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Dafna11 [192]
3 years ago
7

How many kilometers they traveled by bike

Mathematics
1 answer:
ad-work [718]3 years ago
5 0
So if you divide the total in half its 162.5. So if they traveled 75km more by bike, you add 75 to that which equals 237.5. So your answer is 237.5
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jesse walks 3 miles per hour to school.the school is 1.5 miles away.How long would it take jesse to walk to school
Pavlova-9 [17]
1 hour 30 minutes!
Please mark this the brainlest answer
5 0
2 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
Is this a function or a non function?​
ElenaW [278]

Answer:

This is a function

Step-by-step explanation:

If you do the Vertical Line Test you can see that the line passes through only one dot at a time. Therefore it is a function. If the line passed through more than one dot at a time then it wouldn't be a function.

4 0
2 years ago
Find the area of the following figure. Explain how you found your answer.
iragen [17]

Answer:

Below

Step-by-step explanation:

Let's say that each square on the grid represents 1 cm

First find the area of the two triangles

For the larger one: A = bh/2

A = 3 x 3 / 2

  = 4.5 cm^2

For the smaller one : A = bh/2

A = 2 x 2 / 2

   = 2 cm^2

For the rectangle : A = lw

A = 4 x 5

   = 20 cm^2

Add them all up to get the area

4.5 + 2 + 20 = 26.5 cm^2

Hope this helps!

5 0
2 years ago
Read 2 more answers
There are 72 students in the marching band. The ratio of girls to boys is 19 to 17.
8090 [49]

Answer:

34 boys

Step-by-step explanation:

72 students

G-19:B-17 Ratio

19 + 17 = 36

72/36 = 2

19 x 2 = 38

38 girls

17 x 2 = 34

34 boys

4 0
3 years ago
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