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stiv31 [10]
3 years ago
14

Find all solutions of the equation. 5 sin x − 82√ = 3 sin x − 72√

Mathematics
1 answer:
Andrei [34K]3 years ago
6 0

Answer:

  • x = arcsin(√20.5 -3√2) +2kπ . . . k any integer
  • x = π - arcsin(√20.5 -3√2) +2kπ . . . k any integer

Step-by-step explanation:

Add √(82) -3sin(x) to both sides to get ...

  2sin(x) = √82 -√72

Now, divide by 2 and find the arcsine:

  sin(x) = (√82 -√72)/2

  x = arcsin((√82 -√72)/2)

Of course, the supplement of this angle is also a solution, along with all the aliases of these angles.

___

In degrees, the solutions are approximately 16.562° and 163.438° and integer multiples of 360° added to these.

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2x+3y=12 find four solutions​
Nana76 [90]

Answer:

y = 0 and x = 6

y = 2 and x = 3

y = 4 and x = 0

y = 6 and x = -3

Step-by-step explanation:

2x+3y=12 is the equation of a straight line.

There are infinite number of solutions, but here you're probably looking for solutions where x and y are whole numbers. Trial and error will find you some, although if you examine the equation closely you see that if x is a multiple of 3 and y is a multiple of 2, then they produce terms that are the LCM (least common multiple) of 2 and 3, namely 6. That's the logic in the whole number solutions.

7 0
3 years ago
What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12
Varvara68 [4.7K]

The answer is (-2,3)

hope you have a great day ;)

5 0
2 years ago
Read 2 more answers
Which equation represents the line that passes through the points (1, 3) and (-2,5)?
Marina86 [1]

Answer:

BOOOOOOOOOOOOOOOOOOOOOOMER

Step-by-step explanation:

7 0
2 years ago
Ryans living room is 10 feet wide, 12 feet long, and 10 feet high. If one gallon of paint covers 400 square feet of surface area
Delicious77 [7]
We have to calculate the suface of the four walls and the ceiling.
Surface of the four walls=2(10 ft * 10ft ) + 2(12 ft * 10 ft)=200 ft² + 240 ft²=
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Surface of the ceiling=10 ft * 12 ft=120 ft²

Total surface=440 ft² + 120 ft²=560 ft²

Now, we have to caluclate the number of gallons of paint.

1 gallon------------------------400 ft²
x----------------------------------560 ft²

x=(1 gallon * 560 ft²) / 400 ft²=1.4 gallons.

answer: Ryan need to paint all four walls and the ceiling 1.4 gallons.
6 0
3 years ago
Solve the inequality. Graph the solution set.<br><br> 2r−9≤−6
Ahat [919]
We have that

2r−9≤−6------> 2r ≤ -6+9-------> 2r ≤  3-----> r ≤ 1.5

the solution is the interval  (-∞, 1.5]

using a graph tool
see the attached figure

5 0
3 years ago
Read 2 more answers
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