The angle is in the second quadrant so only the sine is positive .
Length of the hypotenuse = sqrt (-1^2 + 3^2) = sqrt10
sine = 1/sqrt10 = 0.3162 to 4 dec places
tangent = 1 / -3 = -0.3333 to 4 d p's
cosine = -3/sqrt10 = -0.9487 to 4 d, p's.
Answer:
- infinitely many
- one solution
- no solution
- one solution
Step-by-step explanation:
1. 4x−x=2x+x
Simplifies to 3x = 3x, which is true for all values of x. Hence there are infinitely many solutions.
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2. 2x+1=5
True only for x=2; one solution.
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3. 4x+2=5x−x+4
Simplifies to ...
4x +2 = 4x +4
2 = 4 . . . . . . . not true for any value of x; no solution.
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4. 2(x+4)=4(x+2)
Simplifies to ...
2x +8 = 4x +8
0= 2x . . . . . . . . . subtract 2x+8
True only for x=0; one solution.
Answer:
70.1 yards
Step-by-step explanation:
See the attached diagram.
Let AC is the reservoir with A as the bottom and C is the top.
Now, B is the position of Howard which is 109 yards from A i.e. AB = 109 yards.
Again, the angle elevation from B to C is 50 degrees.
So, ∠ ABC = 50°
Now, 
⇒ x = 109 cos 50 = 70.1 yards.
Therefore, the distance between the top of the reservoir and Howard i.e. BC is equal to 70.1 yards. (Answer)
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