All categories

3 years ago

If v1 = (2,-5) and v2 = (4,-3), then the angle between the two vectors is _________. Round your answer to two decimal places.

1 answer:

3 0

The angle between two vectors is given by:
cos (x) = (v1.v2) / (lv1l * lv2l)
We have then:
v1.v2 = (2, -5). (4, -3)
v1.v2 = (2 * 4) + (-5 * (- 3))
v1.v2 = 8 + 15
v1.v2 = 23
We look for the vector module:
lv1l = root ((2) ^ 2 + (-5) ^ 2)
lv1l = 5.385164807
lv2l = root ((4) ^ 2 + (-3) ^ 2)
lv2l = 5
Substituting values:
cos (x) = (23) / ((5.385164807) * (5))
x = acos ((23) / ((5.385164807) * (5)))
x = 31.33 degrees
Answer:
The angle between the two vectors is:
x = 31.33 degrees

You might be interested in

A circular swimming pool has a radius of 15 ft. There is a path all the way around that pool that is three feet wide. A circle h

LuckyWell [14K]

The circumference of the outer edge of the path around the pool is 113.04 ft.

<h3>What is the circumference?</h3>

The Circumference (or) perimeter of circle = 2πR. where, R is the radius of the circle.

Given

A circular swimming pool has a radius of 15 ft.

There is a path all the way around that pool that is three feet wide.

A circle has a radius of 15 feet.

A larger circle goes around the smaller circle that is 3 feet wide.

The radius of the outer edge of the path around the pool = Radius of circle + width of outer circle.

The radius of the outer edge of the path around the pool = 15 + 3

The radius of the outer edge of the path around the pool = 18ft

The circumference of the outer edge of the path around the pool is;

$\rm Circumference=2\pi r\\\\Circumference = 2\times 3.14 \times 18\\\\Circumference=113.04 \ ft$

Hence, the circumference of the outer edge of the path around the pool is 113.04 ft.

To know more about circumference click the link given below.

brainly.com/question/5023328

8 0

2 years ago

Let w = 4. Enter >, <, or = to compare the expressions. 3w² + 1 10w + 8

Svetach [21]

Answer: ≥ without the line on the bottom.

Step-by-step explanation:

I am assuming the expression you are talking about are

$3w^{2} +1$ and $10w+8$ .

If we were to replace w with 4 and calculate, we will find the answer:

$3*4^{2} +1=3*16+1=48+1=49$

$10*4+8=40+8=48$

Since the first expression, $3w^{2} +1$ , is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.

6 0

2 years ago

58 = –2(m + 4) + m –22 –50 –66 –33

Anika [276]

Assignment: $\bold{Solve \ Equation: \ 58=-2\left(m+4\right)+m}$

<><><><><>

Answer: $\boxed{\bold{m=-66}}$

<><><><><>

Explanation: $\downarrow\downarrow\downarrow$

<><><><><>

[ Step One ] Switch Sides

$\bold{-2\left(m+4\right)+m=58}$

[ Step Two ] Expand $\bold{-2\left(m+4\right)+m}$

$\bold{-m-8}$

[ Step Three ] Rewrite Equation

$\bold{-m-8=58}$

[ Step Four ] Add 8 To Both Sides

$\bold{-m-8+8=58+8}$

[ Step Five ] Simplify

$\bold{-m=66}$

[ Step Six ] Divide Both Sides By -1

$\bold{\frac{-m}{-1}=\frac{66}{-1}}$

[ Step Seven ] Simplify

$\bold{x=-66}$

<><><><><><><>

$\bold{\rightarrow Mordancy \leftarrow}$

3 0

3 years ago

Read 2 more answers

How do you solve 7/8+(4/8-2/4)

SCORPION-xisa [38]

The answer is 7/8 find a common denominator or cross multiply

4 0

2 years ago

Question 2 of 5

Mice21 [21]

Answer:

Step-by-step explanation:

4 0

3 years ago