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konstantin123 [22]
2 years ago
15

Let vector a = 3i + j - k. Find the vector b in the direction of vector a such that |b| = 5

Mathematics
1 answer:
Serjik [45]2 years ago
3 0

Answer:

5i +(5/3)j - (5/3)k

Step-by-step explanation:

Vector b is in the same direction as vector a, so it is a scalar multiple of a.

b = ca for some positive real number c.

b = c(3i + j - k) = 3ci + cj - ck

|b| = sqrt[(3c)^2 + c^2 - c^2] = sqrt(9c^2) = 3c

If |b| = 5, then 3c = 5 and c = 5/3

That makes b = (5/3)(3i + j - k) = 5i +(5/3)j - (5/3)k

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Thompson High School had a population of 1800 students in 2010. Every year since then, the population has grown by 50 students a
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3 years ago
Here is a list of the normal monthly precipitation (in inches) for January for 20 different U.S. cities. 4.0, 1.0, 1.5, 1.6, 2.0
shutvik [7]

Answer:

minimum value = 1.0 , the lower quartile = 2.3, the middle value = 3.5.

the upper quartile = 3.95, the maximum value  = 7.3.

Step-by-step explanation:

Five Number Summary of any data consists basically of 5 data sets.

1) The minimum Value

2)The first (lower) quartile

3) The middle value (Median)

4) The third (upper) quartile

5)The maximum value

Now, the given data is  4.0, 1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.1, 5.8, 4.1, 7.3

Arrange it in the ascending order,

1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.0, 4.1, 4.1, 5.8, 7.3

Here,

1) The minimum Value  is 1.0

2)The first (lower) quartile  is  2.3.

3) The middle value (Median)  is 3.5.

4) The third (upper) quartile is  3.95.

5)The maximum value  is 7.3.

7 0
3 years ago
2.
Artyom0805 [142]

Answer:

C) y = \frac{1}{2} × 4^x

6 0
2 years ago
Read 2 more answers
We have two stacks of styrofoam cups. One stack has 6 cups, and its height is 15 cm. The other stack has 12 cups, and its height
Irina18 [472]

Complete Question

We have two stacks of styrofoam cups. One stack has 6 cups, and its height is 15 cm. The other stack has 12 cups, and its height is 23 cm. How many cups are needed for a stack with a height of 50 cm

Answer:

37.5 cups

Step-by-step explanation:

Height 1 = 15cm

Number of cups = 6

Height 2 = 23 cm

Number of cups = 12

Hence:

H1 - H2/N1 - N2

= 15 - 23/6 - 12

= -8/-6

= 4/3

The number of cups that are needed for a stack with a height of 50 cm is calculated as:

50 cm ÷ 4/3

= 50 × 3/4

= 37.5 cups

3 0
2 years ago
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