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

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:

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

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

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

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)

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.

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.

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.

-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

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


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.

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]

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

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

Answers

Answer:

1/a^3 and 1/b^5

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

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

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

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!

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].

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

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

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

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!

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

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

Someone help





Plssssssssssssssssssssssssss

Answers

You can use the Reflections or translation

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:




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

Answers

Answer:

the answer is 360 degrees

Step-by-step explanation:

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

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

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