Answer:
Alice reaches 11 metres below the centre as lowest height.
Step-by-step explanation:
Cosine is a bounded function between -1 and 1, so that the lowest height that Alice achieves in Ferris wheel is:
Where:
- Time, measured in seconds.
- Height with respect to centre, measured in metres.
If 
, then:
Alice reaches 11 metres below the centre as lowest height.
Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:
So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:
Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:
So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get:
Question:
What are the solution(s) to the quadratic equation 50 – x2 = 0?
A) x = ±2Plus or minus 2 StartRoot 5 EndRoot
B) x = ±6Plus or minus 6 StartRoot 3 EndRoot
C) x = ±5Plus or minus 5 StartRoot 2 EndRoot
D) no real solution
Answer:
C) x = ±5Plus or minus 5 StartRoot 2 EndRoot
Answer:
$1800
Step-by-step explanation:
First, rewrite out the information you already have:
-for 4 hrs-cost $850
-for 7 hrs-cost $1300
-for 12 hrs-$?
Next, we have to find out the amount of cost for hire per hour, so we can multiply that by 12 hrs:
-start by subtracting $850 from $1300:
1300-850=$450
-now subtract 4 hrs from 7 hrs:
7-4=3 hrs
In doing this, we see that the cost for 3 hrs hire is $450. Now, to find the unit cost per hr hire, divide $450 by 3 hrs:
450÷3=$150/hr
It costs $150 per hr hire.
Now, we have to find the cost for 12 hrs hire, so just multipy the unit cost by 12:
150*12=$1800 for 12 hrs hire
It costs $1800 for 12 hrs hire.
Answer:
The parametric equations for the tangent line are
:
x = Cos(10) - t×Sin(10)
y = Sin(10) + t×Cos(10)
z = 20 + 2t
Step-by-step explanation:
When Z=20:
Z=2t=20 ⇒ t=10
The point of tangency is:
r(10)= Cos(10) i + Sin(10) j + 20 k
We have to find the derivative of r(t) to get the tangent line:
r'(t)= -Sin(t) i + Cos(t) j + 2 k
The direction vector at t=10 is:
r'(10)= -Sin(10) i + Cos(10) j + 2 k
So, the equation of the tangent line is given by:
x = cos 10 -t×Sin(10)
y = sin 10 + t×Cos(10)
z = 20 + 2t
