Answer:
Step-by-step explanation:
<u>Arithmetic Sequences</u>
The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the first terms of a sequence:
-12, -28, -44,...
Find the common difference by subtracting consecutive terms:
r = -28 - (-12) = -16
r = -44 - (-28) = -16
The first term is a1 = -12. Now we calculate the term n=61:
Answer:
29,035.43 meters
Step-by-step explanation:
What we know:
- The elevation of the shore of the Dead Sea is -1,344.99 meters.
- The summit of Mt. Everest is 30,380.42 meters above the Dead Sea.
So, we just add the two values.
30,380.42 + (-1,344.99)
We can rewrite this as 30,380.42 - 1,344.99 since adding a negative is the same as subtracting that number.
And we get 29,035.43 meters as the elevation or height of Mt. Everest.
Answer:
D) Multiply A by -4 and B by 5
Step-by-step explanation:
5x-2y=10
4x+3y=7
----------------
-4(5x-2y)=-4(10)
5(4x+3y)=5(7)
----------------------
-20x+8y=-40
20x+15y=35
---------------------
23y=-5
y=-5/23
5x-2(-5/23)=10
5x+10/23=10
5x=10-10/23
5x=230/23-10/23
5x=220/23
x=(220/23)/5
x=(220/23)(1/5)
x=220/115
x=44/23
I guess you want to calculate the value of e. If so then:
-8.e = 4 . Divide both sides by 4:
-2.e = 1. Divide both sides by 2:
-e = 1/2. Multiply both sides with (-):
e = - 1/2
Answer:
y_c = 2 + 10*x
Step-by-step explanation:
Given:
y'' = 0
Find:
- The solution to ODE such that y(0) = 2, y'(0) = 10
Solution:
- Assuming a solution y = Ce^(mt)
So, y' = C*me^(mt)
y'' = C*m^2e^(mt)
- Back substitute into given ODE, we get:
y'' = C*m^2e^(mt) = 0
e^(mt) can not be equal to zero
- Hence, m^2 = 0
m = 0 , 0 - (repeated roots)
- The complimentary function for repeated roots is:
y_c = (C1 + C2*x)*e^(m*t)
y_c = C1 + C2*x
- Evaluate @ y(0) = 2
2 = C1 + C2*0
C1 = 2
-Evaluate @ y'(0) = 10
y'(t) = C2 = 10
Hence, y_c = 2 + 10*x
