State if the two vectors are parallel, orthogonal, or neither.

u=18i+8j

v=9i+4j

Answers

Answer 1

Answer:

Parallel, since [tex]\vec u = 2\cdot \vec v[/tex].

Step-by-step explanation:

The relation between both vectors is determined by the use of the dot product, whose expression is:

[tex]\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}[/tex]

Where:

[tex]\cos \theta = 1[/tex] if vectors are parallel to each other and [tex]\cos \theta = 0[/tex] if vectors are orthogonal. Then, norms and dot product are calculated hereafter:

[tex]\|\vec u\| = \sqrt{18^{2}+8^{2}}[/tex]

[tex]\|\vec u\| \approx 19.698[/tex]

[tex]\|\vec v \| = \sqrt{9^{2}+4^{2}}[/tex]

[tex]\|\vec v\| \approx 9.849[/tex]

[tex]\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)[/tex]

[tex]\vec u \bullet \vec v = 194[/tex]

[tex]\cos \theta = \frac{194}{(19.698)\cdot (9.849)}[/tex]

[tex]\cos \theta = 1[/tex]

The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,

[tex]18i + 8j = 2\cdot (9i + 4j)[/tex]

[tex]\vec u = 2\cdot \vec v[/tex]


Related Questions

A manufacturer of bolts has a​ quality-control policy that requires it to destroy any bolts that are more than 4 4 standard deviations from the mean. The​ quality-control engineer knows that the bolts coming off the assembly line have mean length of 13 13 cm with a standard deviation of 0.10 0.10 cm. For what lengths will a bolt be​ destroyed?

Answers

Answer:

13.4 centimeters

Step-by-step explanation:

In this case to calculate the distance we must take into account the data that they give us in the exercise.

The final length would be equal to the initial length added to the product of standard deviations from the mean and standard deviation given by the engineer, like this:

L = 13 + 4 * 0.10

L = 13 + 0.4

L 13.4

That means that lengths will a bolt be destroyed when the value is 13.4 centimeters

PLEASE ANSWER AS QUICKLY AS POSSIBLE

Answers

Answer: D

Step-by-step explanation: Both the Equality property and the Identity property

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!

Answers

Answer:

All positive real numbers i think

Answer:

B

Step-by-step explanation:

4^x can never be 0 or negative, the graph has a horizontal asymptote at y = 0

So the range only includes positive values

Question 11 of 15

Micah is filling up his cone-shaped cup with water. The cup (as shown) has a diameter of 72 millimeters and a slant height of 45

millimeters. How much water can Micah fill in his cup?

Answers

Answer:

  36.644 mL . . . . depending on your value of π (see below)

Step-by-step explanation:

The height of Micah's cup is found from the radius and slant height. The radius is half the diameter, so is 36 mm. Then the height h is ...

  45² = 36² +h²

  h = √(45² -36²) = 27 . . . . . mm

The volume is given by the formula ...

  V = (1/3)πr²h

  V = (1/3)π(36 mm)²(27 mm) = 11664π mm³

For π = 3.14

  11664(3.14) mm³ ≈ 36,625 mm³ = 36.625 mL

For π = 3.14159265

  11665π mm³ = 36,644 mm³ = 36.644 mL

_____

Comment on units

A unit of measure used for relatively small volumes, especially of liquid, is milliliters (mL). 1 mL = 1000 mm³.

Answer:

The answer is 11664pimm^3

Step-by-step explanation:

Trina has a total of 32 crayons. How much boxes of crayons did she buy.

Answers

Answer:

Depends on the type of box, but most likely one box of crayons because 32 packs are sold.

Do you have answer choices?

Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above

Answers

Answer:

The problem is clearly solved in the attachment

OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT

Answers

These aren't too hard -- you should really try to do them yourself.

The upper triangle has base 2+2=4 and height 3.2.  The lower one has base 4 and height 4.  Of course the area of a triangle half base times height.

Area = (1/2) 4(3.2) + (1/2)(4)(4) = 2(7.2) = 14.4

Answer: 14.4 sq ft

how do u solve 3(1 - 3g) = -8g + 14 ?

Answers

Answer:

3 - 9g = -8g + 4

-9g + 8g = 4 -3

g = -1

find the second term in the sequence b(1)=16 b(n)=b(n-1)+1

Answers

Answer:17

Step-by-step explanation:

b(1)=16

b(n)=b(n-1)+1

b(2)=16(2-1)+1

b(2)=16(1)+1

b(2)=16+1

b(2)=17

Need Help ASAP !!!!!

