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12345 [234]
2 years ago
6

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 = <em>undefined</em>

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

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kicyunya [14]

Answer:

ok sooo is there something you need to be figured out orr are you just saying

Step-by-step explanation:

7 0
3 years ago
A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is
Luba_88 [7]

Answer:

P(t) = 100e^{0.0251t}

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

P(t) = P(0)e^{kt}

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that P(0) = 100. So

P(t) = 100e^{kt}

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that P(60) = 450, and we use this to find k. So

450 = 100e^{60k}

e^{60k} = 4.5

\ln{e^{60k}} = \ln{4.5}

60k = \ln{4.5}

k = \frac{\ln{4.5}}{60}

k = 0.0251

So

P(t) = 100e^{0.0251t}

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

200 = 100e^{0.0251t}

e^{0.0251t} = 2

\ln{e^{0.0251t}} = \ln{2}

0.0251t = \ln{2}

t = \frac{\ln{2}}{0.0251}

t = 27.65

The doubling time is of 27.65 minutes.

7 0
3 years ago
Mark the angles and sides of each pair of triangles to indicate that they are congruent.
Sophie [7]
5 because I believe I think I believe it’s 5 I believe yea it’s 5 definitely
4 0
3 years ago
Read 2 more answers
Helppp meeee please
nekit [7.7K]

Answer:

The Equation for lyft is:

4.50x

The Equation for uber is

2.50x+5

Step-by-step explanation:

If you want to determine which one is better then you can just plug in the distance in place of x. For example if it asked you which one was better for 5 miles, uber or lyft you could plug 5 into the equation.

It would look like this

Lyft: 4.50 (5)= 22.5

Uber

2.50 (5) +5= 17.5

If the distance were 5 miles uber would be the better option.

5 0
2 years ago
Read 2 more answers
Select all equations that have infinitely many solutions.
ella [17]

Answer:

C

Step-by-step explanation:

Test Numbers with each equation or Simplify

Simplified, C's equation equates to 0 which would make it infinite

8 0
3 years ago
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