Let u = (−2, 3, 1), v = (−1, −1, 2), and 3u − 2v − 4w = (3, 2, −3). Find: a. The vector w.b. -2u + 3v - 5w

Answers

Answer 1

Answer:

(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Step-by-step explanation:

Given:

u = (−2, 3, 1)

=> u = -2i + 3j + k                           --------------------------(i)

v = (−1, −1, 2)

=> v = -i - j + 2k                                --------------------(ii)

3u − 2v − 4w = (3, 2, −3)

=> 3u − 2v − 4w = 3i + 2j - 3k             ------------------(iii)

(A) TO FIND THE VECTOR w

Let:

w = (a, b, c) = ai + bj + ck

(a) Substitute u, v and w into equation (iii)

3u − 2v − 4w = 3i + 2j - 3k

3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k

(b) Solve the equation in step (a) by opening the brackets and collecting like terms

(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k

open brackets

-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k

collect like terms

-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k

i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k

(c) Solve for a, b and c in step (b)

Comparing both sides of the equation, we have;

-4 - 4a = 3              ----------(*)

11 - 4b = 2              -----------(**)

-1 - 4c = -3             ------------(***)

From (*)

4a = -4 - 3

4a = -7

a = [tex]\frac{-7}{4}[/tex]

From (**)

4b = 11 - 2

4b = 9

b = [tex]\frac{9}{4}[/tex]

From (***)

-1 - 4c = -3

4c = -1 + 3

4c = 2

c = [tex]\frac{2}{4}[/tex]

c = [tex]\frac{1}{2}[/tex]

Remember that

w = (a, b, c)

w = ai + bj + ck

Therefore,

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(B) TO FIND -2u + 3v - 5w

Remember that;

u = (−2, 3, 1)

v = (−1, −1, 2),

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Substitute u, v, w into the expression as follows;

-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Expand

(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]

Collect like terms

(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])

Solve

([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])


Related Questions

-2.5 + d = -3.6 What is the sum?

Answers

Answer:

-1.1

Step-by-step explanation:

we take -3.6 minus -2.5

which we get -1.1 hav a nice day :]

Answer:

d = -1.1

Step-by-step explanation:

-3.6 - ( -2.5) = -1.1

Where is the point of intersection? x − 2y + 2 = 3 and x − y = 3

Answers

Answer:

Step-by-step explanation:

x -2y = 1

x - y = 3

x - 2y = 1

-x + y = -3

-y = -2

y = 2

x - 2 = 3

x = 5

(5, 2)

Employee Time Card
DATE
IN
OUT
IN
OUT
HOURS
Sun.
Mon.
7:00 AM
11:00 AM
12:00 P.M.
a.
4:04 PM
3:59 P.M.
Tue.
7:05 AM
11:55 PM
b.
Wed.
7:01 AM
11:10 AM
10:59 AM
10:55 AM
12:05 PM
C.
Thur.
6:59 AM
3:58 P.M.
4:03 P.M.
3:49 PM
12:01 PM
12:02 PM
d.
Fri.
6:55 AM
11:01 AM
e.
Sat
TOTAL HOURS

Answers

31 hours 57 minutes.
In most jobs, the employees round up so that would make it 32 hours.
32x7.50= 240
If they wanted to be technical you could do 31.57x7.5 and that would make it 236.78
It’s up to you which one you go with

Answer:

31 hours 57 minutes.

In most jobs, the employees round up so that would make it 32 hours.

32x7.50= 240

If they wanted to be technical you could do 31.57x7.5 and that would make it 236.78

It’s up to you which one you go with

Step-by-step explanation:

A carpenter sands of a dresser in hour. At this rate, how long does it take the
carpenter to sand 1 dresser?
o hour
o hour
O 1 hours
O 23 hours

Answers

Question:

A carpenter sands 1/2 of a dresser in 3/4 hour. At this rate, how long does it take the carpenter to sand 1 dresser?

Answer:

[tex]1\ dresser = \frac{3}{2} hour[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]

Required

How long will it take to sand 1 dresser

[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]

Multiply both sides by 2

[tex]2 * \frac{1}{2} dresser = \frac{3}{4} hour * 2[/tex]

[tex]1\ dresser = \frac{3}{4} hour * 2[/tex]

[tex]1\ dresser = \frac{3}{2} hour[/tex]

Hence;

It'll take 3/2 hour to sand 1 dresser

Answer:

Step-by-step explanation:

hey babe

Miles traveled, miles to go, fill in the “?”

