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2 years ago

Which two values of x satisfy the equation square root 3-2cos x = 2?

Mathematics

1 answer:

Andrei [34K]2 years ago

8 0

Answer: x=2π/3 and x=4π/3

Step-by-step explanation:

The equation we have is $\sqrt{3-2cosx} =2$ . All we have to do is get cosine alone to find the 2 values of x.

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

Now that we have our cosine left, we can use our unit circle to figure out when does cosx=-1/2. Cosine is the x value of the coordinate.

x=2π/3

x=4π/3

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I Really need help with this!

Scrat [10]

Where the heck did x come from!

5 0

3 years ago

Read 2 more answers

Can u plz help me?...

Westkost [7]

Answer:

a 4 1/5

b 7 7/24

Step-by-step explanation:

a 7/9 * 5 2/5

Change the mixed number to an improper fraction

7/9 * (5*5+2)/5

7/9 * 27/5

Rewrite

7/5 * 27/9

7/5 * 3

21/5

Change this back to a mixed number

5 goes into 21 4 times (4*5 = 20 ) with 1 left over

4 1/5

b 1 3/4 * 4 1/6

Change to improper fractions

(4*1+3)/4 * (6*4+1)/6

7/4 * 25/6

175/24

Change back to a mixed number

24 goes into 175 7 times (7*24 =168 ) with 7 left over

7 7/24

3 0

3 years ago

An angle measures 44° less than the measure of its complementary angle. What is the measure of each angle?

ryzh [129]

a+b=90°

a=b+44°

b+44°+b=90°

2b+44°=90°

2b=90°-44°

2b=46°

b=23°

a=23°+44°

a=67°

8 0

2 years ago

Find the area of the polygon.

professor190 [17]

The formula for the area of the triangles is base x hight divided by 2 (bh/2)
The formula for the square is length times width (l x w)

therefore...

bh/2 = (12)(6) / 2 = 36 (this is the area of one triangle)

then you need to times 36 by 4 because you have 4 triangles.
36 x 4 = 144

l x w = 12 x 12 = 144 (this is the area of the square)

last you need to add the area of the triangles (144) and the area of the square (144) because that will give you the total surface area of the shape.

144+144= 288

so your answer is 288cm squared (288cm2)

6 0

3 years ago

Read 2 more answers

What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know

xeze [42]

Answer:

Step-by-step explanation:

Hello!

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = P(+ ∩ S)

P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = P(- ∩ H)

P(H)

For this particular blood disease the following probabilities are known:

1% of the population has the disease: P(S)= 0.01

95% of those who are sick, test positive for it: P(+/S)= 0.95 (sensibility of the test)

2% of those who don't have the disease, test positive for it: P(+/H)= 0.02

The probability of a person having the blood sickness given that the test was positive is:

P(S/+)= P(+ ∩ S)

P(+)

The first step you need to calculate the intersection between both events + and S, for that you will use the information about the sickness prevalence in the population and the sensibility of the test:

P(+/S) = P(+ ∩ S)

P(S)

P(+/S)* P(S) = P(+ ∩ S)

P(+ ∩ S) = 0.95*0.01= 0.0095

The second step is to calculate the probability of the test being positive:

P(+)= P(+ ∩ S) + P(+ ∩ H)

Now we know that 1% of the population has the blood sickness, wich means that 99% of the population doesn't have it, symbolically: P(H)= 0.99

Then you can clear the value of P(+ ∩ H):

P(+/H) = P(+ ∩ H)

P(H)

P(+/H)*P(H) = P(+ ∩ H)

P(+ ∩ H) = 0.02*0.99= 0.0198

Next you can calculate P(+):

P(+)= P(+ ∩ S) + P(+ ∩ H)= 0.0095 + 0.0198= 0.0293

Now you can calculate the asked probability:

P(S/+)= P(+ ∩ S) = 0.0095 = 0.32

P(+) 0.0293

I hope it helps!

6 0

2 years ago