to land in the ravine of lava and become Roasty Ronald? Give geometric constructions backed by mathematics to support your reasoning!!!
Answers
Answer:
6. The distance Rampy Ronald would have travelled horizontally is approximately 48.428 feet for an actual maximum height of 21.486 feet
7. Rampy Ronald is going to make the jump
Please find attached the graph of the motion of Rampy Ronald, created with Microsoft Excel
Step-by-step explanation:
6. The given parameters are;
The width of the ravine = 80 ft
The inclination of the ramp with which Rampy Ronald will jump = 30°
The distance from the edge of the ravine the ramp ends = 5 feet
The speed with which Rampy Ronald will make the jump = 60 mph
The maximum height he will reach = 30 feet
Therefore, we have;
The height of the end of the ramp = 15 × sin(30°) = 7.5
The height of the end of the ramp = 7.5 feet
The height of the jump = 30 - 7.5 = 22.5
The vertical velocity = 60 × sin(30°) = 30
The vertical velocity = 30 mph
The horizontal velocity = 60 × cos(30°) = 30·√3
The horizontal velocity = 30·√3 mph
From the kinematic equation, v² = u² - 2gh, we have;
u² = 2gh
h = u²/2g = 900/(2 × 32.17405) ≈ 13.986
The maximum height reached 13.986 + 7.5 = 21.486
From v = u - gt
t = u/g = 30/32.17405 ≈ 0.932
t ≈ 0.932 s
The distance Rampy Ronald would have travelled horizontally = 30·√3 × 0.932 ≈ 48.428
The distance Rampy Ronald would have travelled horizontally ≈ 48.428 feet
7. The time before Rampy Ronald reaches ground level again, is given by the following relation;
h = 1/2·g·t²
21.846 = 1/2 × 32.17405 × t²
t = √(21.846/16.087025) ≈ 1.165
t ≈ 1.366 s
The horizontal distance traveled is therefore;
The horizontal distance traveled from maximum height is 30·√3 × 1.165 ≈ 60.535
The horizontal distance traveled from maximum height is ≈ 70.979 feet
The total horizontal distance traveled ≈ 48.428 + 60.535 = 108.963
The total horizontal distance traveled ≈ 108.963 feet
The total horizontal distance required to make it across the ravine = 5 feet + 80 feet = 85 feet
Therefore, Rampy Ronald is going to make the jump
Mrs. Garcia borrowed some money at the rate of 4% per annum for the first year, at the rate of 6% pe r annum for the next 2 years, and at the rate of 7.5% per annum for the period beyond 3 years. If he pays a total interest of ₱ 15 750 at the end of 5 years, how much money did he borrow?
Answers
Answer: ₱40,909.1
Step-by-step explanation:
Given data:
Rate for first year = 4%
Rate for next two years = 6%
Rate for the next 3 years = 7.5%
Interest paid back after 5years = ₱ 15,750
Solution:
How much did she borrow.
= let the sum borrowed be P
= P * 4 / 100
= 4P/100
= 1P/25.
For the next two years
= P* 6 * 2/100
= 12P/100
= 3P/25
For the next 3years
= P* 7.5*3/100
= 22.5P/100
= 9P/40.
1P/25 + 3P/25 + 9P/40 = 15750
77P/200 = 15750
P = 15750 * 200 / 77
P = 315,0000/77
P = ₱40,909.1
The amount borrowed is ₱40,909.1
Find the hypotenuse, c, of the triangle.
А
4
B.
C С
12
Answers
Answer:
A.
Step-by-step explanation:
Here a easy question for yall.
Hannah has 10 apples and she gave her friend 5 out of it. how much does hannah has now?
Easy~ UwU
Answers
Answer:
5
Step-by-step explanation:
The answer is 5 because it just is
Answer:
5Step-by-step explanation:
__________________________________________________________
Hannah gave her friend 5, so now she has 5!
__________________________________________________________
We can solve this by subtracting!
__________________________________________________________
10 - 1 = 9
10 - 2 = 8
10 - 3 = 7
10 - 4 = 6
10 - 5 = 5
__________________________________________________________
Hope this helps! uwu
__________________________________________________________