Answers

Answer:

The blank is 170

Step-by-step explanation:

The ratio from miles traveled to miles to go is 1:-1

520-0=520

520-100=420

520-200=320

520-350=170

520-520=0

Rewrite with positive exponents a^-3 b^-5

Answers

Answer:

1/a^3 and 1/b^5

I am a pair of numbers and my product is 1, what am I?

Answers

Answer:

Step-by-step explanation:

How I Al's have doubts

Determine whether the equation is always, sometimes, or never true.


2/3 x + 4 = 2x

Answers

Answer:

Always true

Step-by-step explanation:

Given

[tex]\frac{2}{3}x + 4 = 2x[/tex]

Required

Determine its type of solution

[tex]\frac{2}{3}x + 4 = 2x[/tex]

Collect Like Terms

[tex]2x - \frac{2}{3}x = 4[/tex]

Take LCM

[tex]\frac{6x - 2x}{3} = 4[/tex]

[tex]\frac{4x}{3} = 4[/tex]

Multiply both sides by [tex]\frac{3}{4}[/tex]

[tex]\frac{4x}{3} * \frac{3}{4}= 4 * \frac{3}{4}[/tex]

[tex]x = 4 * \frac{3}{4}[/tex]

[tex]x = 3[/tex]

Hence, the equation is always true for x = 3

Evaluate the expression when c=-6.
c? +6c+5

Answers

Answer: -31

Step-by-step explanation: 1.) Plug in -6 for c

2.) equation will then be: 6(-6)+5

3.) use PEMDAS: multiply first then addition

4.) 6(-6) equals -36

5.) add -36+5 which equal -31

Therefore your answer should be -31

The answer should be -31


Explanation:




Use the position function s(t) = –4.9t2 + 500, which gives the height (in meters) of an object that has fallen for t seconds from a height of 500 meters. The velocity at time t = a seconds is given by the following.
lim t->a: (s(a) - s(t)) / (a - t)
Find the velocity of the object when t = 3. (Round your answer to two decimal places.)

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  value is  [tex]v(3) =  29.4 \  m/s[/tex]

Step-by-step explanation:

From the question we are told that

    [tex]s(t) =  -4.9t^2 + 500[/tex]

And  

    [tex]\lim_{t \to a}  \frac{s(a) - s(t)}{a-t}[/tex]

Generally s(t) at t = a is mathematically evaluated as

      [tex]s(a) =  -4.9a^2+ 500[/tex]

So

    [tex]s(a) - s(t) =  -4.9a^2 + 500 - ( -4.9t^2+500)[/tex]

     [tex]s(a) - s(t) =  -4.9a^2 + 500 +4.9t^2-500)[/tex]

      [tex]s(a) - s(t) = 4.9(t^2 - a^2)[/tex]

Thus the velocity is represented as

     [tex]v(t) =\lim_{t \to a}  \frac{s(a) - s(t)}{a-t} \equiv \lim_{t \to a} \frac{4.9(t^2 -  a^2 )}{ a-t}[/tex]

=>     [tex]v(t) = \lim_{t \to a}  - 4.9(a + t )[/tex]

=>      [tex]v(t) = -4.9 (a + a )[/tex]

=>      [tex]v(t) = -9.8a[/tex]

Now at  t =  3

=>  [tex]v(3) = -9.8 (3)[/tex]

=>   [tex]v(3) =  29.4 \  m/s[/tex]

Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number.

Answers

Answer:

[tex]\frac{1}{w^{29}}[/tex]

Step-by-step explanation:

The given expression is [tex]\frac{w^{-7}(w^{-9})^2}{w^4}[/tex].

Since, [tex]w^{-7}=\frac{1}{w^7}[/tex]

And [tex]w^{9}=\frac{1}{w^9}[/tex]

Expression will become,

[tex]\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}[/tex]

               [tex]=\frac{\frac{1}{w^7\times w^{18}}}{w^4}[/tex]

               [tex]=\frac{\frac{1}{w^{(7+18)}}}{w^4}[/tex]

               [tex]=\frac{1}{w^{25}}\times \frac{1}{w^4}[/tex]

               [tex]=\frac{1}{w^{25}\times w^4}[/tex]

               [tex]=\frac{1}{w^{29}}[/tex]

Therefore, Simplified form of the given expression will be [tex]\frac{1}{w^{29}}[/tex].

