(a) Write down the angle between the vector i + j and the vector i- j.
(6) Calculate the angle between the vector 2i + 5j and the vector 4i.
(2)
(c) Two forces, A = (14i +2j) N and B = (2i - 6j) N, act on a ball.
Show that the magnitude of A is Root k times larger than the magnitude of B, where k is
an integer
(3)
Answers
(i + j) • (i - j) = ||i + j|| ||i -j|| cos(θ)
We also recall that for any vector x,
||x||² = x • x
We have
(i + j) • (i - j) = (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= ||i||² + (i • j) - (i • j) - ||j||²
= 1 + 0 - 1
= 0
and
||i + j|| = √(1² + 1²) = √2
||i - j|| = √(1² + (-1)²) = √2
So,
0 = 2 cos(θ)
cos(θ) = 0
θ = arccos(0) = 180°
(b) By the same process, we find
(2i + 5j) • 4i = 8
||2i + 5j|| = √(2² + 5²) = √29
||4i|| = 4
Then if θ is the angle between 2i + 5j and 4i, we have
8 = 4√29 cos(θ)
cos(θ) = 2/√29
θ = arccos(2/√29) ≈ 68.1986°
(c) Compute the magnitudes:
||A|| = √(14² + 2²) = √200 = 10√2
||B|| = √(2² + (-6)²) = √40 = 2√10
Now we can write
||B|| = 2√10 = 2 √(5 × 2) = 2√5 × √2 = 1/√5 × 10 √2 = 1/√5 ||A||
or
||A|| = √5 ||B||
so that k = 5.
Related Questions
This stem and leaf plot shows the height of several trees.
Height in Feet and Inches of Several Trees
5 || 8
6|| 2,3,7,8,9,9
7 || 0,1,4,5
8 ||6,7,8,9,10
What is the number of trees that are LESS than 7 feet tall?
Question Help: Message instructor
Submit Question
Answers
Answer:
7 trees.
Step-by-step explanation:
Number < 7 ft consists of the first 2 stems:
5 || 8 - 1 tree
6|| 2,3,7,8,9,9 - 6 trees
= 1 + 6
= 7.
The number of trees that are less than 7 trees as shown in the stem-and0leaf plot is: 7 trees.
What is a Stem-and-leaf Plot?In a stem-and-leaf plot, data points are represented in leaves and stems. For example, representing height of trees as 5 || 8, means a data point representing a height of a tree measuring 5 ft and 8 inches tall.
From the stem-and-leaf plot given, the data points that are below 7 feet are 7 in number, which range from 6 ft and 9 inches down to 5 ft and 8 inches.
The answer is: 7 trees.
Learn more about stem-and-leaf plot on:
https://brainly.com/question/8649311
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You work 44 hours at Candelaria's Tortilla Factory (CTF), You earn $15.00 per hour and you get paid 1.5 times
your base rate for hours worked over 40 hours. You pay 6.25% for Social Security, and 1.45% for Medicare.
You also pay $83.00 for your health insurance. You also put 3% of your gross pay into 401(k). How much is
your take home pay?
Answers
Answer:
$537.87
Step-by-step explanation:
First, we need to determine our total pay which will be 40 hours times our $15 per hour to be $600. For the extra hours above 40, we are payed 1.5 times as much.
$15 * 1.5 = $22.5 * (44-40) = $90 additional pay
$600 + $90 = $690 total pay
Now, we calculate all of our deductions.
Subtract social security to be
690 * (1-0.0625) = $646.875
Medicare Deduction
646.875 * 0.9855 = $637.50
Health Insurance
$637.50-83 = $554.50
401k Deduction
$554.50 * 0.97 = $537.87
Find the measure picture below
Answers
By the vertical angle theorem, angle K is equal to the angle of measure 28 degrees.
--> so k is 28 degrees
Def. of vertical angle theorem: states that the opposite (vertical) angles of two intersecting lines are congruent
Hope that helps!
which combinations hold the same amount of liquid as an 8-pint bowl
Answers
1 quart = 32 fl oz
1 pt = 16 oz
Using these conversions you will multiply the number of quarts or pints by the number of ounces in each and then add the totals together to find if they equal 128 oz.
C. 4 x 32 = 128 oz
D. 2 x 32 + 8 x 8 = 128 oz
E. 3 x 32 + 2 x 16 = 128 oz
Find the median of the following data: 19, \ 21, \ 18, \ 17, \ 18, \ 22, \ 4619, 21, 18, 17, 18, 22, 46
Answers
Check the picture below.
i need help with this
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
In the given figure, Angle y is equal to Angle adjacent to 52° and 90° by Vertical opposite angle pair
And since they for straight line, their Angle sum will be equal to 180°
that is :
[tex]\qquad \tt \dashrightarrow \:y + 52 + 90 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y + 142 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \:y = 180 - 142[/tex]
[tex]\qquad \tt \dashrightarrow \:y =38 \degree[/tex]
Answer:
y = 38°
Step-by-step explanation:
We know that the angles in a straight line are added up to 180°.
