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2 years ago

find the angle between vectors a =(1,2) and b = (1,-1/2). Brainliest for correct answer. Look at photo.

Mathematics

1 answer:

rosijanka [135]2 years ago

8 0

Answer:

90°

Step-by-step explanation:

The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.

The slope to point 'a' is y/x = 2/1 = 2.

The slope to point 'b' is y/x = (-1/2)/1 = -1/2.

The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.

We can also use the trig formula for the tangent of the difference of angles.

tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangents are the slopes, calculated above, so we have ...

tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = undefined

The tangent is undefined for angles that are odd multiples of 90°. The angle between the vectors is 90°.

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01.05 what is the slope intercept form equation of the line that's passing through (1,3) and (3,7)

Butoxors [25]

Hello!

To find the slope-intercept form equation of the line that passes through the two points is found by first, calculating the slope using the slope formula and substitution, and secondly, finding the y-intercept of the equation through substitution.

Remember, slope-intercept form is written as: y = mx + b, where m is the slope and b is the y-intercept.

1. Find the slope

The slope formula is: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ . To use this formula, you need two points and also, you need to assign these points to $x_{1}$ , $x_{2}$ , $y_{1}$ , and $y_{2}$ .

In this case, $x_{1}$ and $x_{1}$ is assigned to the ordered pair (1,3), while $x_{2}$ and $y_{2}$ is assigned to (3, 7). After assigning these points, you can substitute the pairs into the formula and simplify.

$\frac{7-3}{3-1} =\frac{4}{2} = 2$

The slope of these two points is 2.

2. Find the y-intercept

To find the y-intercept, you substitute an ordered pair into the slope-intercept equation with the slope that was just calculated. We can use either ordered pair because it will result in the same y-intercept.

y = 2x + b (substitute)

3 = 2(1) + b (simplify)

3 = 2 + b (subtract 2 from both sides)

1 = b

The y-intercept of the two points is (0, 1).

With the necessary values to complete the equation, we can write the final equation.

The slope-intercept form equation of the line that passes through the points (1, 3) and (3, 7) is y = 2x + 1.

7 0

3 years ago

15/35 in simplest form

Aleksandr-060686 [28]

Find the GCF of 15 and 35
15=3*5
35=7*5
The Greatest Common Factor here is 5
Divide both the numerator and denominator by this value to get the simplest form.
15/5=3
35/5=7
Final answer: 3/7

5 0

3 years ago

Read 2 more answers

For the rectangular prism shown, answer the following questions. Write your number

rewona [7]

The area is 20
The height is 5
The volume is 60
The surface area is 94

6 0

2 years ago

HELP ASAP (MATH)

alexdok [17]

PART - A : tent - 1 volume = 400 cubic ft

Tent -2 volume = 384 cubic ft.

PART - B : I recommend Joe to make the tent -1 with base 10x10 ft. as it has more volume

Step-by-step explanation:

PART - A:

tent 1 :

Base = 10 x 10ft

Height= 12 ft

Volume = (1/3) (10x 10) (12)

= (1/3) (100) (12)

= 400 cubic ft.

Tent 2:

Base = 12 x 12 ft

Height= 8 ft.

Volume = (1/3) (12 x 12) (8)

= 384 cubic ft.

PART - B:

I recommend Joe to make the tent -1 with base 10x10 ft. as it has more volume

8 0

3 years ago

He fourth-grade students at Curtis Estabrook make up 0.3 of all students at the school. What fraction is equivalent to 0.3?

BartSMP [9]

Answer:

3/10

Step-by-step explanation:

fouth grade students at Estrabook make up 0.3 percents of the students at school

The fraction is therefore equivalent to

= 3/10

4 0

2 years ago