Answer:
80 I THINK, SORRY IF NOT RIGHT
Step-by-step explanation:
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
Answer:
The unit vector u is (-5/√29) i - (2/√29) j
Step-by-step explanation:
* Lets revise the meaning of unit vector
- The unit vector is the vector ÷ the magnitude of the vector
- If the vector w = xi + yj
- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w
- The unit vector u in the direction of w is u = w/IwI
- The unit vector u = (xi + yj)/√(x² + y²)
- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j
* Now lets solve the problem
∵ v = -5i - 2j
∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29
- The unit vector u = v/IvI
∴ u = (-5i - 2j)/√29 ⇒ spilt the terms
∴ u = (-5/√29) i - (2/√29) j
* The unit vector u is (-5/√29) i - (2/√29) j
Answer:
6045000000000000000000000 kg.
Step-by-step explanation:
We have been given that the mass of Earth is 
kg. The mass of the Moon is 
kg.
To find the total mass we will add mass of Earth and Moon.
First of all let us convert the given masses in standard form.
Therefore, the mass of Earth and Moon is 6045000000000000000000000 kg.
Answer:
B, Work with the math instructors to create a list of students currently taking a math class. Randomly select
Step-by-step explanation:
Let's think of each scenario at a time.
(A) We select 100 students enrolled in college randomly that should be fine because we are taking only students that can take classes. this rules out faculty members and any other persons but also there may be students that will never take any math course as part of their study plan, this is ruled out on that basis.
(B)if we take 100 students from the list of math instructor, that will ensure that we have taken students that are taking math class now, and math is part of their study plan, seems fine.
(C) visiting cafeteria randomly on multiple days will give us random persons that may not even be enrolled in university. this can be ruled out on that basis.
(D)Ten class at random and surveying each student in every class will make sampling size large or small depending on students enrolled in each of the class this will not give us reliable results.
We can conclude that (B) is the beast method for obtaining reliable results.