Answers

Answer:

Luke worked 7 hours and Joshua worked 4 hours

Step-by-step explanation:

Let's call the number of hours that Luke worked l, and the number of hours that Joshua worked j. Since we know that Luke worked for 3 more hours than Joshua, we can express the amount of hours he worked as (j+3). Now, you can set up the following equation:

25j+35(j+3)=345

Expand parentheses:

25j+35j+105=345

Subtract 105 from both sides and combine like terms:

60j=240

j=4

Since Luke worked 3 more hours, he worked 7 hours. Hope this helps!

Show steps how to solve for y!!!!!
2y+2=3y/2
Please help me

Answers

[tex]\text{Solve for y:}\\\\2y+2=\frac{3y}{2}\\\\\text{Multiply both sides by 2 to cancel the denominator}\\\\4y+4=3y\\\\\text{Subtract 3y from both sides}\\\\y+4=0\\\\\text{Subtract 4 from both sides}\\\\\boxed{y=-4}[/tex]

Answer:-4

Step-by-step explanation:

2y+2=3y/2

Cross multiply

2(2y+2)=3y

Open bracket

4y+4=3y

Collect like terms

4y-3y=-4

y=-4

Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne’s shadow is 15 feet long and Dixon’s shadow is 18 feet long. If Ariadne is 5 feet tall , how tall is Dixon ?

Answers

Hey there! I'm happy to help you!

To solve this, we can set up a proportion below! I will put the data in table, fraction, and ratio form so you can see different ways to visualize it.

                       HEIGHT         LENGTH OF SHADOW

DIXON               ?                              18

ARIADNE           5                              15

 

                     or

[tex]\frac{height}{length} =\frac{5}{15} =\frac{h}{18}[/tex]

                     or

5:15= h:18

As we can see, we see that Ariadne's length of shadow is three times as large as her height. Therefore, that means that Dixon's height will be 1/3 of the length of his shadow!

18/3= 6

We can also use the cross multiplying method with our proportion and then solve for h!

h=5*18/15

h=90/15

h=6

Therefore, Dixon is six feet tall.

I hope that this helps! Have a great day!

There were 208 tickets purchased for a major league baseball game. The lower box  tickets cost ​$12.50 and the upper box tickets cost ​$10.00. The total amount of money spent was ​$2187.50. How many of each kind of ticket were​ purchased?

Answers

Answer:

so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold

Step-by-step explanation:

lets take "x" as the # of lower box tickets

and "y" as the number of upper box tickets

so in total the number of tickets sold was 208

so  x+y=208

next, we know that each lower box ticket costs 12.50 and each upper box tickets costs 10 and the total amount of money spent was $2187.50 so:

12.5x+10y=2187.50

lets subtract "x" from both sides in first equation to find value of y

y=208-x

now substitute y in equation number 2:

12.5x-10(208-x)=2187.5

12.5x-2080+10x=2187.5

22.5x-2080=2187.5

22.5x=4267.5

x=189.666

so 189 tickets lower box tickets were purchased now, substitute 190 in equation 1 to find value of "y"

y=208-190

y=18

so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold

Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Answers

Answer:

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And the confidence interval is given by:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 186[/tex] the sample mean for the first sample

[tex] \bar X_2 = 171[/tex] the sample mean for the second sample

[tex]s_1 =33[/tex] the sample deviation for the first sample

[tex]s_2 =23[/tex] the sample deviation for the second sample

[tex]n_1 = 8[/tex] the sample size for the first group

[tex]n_2 = 7[/tex] the sample size for the second group

The confidence interval for the true difference is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We can find the degrees of freedom are given:

[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]

The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:

[tex] t_{\alpha/2}= \pm 1.77[/tex]

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And replacing into the formula for the confidence interval we got:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

What is the length of AC? PLEASE HELP ASAP WILL GIVE BRAINLIEST TY

Answers

Answer:

2.33 units

Step-by-step explanation:

[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]

line s has a slope of 2/5. line t is perpendicular to s. what is the slope of line t​

Answers

Answer:

-5/2

Step-by-step explanation:

In order to find the slope of a perpendicular line: negate the reciprocal of the original slope

What is the Surface Area of the figure below?




A
60 units2
B
60 units3
C
104 units2
D
104 units3

Answers

Answer:

D

Step-by-step explanation:

I'm really sry if it's wrong!

Help timed test! At which root does the graph...

Answers

Answer:

x = -2

Step-by-step explanation:

The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

To find where it will touch the axis set the factor equal to zero and solve.

(x + 2) = 0

subtract 2 from both sides

x = -2

Please Help!!!!!!! I am very confused. Can someone explain?

Answers

Answer:

1/6a-1/6, a=1

Step-by-step explanation:

Hey there! I can definitely explain :)

-2/3a+5/6a-1/6

Multiply the two terms (the first two), to have common denominators!

