The arc length of the curve is
which has a value of about 5.99086.
Let 
. Split up the interval of integration into 10 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]
The left and right endpoints are given respectively by the sequences,
with 
.
These subintervals have midpoints given by
Over each subinterval, we approximate 
with the quadratic polynomial
so that the integral we want to find can be estimated as
It turns out that
so that the arc length is approximately
Answer:
f(4)=-3
Step-by-step explanation:
f(1)=2
f(n)=f(n-1)^2-n
If n=2
f(2)=f(2-1)^2-2
f(2)=f(1)^2-2
f(2)=2^2-2
f(2)=4-2
f(2)=2
If n=3
f(3)=f(3-1)^2 - 3
f(3)=f(2)^2 - 3
f(3)=2^2-3
f(3)=4-3
f(3)=1
if n=4
f(4)=f(4-1)^2 - 4
f(4)=f(3)^2 - 4
f(4)=1^2 - 4
f(4)=1-4
f(4)=-3
Answer:
im not sure but i got 30.1
Step-by-step explanation:
*Given
Money of Phoebe - 3 times as much as Andy
Money of Andy - 2 times as much as Polly
Total money of Phoebe, - <span>£270
</span> Andy and Polly
*Solution
Let
B - Phoebe's money
A - Andy's money
L - Polly's money
1. The money of the Phoebe, Andy, and Polly, when added together would total <span>£270. Thus,
</span>
B + A + L = <span>£270 (EQUATION 1)
2. Phoebe has three times as much money as Andy and this is expressed as
B = 3A
3. Andy has twice as much money as Polly and this is expressed as
A = 2L</span> (EQUATION 2)
<span>
4. This means that Phoebe has ____ as much money as Polly,
B = 3A
B = 3 x (2L)
B = 6L </span>(EQUATION 3)<span>
This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.
5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,
6L + 2L + L = </span><span>£270
</span> 9L = <span>£270
</span> L = <span>£30
So, Polly has </span><span>£30.
6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.
</span>
A = 2L
A = 2(£30)
A = £60
Andy has £60
B = 6L
B = 6(£30)
B = £180
Phoebe has £180
Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
Answer:
are corresponding angles and are congruent to each other.
are alternate exterior angles and thus congruent to each other.
are interior angles on the same side, and they are supplementary(sum=180°).
Step-by-step explanation:
Given:
Line 
Line 
is traversal.
By angle properties we can name the angle relationship of given angle pairs.
are corresponding angles and are congruent to each other.
are alternate exterior angles and thus congruent to each other.
are interior angles on the same side, and thus they are supplementary.
