Answer:
4.5 units
Step-by-step explanation:
The formula given is used to calculate the length of a segment given the coordinates of the endpoints.
let (x₁, y₁ ) = A(-1, 1) and (x₂, y₂ ) = (3,3), then
AB = 
= 
= 
= 
≈ 4.5 ( nearest tenth )
Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
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The 20th term is f(20):
f(20) = 20^2 +1 = 401
_____
<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
I have the same problem here with a slight change in the given values:
radius is 2 & height of 6 indicates the bounding line is y = 3 x---> x = y / 3....
<span>thus the [ π radius ² thickness ] yields π (y² / 9 ) <span>dy ,</span> y in [ 0 , 6 ] for the volume... </span>
a Riemann sum is then : y_i = 0 + i [ 6 / n ] = 6 i / n , i = 1,2,3...n and do a right side sum
<span>π Σ { i = 1,2,3..n } [ 36 i² / 9 n² ] [ 6 / n ]
</span>
I hope my guide has come to your help. God bless and have a nice day ahead!
<span>Answer:
Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home.
:
Let s = original speed
then
(s+11) = return speed
:
Write a time equation: Time = distance%2Fspeed
:
Original time = return time + 1 hr
330%2Fs = 330%2F%28%28s%2B11%29%29 + 1
:
Multiply equation by s(s+11) and you have:
330(s+11) = 330s + s(s+11)
:
330s + 3630 = 330s + s^2 + 11s
:
0 = 330s - 330s + s^2 + 11s - 3630
:
A quadratic equation:
s^2 + 11s - 3630 = 0
Factor this to:
(s + 66)(s - 55) = 0
Positive solution
s = 55 mph is original speed.
:
Find the time
330/55 = 6 hr, original time
and
330/66 = 5 hrs, faster time; confirms our solution.</span>