So,
90 + y + 52 = 180
142 + y = 180
y = 180 - 142
y = 38°
Using the illustrations below, determine the relationship between the volumes of
the two given solid figures. Put a check ( / ) on the blank if the sentence states
the correct relationship
Answers
Answer:
I don't see the illustrations
SOMEONE HELP ME PLEASE!! 100 POINTS FOR ANSWER!!
I took a screenshot of my problem.
Answers
Answer:
B it originally cost 12000
Step-by-step explanation:
the depriciation factor is 0.75^t and the original value was 12000
Answer:
(2) The motorcycle cost $12,000 when purchased.
Step-by-step explanation:
[tex]V(t)=12000(0.75)^t[/tex]
[tex]V(0)=12000(0.75)^0=12000[/tex]
[tex]V(1)=12000(0.75)^1=9000[/tex]
[tex]V(2)=12000(0.75)^2=6750[/tex]
etc.
⇒ Initial cost = $12,000
⇒ The motorcycle's value is decreasing by 25% each year.
what is probability scale to the sea will disapper
Answers
A printer can print 32 pages in 80 sec.
The rate in lowest terms is______?
Answers
Answer:
0.4 pages per second
24 pages per minute
1 page can be printed every 2.5 seconds
Each answer is technically correct, use the one that's most appropiate
Step-by-step explanation:
32 pages in 80 seconds
32 / 80 = 0.4 pages per second
0.4 / 1
If they want it in minutes, multiply both sides by 60 seconds
0.4 * 60 / 1 * 60
24 pages per minute
What is the difference between a copyright and a trademark, and how are they used to protect intellectual property?
Answers
Answer: Copyright protects original work, whereas a trademark protects items that distinguish or identify a particular business from another.
The trademark laws protect the product or service name and any slogans used in the advertising, while the copyright laws protect the additional creative written expression contained in the ad. Hope this helps!
Step-by-step explanation:
all of these are service industries except zoo bakery law firm or travel agency
Answers
Answer:
A zoo
Step-by-step explanation:
A zoo can't be consisdered a "service industry" compared to the other ones.
So
A.) Zoo
is your answer
three different purposes for determining the derivative.
Answers
Answer:
A derivative is a slope function. If you want to find the slope anywhere along the function, you can.
Explanation:
Given: What is the purpose of a derivative?
A derivative is a slope function: m=f'(x=value). If you want to find the slope anywhere along the function, you can.
If you want to find a tangent line at a specific point along the function you can, using the slope and the point: y−y1=m(x−x1)
Answer:
See below
Step-by-step explanation:
A derivative is a slope function, so it allows you to find the slope anywhere along a function where it's continuous.
For example, the derivative of velocity is acceleration, which is applicable in real life.
You can also find a tangent line at a specific point by finding the slope of the function at that point and then using point-slope form [tex]y-y_1=m(x-x_1)[/tex] to get your tangent line.
Name the theorem or postulate that justifies the congruence.
JAJSAS
[B] ASA
[C] AAS
[DJ HL
Answers
Explain why 0.323232 is greater than 0.32
Answers
Answer:
0.323232 is the greater number
Step-by-step explanation:
This is because if you write the numbers the same way, there is a difference between the first 0 and the 3.
Look here: 0.323232 0.320000
You can see that there is a 3 after the first 2, therefore that shall deem the greater number.
A copy machine makes 44 copies per minute. How many copies does it make in minutes 5 and 15 seconds?
Answers
Answer:
231
Step-by-step explanation:
5 minutes + 15 seconds = 5.25 minutes
44 × 5.25 minutes = 231 copies
the average of 15 pupils in a room is 11. if a man of 27 years enter the room. what will be the new average age?
Answers
Answer:
12
Step-by-step explanation:
→ Find the total age of the children
15 × 11 = 165
→ Add the mans age
165 + 27 = 192
→ Divide by 16
192 ÷ 16 = 12
Help picture below problem 8
Answers
Answer:
C. never
Step-by-step explanation:
A trapezoid has exactly one pair of opposite sides parallel.
A parallelogram has exactly two pairs of opposite sides parallel.
A trapezoid is never a parallelogram.
Pls pls help with this!
What equation represents the linear relationship in this graph?
A :y = 10x
B: y = 6x
C:y = 1/3x
D: y = 3x
Answers
Answer:
D: y = 3x
Step-by-step explanation:
The relationship shown is a proportion. The only "unknown" is the constant of proportionality, the slope of the line. That is most easily found by looking for the value of y that corresponds to the value x=1.
