We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: 
, where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
Answer:
$455
Step-by-step explanation:
The computation of the principal is shown below:
As we know that
Amount = Simple interest + Principal
Let us assume the principal be X
So,
Amount = $500
Simple interest = Principal × rate of interest × time period
= X × 5% × 2 years
= X × 0.1
So, the principal is
$500 = X × 0.1 + X
$500 = 1.1 × X
So, the X is $455 i.e principal
Answer:
The restaurant cooked 3/10 as many cashews on Tuesday
Step-by-step explanation:
If the word problem says that they used 3/5 of a bag of cashews on Monday, and they used 1/2 AS MANY.
So "as many" gives us a clue to multiply.
3/5 * 1/2 = 3/10
So the restaurant cooks 3/10 bag of cashews on Tuesday
Answer:
a. 38.19m/s
b. 38.605m/s
c. 38.937m/s
d. 39.0117m/s
e. 39.01917m/s
Step-by-step explanation:
The average velocity is defined as the relationship between the displacement that a body made and the total time it took to perform it. Mathematically is given by the next formula:
Where:
a. Let's find h(3) and h(4) using the data provided by the problem:
The average velocity over the interval [3, 4] is :
b. Let's find h(3.5) using the data provided by the problem:
The average velocity over the interval [3, 3.5] is :
c. Let's find h(3.1) using the data provided by the problem:
The average velocity over the interval [3, 3.1] is :
d. Let's find h(3.01) using the data provided by the problem:
The average velocity over the interval [3, 3.01] is :
e. Let's find h(3.001) using the data provided by the problem:
