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-BARSIC- [3]
3 years ago
13

Find the component form of the vector v ⃗ with ‖v ⃗ ‖=4√3 when drawn in standard position v ⃗ lies in Quadrant II and makes a 30

° angle with the positive y-axis. Give exact values.
Mathematics
1 answer:
nydimaria [60]3 years ago
8 0
The answer:

first of all, we should know that the expression of a vector V (a, b) can be written as follow:

V = r (Vx i + Vyj), where r is the length of the vector, it is r = sqrt(V²x + V²y)
Vx is the component lying on the x-axis and Vy on the y-axis

<span>v ⃗ lies in Quadrant II, means Vx is less than 0 (negative)
</span>
so Vx= -r sin30° and Vy= rcos30° 

r= <span>‖v ⃗ ‖=4√3 
</span>
so we have   v = - 4√3sin30° i  + 4√3 cos30° j

the components are 

v(- 4√3sin30°,  4√3 cos30°) = (-2√3, 4√3 cos30°)
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H = {(2, 5), (3, 5), (4, 5), (5, 5), (6, 5)} Is H a function and why?.
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Answer:

Yes, each x-value has a unique y-value.

Step-by-step explanation:

This is a function because each x-value has its own y-value. If this is not the case then it is not a function, because then, two points with the same x-value and different y-values would fail the VLT.

Your graph does not have overlaps and each x-value has a unique y-value

VLT

The vertical line test (VLT) is a <u>simple method that mathematicians made because</u><u> they were lazy</u><u> to make a table of values and find duplicates. </u>

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  • Passing the VLT means that if you drew a vertical line anywhere on the graph, it would only go through one point.
  • Failing the VLT would mean that the vertical line

A quick way to check if it is a function is by looking for duplicates of x-values and check that the duplicates have the same y-value.

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(x+2) (y-5)=0<br> please help me graph and solve this!!
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4 0
3 years ago
You flip an unfairly weighted coin 4 times. If the probability of getting a tail is 0. 38.
anygoal [31]

Answer:

0.84306608

Step-by-step explanation:

The probability of an event, e, occurring exactly r times over n trials follows the formula

(n combination r) * p^r * q ^ (n-r)

with p being the probability the event will occur and q being the probability the event will not occur.

I assume you have a calculator/can find one online that can do combinations.

Here, we want to figure out if you get:

- 0 tails

- 1 tail

- 2 tails

If you get 3 or 4 tails, we are getting more than the 2 tails desired

For 0 tails:

- p is the probability a tail will occur = 0.38

- we want it to occur 0 times, so r = 0

- q is (1-p) = 1- 0.38 = 0.62

- we have 4 trials, as we flip it 4 times

(n combination r) * p^r * q ^ (n-r) = (4 combination 0) * (0.38) ^0 * (0.62) ^(4-0) = 1 * (0.38) ^0 * (0.62) ^(4-0) = 0.14776336

For 1 tail:

- p = 0.38, q = 0.62 as with 0 tails

- r = 1, n = 4

(n combination r) * p^r * q ^ (n-r) = (4 combination 1) * (0.38) ^1 * (0.62) ^(4-1) = 4* (0.38) ^1 * (0.62) ^(4-1) = 0.36225856

For 2 tails:

- p = 0.38, q = 0.62 as with 0 tails

- r = 2, n = 4

(n combination r) * p^r * q ^ (n-r) = (4 combination 2) * (0.38) ^1 * (0.62) ^(4-2) = 6* (0.38) ^2 * (0.62) ^(4-2) = 0.33304416

add our 3 probabilities together

0.33304416 + 0.36225856 + 0.14776336 = 0.84306608 as our answer

8 0
2 years ago
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