__
This graph shows that 1 song costs $3, so the equation is ...
y = 3x
1/3 + 1/3=
5/10-2/10=
=
4/5-2/5=
11+1=
=
Answers
Answer:
Step-by-step explanation:
1/3 + 1/3= 2/3
5/10-2/10=3/10
4/5-2/5=2/5
11+1=12
A rectangular sheet of metal measures 8 inches by 12 inches. The metal is worth $2.00 per square inch. How much is the sheet of metal worth?
Answers
Answer:
Step-by-step explanation:
Find the area of the sheet metal
Area = L * w
L = 12
w = 8
Area = 12 * 8
Area = 96 square inches.
Find the value of the sheet metal
1 square inch costs $2.00
96 square inches cost 2 * 96 = $192.00
Please help I'll mark brainliest 2
Answers
Answer:
True
Step-by-step explanation:
To find the amount of observations all you need to do is just add up the dots. Adding the number of observations in each range should be true
nvm someone answered lol good luck!
2. 28 - 3t = 10
Work out the value of t.
Answers
Answer:
t = 6
Step-by-step explanation:
28 - 3t = 10
-3t = 10 - 28
-3t = -18
t = -18/-3
t = 6
Note: (-)/(-) = +
Answer:
t=6
Step-by-step explanation:
—3t=—18
t=6
PLEASE HELP NOW I WILL FOLLOW AND GIVE BRAINLIST
Answers
Answer:
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
[tex] \frac{4}{10} = \frac{2}{5} [/tex]
good luck
Answer/Step-by-step explanation:
At least, meaning 2 1/2 or more
Now, I'm not exactly sure how they want it written so it could be two answers.
4/10
OR
4
Hope this helps :)
5. You get a car loan for $13,000 to buy a used car. The car dealer who gives you the loan charges
8.4% interest, compounded monthly, for 4 years.
(a) What's the total amount you will have to pay back for this loan?
(b) What is your monthly payment for this loan?
Answers
Answer:
Total = $15,351.10
Monthly = $319.81
Find the measure picture attached
Answers
Answer:
30
Step-by-step explanation:
90 - 60 = 30
Three students measured the heights of the daffodils they are growing.
2/3
Sofia's daffodil is 4/6
of a foot high
Mateo's daffodil is
of a foot high.
3/8
Deshawn's daffodil is
of a foot high
Which statement correctly compares two of these fractions?
L
Answers
Mr. Jones is building the garage shown below. What is the volume of the garage?
Answers
Answer: 891 ft³
Step-by-step explanation:
We can break the garage into two different parts. The roof, triangular, and the rest, rectangular. I will start by solving for the rectangular part.
V = L * W * H
V = 12 ft * 9 ft * 7.5 ft
V = 810 ft³
Now, I will solve for the triangular part, the roof. First, 9 ft - 7.5 ft = 1.5 ft, so the height of just the roof is 1.5 ft.
V = [tex]\frac{L * W * H}{2}[/tex]
V = [tex]\frac{12 * 9* 1.5}{2}[/tex]
V = [tex]\frac{162}{2}[/tex]
V = 81 ft³
Lastly, I will add the two different parts together.
810 ft³ + 81 ft³ = 891 ft³
The value of (2i3)3 is
IS
Answers
Answer:
Assuming you mean (2^3)3, the answer is 24
Step-by-step explanation:
using pemdas you do 2 to the third power first
2x2=4 4x2=8
then you mutiply by the number not in parenthesis; 3
8x3 = 24
Answer this and i mark u branliest
Answers
Step-by-step explanation:
5a.
10 white squares
15 shaded squares
5b.
a1 = 1 = 2×1 - 1
a2 = a1 + 2×2 - 1 = 2×1 - 1 + 2×2 - 1 = 2×(1+2) - 2
a3 = a2 + 2×3 - 1 = 2×(1+2+3) - 3
...
an = 2×(1+2+...+n) - n = 2×n×(n+1)/2 - n = n²
so,
a350 = 350² = 122,500
figure350 has 122,500 squares.
5c.
a1 = 1
a2 = a1 = 1
a3 = a2 + 5
a4 = a3 = 6
a5 = a4 + 9
a6 = a5 = 15
a7 = a6 + 13
a8 = a7 = 28
...
a(2n) = a(2n - 1)
a(2n - 1) = a(2(n-1) - 1) + 1 + 4(n - 1) = n×1 + 4(0+1+2+...+n-1) =
= n + 4×(n-1)×n/2 = n + 2×(n² - n) = 2n² - n
therefore,
a350 = a349
a349 = a(2×175 - 1) = 2×175² - 175 = 61,075
figure350 has 61,075 shaded squares.