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Sunny_sXe [5.5K]
3 years ago
14

Solve the equation cot 2x + cot x =3

Mathematics
1 answer:
rusak2 [61]3 years ago
3 0

tan2x*cotx - 3 = 0

We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx

==> sin2x/cos2x *cosx/sinx = 3

Now we know that sin2x = 2sinx*cosx

==> 2sinxcosx/cos2x * cosx/sinx = 3

Reduce sinx:

==> 2cos^2 x/ cos2x = 3

Now we know that cos2x = 2cos^2 x-1

==> 2cos^2 x/(2cos^2 x -1) = 3

==> 2cos^2 x = 3(2cos^2 x -1)

==> 2cos^2 x = 6cos^2 x - 3

==> -4cos^2 x= -3

==> 4cos^2 x = 3

==> cos^2 x = 3/4

==> cosx = +-sqrt3/ 2

<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>

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aev [14]
<span>2s+5>= 49
Subtract 5 from both sides
2s>=44
Divide 2 on both sides
Final Answer: s>=22</span>
3 0
3 years ago
Need help fast please thanks
murzikaleks [220]

Answer:

c = 41 ft

Step-by-step explanation:

To solve this problem, we can use the pythagorean theorem, which is defined by the formula a^2+b^2=c^2. We are given both the lengths of the legs, so all we need to do is to plug them both in and solve for c:

9^2+40^2 = c^2\\c^2 = 81 + 1600\\c^2 = 1681\\c = 41

This is the first option.

8 0
3 years ago
Jack has a rectangle garden that measures 4 feet wide by 3 feet long he wants to increase the area to 56 feet
olga nikolaevna [1]

Answer:

then you would have as length or width 8 by 7 feet, or any other factors of 56 as the width or length. Since you want to increase the area.

8 0
3 years ago
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Write each percent as a fraction in simplest form<br>60%​
s2008m [1.1K]

Answer:

3/5

Step-by-step explanation:

ir would be 6/10 but simplified it would be 3/5

7 0
2 years ago
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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?
irga5000 [103]
The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5


for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009


The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

6 0
3 years ago
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