The arithmetic sequences are as follow:
<h3>What is Arithmetic Sequence?</h3>
An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.
1) t(n) = 5n + 4
t(1) = 9, t(2) = 14, t(3) = 19
So,
9,14,19,...
d= 14-9 = 5
d= 19-14 =5
Hence, it is an AP
2) 1, 2, 4, 8 , 16
Hence, it is not an AP
3) 3, 6, 9 ,...
It is an AP
4)It is given that it is an AP
5) tn = 2*3^n
t1= 6, t2= 18, t3= 54
So, 6, 18, 54,...
Hence, it is not an AP
6) 3 , 1, 1/3,...
It is not an AP
7) t(n+1)= 6*t(n)
t(1) = -1
t(2)=-6
t(3)= -36
Hence, it is not an AP
8) -3, 1, 5, 9
Hence, it is an AP.
9) 1, 4, 9,...
Hence, it not an AP
10) 2,1,0,1,2,...
It is not an AP
11) t(n)= -2n-5
t(1)= -7, t(2)= -9, t(3)= -11
Hence, it is an AP
12) tn= (1/2)^n
t1= 1/2, t2= 1/4, t3= 1/8
It is not an AP
Learn more about AP here:
brainly.com/question/24873057
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...........Hope this helps :)
Considering the volume of the rectangular prism, it is found that it's height is of 4.5 ft.
<h3>What is the volume of a rectangular prism?</h3>
The volume of a rectangular prism of length l, width w and height h is given by:
In this problem, the measures given are as follows:
l = 13 ft, w = 16 ft, V = 936 ft³.
Hence, the height, in ft, is found as follows:
More can be learned about the volume of a rectangular prism at brainly.com/question/17223528
Given :
Hans is using frequent flier miles to fly to a location 450 miles away, but the airline he is using still charges $15.89 for fees and taxes and $0.17 to redeem each mile.
In the equation below, x represents the distance Hans is flying, and y represents the cost of the trip. y = $0.17x + $15.89 .....1)
To Find :
How much did Hans pay for his trip.
Solution :
x = 450 miles.
Putting value of x in equation 1 we get :
y = $(0.17×450 + 15.89)
y = $(76.5+15.89)
y = $92.39
Therefore, Hans will pay $92.39 for his trip.
Hence, this is the required solution.
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
