For 3 and 4 find the slope of the line that passes through the given points

Based on the graph, which inequality is correct for a number that is to the right of -3?

RSB [31]

Positive infinity is going after three hope this helps

8 0

2 years ago

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

Y^2 x^3-7x = ysin(x+y)

d1i1m1o1n [39]

Answer: -54

Step-by-step explanation: 53 + 1 = 54

3 0

3 years ago

Select the sets of data where it would be better to use a histogram than a

Contact [7]

Answer:

Weight of students in your class

Daily rainfall in Miami over a month

Step-by-step explanation:

A histogram is applied when the data is discrete/ continuous to present a visual understanding of the data by showing the number of data set fitting is a specified range.

A dot plot utilizes data which has only one measured variable, where the variable can be organized into categories.

8 0

3 years ago

For the members of a neighborhood meeting group, the probability of randomly selecting a member who likes to cook is 42%, the pr

Monica [59]

Answer: Probability of randomly selecting a member who likes to cook or likes to sew = 58%

Step-by-step explanation:

Since we have given that

Probability of a randomly selecting a member who likes to cook=P(C) = 42%

Probability of a randomly selecting a member who likes to sew =P(S)= 23%

Probability of a randomly selecting a member who likes to both cook and sew

$P(C\cap S)=7\%$

As we know the "Probability rules " :

$P(C\cup S)=P(C)+P(S)-P(S\cap C)\\\\P(C\cup S)=42+23-7\\\\P(C\cup S)=58$

So, Probability of randomly selecting a member who likes to cook or likes to sew = 58%

5 0

3 years ago