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NikAS [45]
4 years ago
13

What is the rule for a counterclockwise rotation about the origin of 210°

Mathematics
1 answer:
Phoenix [80]4 years ago
8 0

Answer:

  (x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

Step-by-step explanation:

The rule for CCW rotation through an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

So, for α = 210°, the rule becomes ...

  (x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

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Kevin is 39 years old and Daniel is 3 years old.
lina2011 [118]

Answer: 1 year

Step-by-step explanation:

In 1 year, Kevin will be 40 and Daniel will be 4. 40 is 10 times of 4.

8 0
3 years ago
Find the measure of the missing angle in this triangle.
katrin2010 [14]
180-110-45= 25 degrees
8 0
2 years ago
Read 2 more answers
A stock priced at $100 has a 70% probability of moving up and a 30% probability of moving down. If it moves up, it increases by
masha68 [24]

Answer:

The probability that after two period we will have the same value of $100 is:

p =0.21+0.21 = 0.42

Step-by-step explanation:

We can analyze this situation by cases.

Stock moves up two times

For this case the final value would be:

$100 *1.02*1.02= $104.04

And the probability associated to this event is 0.7*0.7=0.49

Stock moves down two times

For this case the final value would be:

$100 *(1/1.02)*(1/1.02)= $96.117

And the probability associated to this event is 0.3*0.3=0.09

Stock moves up and then down

For this case the final value would be:

$100 *(1.02)*(1/1.02)= $100

And the probability associated to this event is 0.7*0.3=0.21

Stock moves down and then up

For this case the final value would be:

$100 *(1/1.02)*(1.02)= $100

And the probability associated to this event is 0.3*0.7=0.21

So then the probability that after two period we will have the same value of $100 is :

p =0.21+0.21 = 0.42

7 0
3 years ago
8^(x-3)=16^(3x+1) solve
rusak2 [61]

Answer:

x = -13/9

Step-by-step explanation:

Solve for x over the real numbers:

8^(x - 3) = 16^(3 x + 1)

Hint: | Take logarithms of both sides to turn products into sums and powers into products.

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):

3 log(2) (x - 3) = 4 log(2) (3 x + 1)

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by log(2):

3 (x - 3) = 4 (3 x + 1)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

3 x - 9 = 4 (3 x + 1)

Hint: | Write the linear polynomial on the right hand side in standard form.

Expand out terms of the right hand side:

3 x - 9 = 12 x + 4

Hint: | Isolate x to the left hand side.

Subtract 12 x - 9 from both sides:

-9 x = 13

Hint: | Solve for x.

Divide both sides by -9:

Answer: x = -13/9

4 0
2 years ago
In a right triangle ABC,right angled at B,the ratio of AB to AC is 1:root 2.Find the value of 2tanA/1-tan square A
Helen [10]
Since we know that ratio of AB : AC is 1 : √2, then we can more or less use those values for the sides, check the picture below.

so we're really looking for tan(2A).  Let's bear in mind that tan²(θ) is just another way to write [ tan(θ) ]².

\bf \stackrel{\textit{Double Angle Identities}}{tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}}\\\\
-------------------------------\\\\
tan(2A)=\cfrac{2tan(A)}{1-tan^2(A)}\implies \cfrac{2\left( \sqrt{2} \right)}{1-(\sqrt{2})^2}\implies \cfrac{2\sqrt{2}}{1-2}\implies -2\sqrt{2}


8 0
4 years ago
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