The common lowest (easiest to deal with) denominator is 18. So, multiply the first term (-2/3a) by 6/6 and the second term (5/6a) by 3/3!

-12/18a+15/18a-1/6

Now, add those together!

3/18a-1/6

Now simplify!

1/6a-1/6

If you want, you can solve for a!

1/6a=1/6

a=1

Hope this helps! Please mark brainliest :)

Someone please help me with math. Thank You

Answers

Answer:

4) 64 cubic inches

Step-by-step explanation:

8x8 = 64

Write the fraction from least to greatest: 1/8, 1/3, 1/8

Answers

Answer:

Start with making them equal.

1/8 --> 3/24

1/8 --> 3/24

1/3 --> 8/24

Now order them.

1/8, 1/8, 1/3.

Hope this helps ;)

FInd the permiter of a square with an area of 702.25 square yards

Answers

Answer:

The perimeter of the square is 106yd

Step-by-step explanation:

To solve this we first have to know the formula to calculate the area of ​​a square

a = area = 702.25yd²

s = side

a = s * s

we replace the values

702.25yd² = s * s

702.25yd² = s²

√(702.25yd²) = s

26.5yd = s

The side of the square is 26.5yd

Now we have to use the formula to calculate the perimeter of ​​a square

p = perimeter

s = side = 26.5yd

p = 4 * s

we replace with the known values

p = 4 * 26.5yd

p = 106yd

The perimeter of the square is 106yd

Answer:106 yards

Step-by-step explanation:

Length=L

Area=702.5

Area of square=L x L

702.5=L X L

702.5=L^2

L=√(702.5)

L=26.50

perimeter of square=4 x L

Perimeter of square=4 x 26.50

Perimeter of square=106

Perimeter of square=106 yards

What is the estimated sum?

Round each number to the nearest hundred before adding.

521,370 + 26,839




A 548,100


B 548,200


C 548,000


D 547,000
Pls help

Answers

Answer:

B

Step-by-step explanation:

521,370 would round to 521,400

26,839 would round to 27,800

and adding them would be

548,200

A bike tire has a diameter of 16 inches. What is the radius of the bike? What is the circumference of the bike?

Answers

Answer:

radius-8 inches cause math

circumference-50.27

Step-by-step explanation:

Pls help with this one I will give brainliest thank you!

Answers

Answer:

B. 10 in.

Step-by-step explanation:

When you do length times width times height 10*10*10 equals 1000

10*10=100 and 100*10=1000

Answer:10 feet

Step-by-step explanation:

edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B

lot showing the weights of puppiespuppies at the shelter where hehe volunteers. HeHe said that since 1 and one half1
1
2plus+22plus+2 and one fourth2
1
4plus+2 and three fourths2
3
4equals=8 and one half8
1
2​, the total weight of the puppiespuppies is 8 and one half8
1
2 lot showing the weights of puppiespuppies at the shelter where hehe volunteers. HeHe said that since 1 and one half1
1
2plus+22plus+2 and one fourth2
1
4plus+2 and three fourths2
3
4equals=8 and one half8
1
2​, the total weight of the puppiespuppies is 8 and one half8
1
2 poundspounds. Use the line plot to answer 4dash–7.

Answers

Answer:

dont know need points sorry

Step-by-step explanation:

Answer:

I'm confused on what to answer in this. Edit the question and put the question in it and then I will be able to answer it

In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.

Answers

Answer:

17.9

Step-by-step explanation:

A flagpole casts a shadow that is 36 feet long, while a yardstick casts a shadow of 48 inches long. About how tall is the flagpole?

Answers

Answer:

  27 ft

Step-by-step explanation:

The object is 3/4 times as tall as the shadow it makes. (1 yd/48" = 3'/4') So, the flagpole will be 3/4 times 36 ft, or 27 ft high.

The flagpole is 27 ft tall.

Find the area of the shape ​plssss help

Answers

ok so find the area of thesquare then triangles and then add them tiriange area is 1/2 times base times heightso 1/2 times 2 times 2 which is 4 divided by 2 which is 2 same with the other traingle so your total area for the traingles is 4. The area for the square is 2 times 2 which is 4. add them up yiouget the whole shape is 8 units squared Answer: 8 units squared

Step-by-step explanation:

Please what is the length of AC? Please 1 day no answer.

Answers

Answer: AC = 2.33

Step-by-step explanation:

use tangent to find the missing side

Tangent = opposite/adjacent

tan B = ?/5

tan 25 = ?/5

multiply each side by 5

? = 2.33153829.....

so

AC = 2.33

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