1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
JulijaS [17]
2 years ago
14

Given that u =< 2,12 >, and z =< -7,5 >

Mathematics
1 answer:
swat322 years ago
7 0

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

u = ⟨2, 12⟩   ⇒   ||u|| = √(2² + 12²) = 2√37

z = ⟨-7, 5⟩   ⇒   ||z|| = √((-7)² + 5²) = √74

u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46

and so

||w|| = √((2√37)² + 2•46 + (√74)²)

… = √(4•37 + 2•46 + 74)

… = √314 ≈ 17.720

Alternatively, without mentioning the dot product,

w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩

and so

||w|| = √((-5)² + 17²) = √314 ≈ 17.720

You might be interested in
Please HELP!! ILL GIVE BRAINLEST! QUCIK PLEASE HELP!!
Elena-2011 [213]

Answer:

d. linear; $25/hour

Step-by-step explanation:

From looking at the graph, we have that renting for 2 hours costs $50, for 4 hours costs $100, for 6 hours costs $150, and for 8 hours costs $200. To find out whether the quantities described in the table are linear, we have to see if there is a constant rate of change of price.

For hour 2 to hour 4, we can see that the price increases by $50. This is the same for hour 4 to hour 6 and hour 6 to hour 8. For every 2 hour time interval, the price increases by $50. Therefore, there is a constant rate of change and the quantities described in the table are linear.

Now we have to find the constant rate of change per hour. We know that the price increases by $50 every 2 hours, so, by dividing both the hours and price increase by 2, the price increases by $25 per hour. So the constant rate of change is $25/hour.

Linear. $25/hour

Answer choice d.

I hope you find my answer and explanation to be helpful. Happy studying.

6 0
3 years ago
10- 3/4z = 8<br><br> Somebody, please help me! I don't get this!
gizmo_the_mogwai [7]

Answer:

z = 8/3

Step-by-step explanation:

10- 3/4z = 8

Subtract 10 from each side

10-10- 3/4z = 8-10

-3/4z = -2

Multiply each side by -4/3

-3/4z * -4/3 = -2 *4/3

z = 8/3

6 0
2 years ago
HELP!!
Contact [7]

Answer:

Yes

Step-by-step explanation:

Statement                                         Reason

ab = bd                                               Given

ac=cd                                                  Given

bc = cb                                                definiton of reflex line

triangle abc is congruent to triangle dbc      side side side postulate

7 0
3 years ago
Read 2 more answers
Emil was dividing his candy among 15 friends and himself. If eachperson received 4 pieces, how many pieces of candy did Emil hav
Neko [114]
I think it’s probably 2
7 0
2 years ago
Plz help i will mark you brainlist this is due in 5 minutes
pshichka [43]

Answer: -10 degress is colder than -4

so the answer will be: C (-10 < -4)

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • I really need help on this question! !!ASAP!!!​
    10·2 answers
  • What is the equation of the line written in general form?
    14·1 answer
  • Will give brainliest to person who answers first. Much appreciated:)
    13·2 answers
  • A circuit shows that the impedance of a component is −56i−56i. Is the component a resistor, a capacitor, or an inductor? Select
    10·1 answer
  • Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralph, and Peter weighs three
    8·1 answer
  • Suppose a quarter of all the elephants in an African wildlife refuge have ear tags. If there are exactly 60 tagged elephants, wh
    7·1 answer
  • Convert 657 milligrams to grams.<br><br> 0.657 g<br> 6.57 g<br> 657 g<br> 6,570 g
    5·2 answers
  • Please help 50 points
    6·2 answers
  • Pamela's age is two times Jiri's age. The sum of their ages is 84. What is Jiri's age?
    15·1 answer
  • 100 POINTS IF U GET THIS RIGHT!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!