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2 years ago

Find polar coordinates of the point whose cartesian coordinates are given. (-2√3 , 2)

Mathematics

1 answer:

gavmur [86]2 years ago

8 0

The polar coordinates of the point whose cartesian coordinates is (-2√3 , 2) is (4cos210, 4sin210)

<h3>Polar form of a rectangular coordinate</h3>

The polar form of a rectangular coordinate (x, y) is expressed as (rcos theta, r sin theta)

Given the coordinate (-2√3 , 2)

r = √(-2√3)²+2²

r = √12+4

r = 4

theta = tan^-1(-2/2√3)

theta = tan^-1(-1/√3)

theta = -30 degrees = 210 degrees

The polar coordinates of the point whose cartesian coordinates is (-2√3 , 2) is (4cos210, 4sin210)

Learn more on polar coordinate here: brainly.com/question/14965899

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Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago

Identify the factor terms by grouping: 5x3 – 4x2 + 20x – 16

Elanso [62]

5x3-4x2-20x+16=0 Three solutions were found : x = 4/5 = 0.800 x = 2 x = -2Reformatting the input :Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :Step 1 :Equation at the end of step 1 : (((5 • (x3)) - 22x2) - 20x) + 16 = 0 Step 2 :Equation at the end of step 2 : ((5x3 - 22x2) - 20x) + 16 = 0 Step 3 :Checking for a perfect cube : 3.1 5x3-4x2-20x+16 is not a perfect cube
Trying to factor by pulling out : 3.2 Factoring: 5x3-4x2-20x+16
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 5x3+16 Group 2: -4x2-20x
Pull out from each group separately :
Group 1: (5x3+16) • (1)Group 2: (x+5) • (-4x)

I hope it helps

8 0

3 years ago

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16|r-5|=-32 HELP i suck at algebra plz

Ivan

Answer:

Step-by-step explanation:

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3 years ago

Rewrite the decimal 47.4 as a mixed number

prohojiy [21]

Answer: