Y = 3•2^x+1 +2 Graph the equation State the domain and range State the asymptote

Find an example for each of vectors x, y ∈ V in R.

rjkz [21]

(a) Both conditions are satisfied with x = (1, 0) for $\mathbb R^2$ and x = (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 x or y is the zero vector, or if x = y. For example, in $\mathbb R^2$ , take x = (0, 0) and y = (1, 1). Then

||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(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 x = (1, 0) and y = (0, 1), then

||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2

and of course √2 < 2.

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

(c) Recall the dot product identity,

x • y = ||x|| ||y|| cos(θ),

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

||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|

Suppose x = (0, 0) and y = (1, 1). Then

||x • y|| = |(0, 0) • (1, 1)| = 0

||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0

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

||x • y|| = |(1, 0) • (1, 1)| = |1| = 1

||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2

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

8 0

3 years ago

Can someone help me?

soldier1979 [14.2K]

Answer:

Step-by-step explanation:

First your going to plug in what p and q are into the equation so 3(2)^5+10(-3)^2 over 7(2)+1.

Your going to first do (2)^5 and (-3)^2 so it’s going to be 3(32)+10(9) over (multiply the 7(2) first) 14+1.

3(32)+10(9) over 14+1 now multiply 3(32) and 10(9) you should get (96)+(90) over 15.

add 96+90 to get 186 over 15.

then divide how many times 15 can go into 186 you should get 12 6/15 and divide 6/15 by 3 to get your final answer 12 2/5.

I hope this helps!

5 0

2 years ago

(x+5)(x+1)+(x+5)(x+8)

gtnhenbr [62]

Answer:

2x² + 19x + 45

Step-by-step explanation:

(x + 5)(x + 1) + (x + 5)(x + 8) ← expand both sets of factors using FOIL

= x² + 6x + 5 + x² + 13x + 40 ← collect like terms

= 2x² + 19x + 45

5 0

2 years ago

Please help, this is due tonight

dolphi86 [110]

Answer:

It's B

Step-by-step explanation:

Just divide y by x. For example: 6.6 / 6 = 1.1. This would be B! Hope this helps!

6 0

2 years ago

Read 2 more answers

Solve the system of equations: y = 2x + 1 y = x2 + 2x - 8

Elan Coil [88]

(3,7),(-3,-5)

that’s what it would look like on a graph

4 0

2 years ago