Answer:
Step-by-step explanation:
The answer to this question is 12+6sqrt3.
This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.
Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.
The square root of 108 simplified=6sqrt3.
Then you add them together and get 12+6sqrt3.
Answer:
56 number of ways
Step-by-step explanation:
This question is a combination question since it involves selection.
Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5
8C5 = 8!/(8-5)!5!
= 8!/3!5!
= 8*7*6*5!/3*2*5!
= 8*7*6/3*2
= 8*7
= 56 number of ways.
This means that the manager can rank 5 applications in 56 number of ways
Answer:
The function of the graph is y = 3 cos (4x) ⇒ answer A
Step-by-step explanation:
- If the equation is y = A cos (B x)
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* Lets look to the graph
- The maximum value is 3 and the minimum value is -3
∵ The height from the maximum point to the minimum point is
3 - (-3) = 3 + 3 = 6
∴ The amplitude is 6/2 = 3
∵ A is the amplitude
∴ A = 3
- The distance between two consecutive peaks is π/2
∵ The period is the distance from one peak to the next peak
∴ The period = π/2
∵ The period = 2π/B
∴ 2π/B = π/2 ⇒ divide both sides by π
∴ 2/B = 1/2 ⇒ by using cross multiplication
∴ B = 4
- Lets write the form of the function
∵ y = A cos (Bx)
∵ A = 3 and B = 4
∴ y = 3 cos (4x)
* The function of the graph is y = 3 cos (4x)
The answer is one solution. Hope this helps
