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
Nadya [2.5K]
2 years ago
6

Which expression is equivalent to

Mathematics
1 answer:
inn [45]2 years ago
5 0
C. It is C because of this answer down here

X^10Y^14 / 729
You might be interested in
A hypothesis is only tentative: to make sure it's valid, you have to ___________.
GREYUIT [131]
A hypothesis is only tentative: to make sure it's valid, you have to test it.
4 0
3 years ago
Find an example for each of vectors x, y ∈ V in R.
rjkz [21]

(a) Both conditions are satisfied with <em>x</em> = (1, 0) for \mathbb R^2 and <em>x</em> = (1, 0, 0) for \mathbb R^3:

||(1, 0)|| = √(1² + 0²) = 1

max{1, 0} = 1

||(1, 0, 0)|| = √(1² + 0² + 0²) = 1

max{1, 0, 0} = 1

(b) This is the well-known triangle inequality. Equality holds if one of <em>x</em> or <em>y</em> is the zero vector, or if <em>x</em> = <em>y</em>. For example, in \mathbb R^2, take <em>x</em> = (0, 0) and <em>y</em> = (1, 1). Then

||<em>x</em> + <em>y</em>|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||<em>x</em>|| + ||<em>y</em>|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2

The left side is strictly smaller if both vectors are non-zero and not equal. For example, if <em>x</em> = (1, 0) and <em>y</em> = (0, 1), then

||<em>x</em> + <em>y</em>|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||<em>x</em>|| + ||<em>y</em>|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2

and of course √2 < 2.

Similarly, in \mathbb R^3 you can use <em>x</em> = (0, 0, 0) and <em>y</em> = (1, 1, 1) for the equality, and <em>x</em> = (1, 0, 0) and <em>y</em> = (0, 1, 0) for the inequality.

(c) Recall the dot product identity,

<em>x</em> • <em>y</em> = ||<em>x</em>|| ||<em>y</em>|| cos(<em>θ</em>),

where <em>θ</em> is the angle between the vectors <em>x</em> and <em>y</em>. Both sides are scalar, so taking the norm gives

||<em>x</em> • <em>y</em>|| = ||(||<em>x</em>|| ||<em>y</em>|| cos(<em>θ</em>)|| = ||<em>x</em>|| ||<em>y</em>|| |cos(<em>θ</em>)|

Suppose <em>x</em> = (0, 0) and <em>y</em> = (1, 1). Then

||<em>x</em> • <em>y</em>|| = |(0, 0) • (1, 1)| = 0

||<em>x</em>|| • ||<em>y</em>|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0

For the inequality, recall that cos(<em>θ</em>) is bounded between -1 and 1, so 0 ≤ |cos(<em>θ</em>)| ≤ 1, with |cos(<em>θ</em>)| = 0 if <em>x</em> and <em>y</em> are perpendicular to one another, and |cos(<em>θ</em>)| = 1 if <em>x</em> and <em>y</em> are (anti-)parallel. You get everything in between for any acute angle <em>θ</em>. So take <em>x</em> = (1, 0) and <em>y</em> = (1, 1). Then

||<em>x</em> • <em>y</em>|| = |(1, 0) • (1, 1)| = |1| = 1

||<em>x</em>|| • ||<em>y</em>|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2

In \mathbb R^3, you can use the vectors <em>x</em> = (1, 0, 0) and <em>y</em> = (1, 1, 1).

8 0
3 years ago
An elevator travels 310 feet in 10 seconds. how far can this elevator travel in 12 seconds?​
anyanavicka [17]

Answer:

372 ft

Step-by-step explanation:

310 divided by 10 is 31 and 31x12 is 372

3 0
3 years ago
Read 2 more answers
N2-m: use m=7 and n=8 Please explain how to do this.
Ivenika [448]
If N = 8
if M = 7
then the equation is 8(2) - 7
do the multiplication first 8(2) = 16
now do the subtraction 16 - 7 = 9
8 0
2 years ago
Randi bought a wallet for $8.33. She paid with a $20 bill. Which of the following could be the change she received?
Feliz [49]
I think the answer is $11.67 
8 0
3 years ago
Read 2 more answers
Other questions:
  • Ahhhhhhhhhhhh help I need help please
    9·1 answer
  • I rly need help pls help me
    8·1 answer
  • Help on one last question! :D
    11·1 answer
  • assume I can see it's a right triangle and giving the condition c equal 2 b equal 45 ,solve for the side lengths of the right tr
    13·1 answer
  • What are two consecutive integers that have a sum of -67
    6·1 answer
  • N equation is shown below:
    5·1 answer
  • △ABC is congruent to △DEF. What is the value of x? Explain how you determined your answer.
    6·1 answer
  • Answer this please! No links please
    5·1 answer
  • Please help me on number (15) Will mark brainliest
    15·1 answer
  • Math Equations. Just need to finish my homework :)
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!