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olga55 [171]
3 years ago
12

What is cos(x°)= cos(57°)cos(94°)-sin(57°)sin(94°)

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
3 0

Note that the given cos(57°)cos(94°)-sin(57°)sin(94°) resembles the formula

cos a cos b - sin a sin b, which is cos (a+b).


Therefore, cos(57°)cos(94°)-sin(57°)sin(94° = cos (57+94) = cos 151.

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When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.
Juliette [100K]
x-the\ number\\\\x^2-(5+3x)=0\\\\x^2-5-3x=0\\\\x^2-3x-5=0

Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution

x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \  0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \  0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \  0

Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}
6 0
3 years ago
If a person tosses a coin 23 times, how many ways can he get 11 heads
EastWind [94]

Tossing a coin is a binomial experiment.

Now lets say there are 'n' repeated trials to get heads. Each of the trials can result in either a head or a tail.

All of these trials are independent since the result of one trial does not affect the result of the next trial.

Now, for 'n' repeated trials the total number of successes is given by

_{r}^{n}\textrm{C}

where 'r' denotes the number of successful results.

In our case n=23 and r=11,

Substituting the values we get,

_{11}^{23}\textrm{C}=\frac{23!}{11!\times 12!}

\frac{23!}{11!\times 12!}=1352078

Therefore, there are 1352078 ways to get heads if a person tosses a coin 23 times.


3 0
4 years ago
What is the solution to the inequality 2n+5| &gt; 1?
hodyreva [135]

Answer:

n < - 3 or n > - 2

Step-by-step explanation:

Inequalities of the type | x | > a , have solutions of the form

x < - a or x > a

Then

2n + 5 < - 1 or 2n + 5 > 1

Solve both inequalities

2n + 5 < - 1 ( subtract 5 from both sides )

2n < - 6 ( divide both sides by 2 )

n < - 3

OR

2n + 5 > 1 ( subtract 5 from both sides )

2n > - 4 ( divide both sides by 2 )

n > - 2

Solution is n < - 3 or n > - 2

3 0
3 years ago
Can you help me please
leonid [27]

Answer

3

Step-by-step explanation:

(4-1)^2+(8-8)^2=9

square root of 9 is 3

8 0
3 years ago
Recently, your parents read in the newspaper that American factory worker jobs have the lowest income ra
Svetllana [295]

Answer:

A. A factory worker does not need a lot of education.

Step-by-step explanation:

The answer is " A " which is a factory worker does not need a lot of education. since most people don't have a PHD degree or anything higher education, it results in a lot of people joining due to the benefit of the factory worker doesn't need a lot of worker which makes it low in demand too.

5 0
3 years ago
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