The sum of all of the exterior angles of an octagon is:

Answers

Answer:

1080°

Step-by-step explanation:

sum = 180 ( n - 2)

note that octagon has 8 sides

therefore

sum = 180 ( 8 - 2)

sum = 1080°

Answer:

c.  1080

Step-by-step explanation:

= 180 x ( 8 - 2)

= 1080

Ellie drives 22.5 miles in 45 minutes. If she drove three hours in total at the same rate, how far did she go?

Answers

Answer:

90

Step-by-step explanation:

3 hours = 180 mins

180 ÷ 45 = 4. so Ellie will drive 4x more miles in 3 hours.

22.5 × 4 = 90

A chocolate company makes chocolate malt balls that have a radius of 0.34
inches. The carton they are to be packed in is approximately a rectangular prism with
dimensions 1.5 inches by 2.5 inches by 6 inches. How many malt balls will fit in the
carton

Answers

Answer:

Approximately 141 malt balls

Step-by-step explanation:

this problem is on the mensuration of solids shapes.

first we need to calculate the volume of the rectangular prism

volume of prsim= l*b*h

given that

length= 1.5 in

breath=2.5 in

hieght= 6 in

volume= 1.5*2.5*6

volume=22.5 in^3

secondly we then calculate the volume of a malt ball

given that

raduis r= 0.34

volume of sphere = 4/3πr^3

volume of sphere = 4/3*3.124*(0.34)^3

volume of sphere = 1.33*3.142*0.039

volume of sphere = 0.16 in^3

now we can calculate the amount of sphere that can fit into the prism as

= volume of prism/volume of sphere

= 22.5/0.16

=140.6

approximately 141 malt balls

Rosa is currently x years old. In 28 years, Rosa will be 3 times the age she is now. Which equation can be used to find Rosa's age?

Answers

Answer:

multiple 28 and 3 u will get the answer

Step-by-step explanation:

I think It will help you

33 points!!! The line contains the point (8,2) and is parallel to a line with a slope of -2/3 The equation of the line is

Answers

Answer:

y=mx+b

y=-2/3x+2

Step-by-step explanation:

-2/3=slope

x= y coord.

What is $12.78 rounded to the nearest dollar?

Answers

Answer:

$13

Step-by-step explanation:

[tex]\$12.78 = \$13[/tex]

Answer:$13

Step-by-step explanation:

.7 rounds to 1 if it is 5 or above it rounds up

How do you do this question?

Answers

Step-by-step explanation:

Use the first fundamental theorem of calculus.

∫₆¹⁰ f'(x) dx = f(10) − f(6) = 8 − 8 = 0

One-third of a number decreased by four

Answers

Answer: (X/3)*4

Step-by-step explanation:

(1/3)*x

decreased by 4: (1/3)*x-4

y varies inversely with x. If y = 5 when x = 60, find y when x = 150

Answers

Answer:

y =2 when x = 150

Step-by-step explanation:

Inverse variation is

xy = k

5*60 = k

300 = k

xy = 300

150y = 300

Divide by 150

150y/150 = 300/150

y = 2

order the number from greatest to least
3 1/3,3.34,300%​

Answers

Answer:

3.34, 3 1/3 300%

3.34,3 1/3,300%

Sorry if I’m wrong

The sum of all of the exterior angles of an octagon is:

Answers

Answer:

the answer is 360 degrees

Step-by-step explanation:

twice this number is 1 less than half of 26

Answers

Answer:

2x = (1/2)(26) - 1

The number is 6.

Step-by-step explanation:

2x = (1/2)(26) - 1

2x = 13 - 1

2x = 12

x = 6

The answer is 6.

Explanation: 2x= 12; 12/2= 6. Therefore, x=6

What is the product of (5/5)(614) ? Simplify your answer.

Answers

Answer:

614

Step-by-step explanation:

5/5 is just 1 because 5÷5=1

1 multiplied by 614 = 614

Hope this helped!

Someone please help me ❤️

Answers

Answer:

week 5!

Step-by-step explanation:

Answer:

yes, week 55️⃣

Step-by-step explanation:

just see the little blue points

How many days are in a week ?the answer is measured in the

Answers

Answer:

7 days are in a week. 5 week days, 2 days for the weekend hope this helps.

