Answer:87
Step-by-step explanation:
Answer:
D. 7.8 miles.
Step-by-step explanation:
So, to solve this, you need to use the Pythagorean theorem to find the distance from the baseball field to his home. You know two of the sides of the triangle formed, 6 and 5. The Pythagorean theorem is a² + b² = c². In this case, it would be 6² + 5² = c². If you solve this, you would find that c is 7.81024967591. Just round it to the nearest tenth like instructed. This would get you 7.8 as the answer.
Extra work just in case:
6² + 5² = c²
36 + 25 = c²
61 = c²
= ![\sqrt{c^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7Bc%5E%7B2%7D%20%7D)
7.8 ≈ c
Visual just in case:
It’s B
(28y+63)
Hope this helps!
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
<u>Step-by-step explanation:</u>
i) sin (2θ) = cos 30°
![\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o](https://tex.z-dn.net/?f=%5Csin%282%5Ctheta%29%3D%5Cdfrac%7B%5Csqrt3%7D%7B2%7D%5C%5C%5C%5C.%5Cquad%202%5Ctheta%3D%5Csin%5E%7B-1%7D%5Cbigg%28%5Cdfrac%7B%5Csqrt3%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C.%5Cquad%202%5Ctheta%3D60%5Eo%5Cqquad%202%5Ctheta%3D120%5Eo%5C%5C%5C%5C.%5Cquad%20%5Ctheta%3D30%5Eo%5Cqquad%20%5Ctheta%3D60%5Eo)
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
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ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
Answer:
Yes, it is
Step-by-step explanation:
Given
![Number = 78](https://tex.z-dn.net/?f=Number%20%3D%2078)
Required
Determine if it is a multiple of 6 or not
A number is a multiple of 6 if and only if it can be divided by 6 without remainder.
Can 78 be divided by 6?
To check, we have:
![Check = \frac{78}{6}](https://tex.z-dn.net/?f=Check%20%3D%20%5Cfrac%7B78%7D%7B6%7D)
![Check = 13](https://tex.z-dn.net/?f=Check%20%3D%2013)
The result of the division has no remainder.
Hence, it is a multiple of 6