7k-k+19 Combine like terms

Answers

Step-by-step explanation:

7k-k+19

6k+19 should be fine

Steps to solve:

7k - k + 19

~Combine like terms

6k + 19

Best of Luck!

What is the solution to the equation?
{+55 - 466
{+55 = 466
O [+55-55-466+55
f=521
+55 = 466
O +55+55-466+55
{ = 521
(+55 = 466
O +55-55-466-55
f=411
f+55 = 466
Of+ 55+55-466-55
f = 411

Answers

Answer:

f=55=466

f+55-55=466-55

Step-by-step explanation:

Find the solution of the term.

Someone help





Plssssssssssssssssssssssssss

Answers

You can use the Reflections or translation


2. A stock price rose 2.2 points in
Week 1. The stock price fell 5.4
points in Week 2. Write and solve
an equation to represent the total
price change in stock.

Answers

Answer: the total  price change in stock is fall of 3.2 points or -3.2 points.

Step-by-step explanation:

In integers , we use positive integers to show rise in amount whereas we use negative integers to show fall .

Given: A stock price rose 2.2 points in  Week 1.

i.e. +2.2 points rise.

The stock price fell 5.4  points in Week 2.

i.e. fall of -5.4.   (Much greater, than it rose)

The equation to represent the total  price change in stock would be

Total  price change = price rose in  Week 1 +  price fell  in Week 2.

= [+2.2 + (-5.4)] points

= 2.2 - 5.4 points   [ (+)(-) = (-)]

= -3.2 points

Hence, the total  price change in stock is fall of 3.2 points.

Other Questions
4. What is the crux of a political institution? Hope wants to add a third use at the end of hernitrogen list.What should Hope do first?fWhat is Hope's next step? explain how the biosphere facilities movement of water from the geosphere to the atomosphere. Find the slope of the line through each pair of points. (-17,-5), (15.-13) Which of the following statements about irrigated and non-irrigated land is true? A. Irrigated land is less valuable than non-irrigated land. B. Irrigated land and non-irrigated land have no value. C. Irrigated land is more valuable than non-irrigated land. D. Irrigated land and non-irrigated land have the same value. Will GIVE BRAINLIEST!!!!!!!! Which statements describe dichotomous keys? Check all that apply. A dichotomous key uses characteristics to separate organisms from one another. A dichotomous key uses characteristics to separate organisms into two groups. Dichotomous keys use questions or statements to identify organisms. Dichotomous keys may be created with yesno questions. Dichotomous keys may have three or more answers for each question or statement. A recipe that makes a dozen cookies calls for 1 1/2 cups of milk, 2.25 cups of flour, and 1 1/4 cups of other ingredients. How many cups of other ingredients, milk and flour are needed to make 36 cookies? (1 dozen is 12 cookies) The planet in our solar system whose orbit actually brings it inside the orbit of another planet isA. PlutoB. MercuryC. MarsD. NeptuneE. Earth Given the equation ay b = c, which expression represents y? a.) c-b/a b.) c+b/y c.) c+b/a d.) c+a/b what makes a star produce energy 12. If a friend always finds something wrong with any situation, then he(she) is a(n):O optimistO pessimistO emotionalO ironicO sarcastic Are terms and ratios related? ne wouldn't.Justin puede ir al bao. Es muy bueno. Write an algorithm to settle the following question: A bank account starts out with $10,000. Interest is compounded monthly at 6 percent per year (0.5 percent per month). Every month, $500 is withdrawn to meet college expenses. After how many years is the account depleted? Here is what I got so far. Can you tell if I am on the right track. Step 1 Start with the table: Month Balance 0 $10,000.00 Step 2 Repeat steps 2a, 2b, 2c while the balance is greater than $0.00 Step 2a. Add a new row to the table. Step 2b. In column 1 of the new row, labeled "Month", put one more than the preceding month value. Step 2c. In column 2 of the new row, labeled "Balance", place the value of this formula b * (1 + 0.005) - 500 where b is the preceding balance value. Step 3 Read the last number in the month column (let's call it months). Report that the account will be depleted in (months / 12) years and (months % 12) months. Can you please please help me with this please its so hard and i will give you a branlist Programming environment is Is the following sentence true or false? A scientific law attempts toexplain an observed pattern in nature. The product of 2 and a number x is 3/4. What is the value of x? x=5/4 x=3/8 x=1 1/4 x=3/2 The Hellenistic Age was characterized by a regular polygon of 2 k + 1 sides has 140 as size of each interior angle find K