Complete question :
An account grows at an annual interest rate of r , so it grows by a factor of x = 1+ r each year. The function A(x)= 800x^4 + 350x^3 + 500x^2 + 600x gives the amount in the account after 4 years when the growth factor is x.
1) What is the total amount in the account if the interest rate for the account is 3% each year?
Answer:
2,431.311498
Step-by-step explanation:
Given that:
Growth factor (x) = (1 + r) per year
If rate (r) = 3% = 0.03
x = 1 + 0.03 = 1.03
Amount in account after 4 years is given by the function :
A(x)= 800x^4 + 350x^3 + 500x^2 + 600x
Put x = 1.03 to obtain the total amount ;
A(1.03) = 800(1.03)^4 + 350(1.03)^3 + 500(1.03)^2 + 600(1.03)
= 2431.311498
Hence, total amount in account after 4 years = 2,431.311498
Answer:
Step-by-step explanation:
The answer is A
The problem statement gives a relation between the amount removed from one bag and the amount removed from the other. It asks for the amount remaining in each bag. Thus, there are several choices for variables in this problem, some choices resulting in more complicated equations than others.
Let's do it this way: let x represent the amount remaining in bag 1. Then the amount removed from bag 1 is (100-x). The amount remaining in bag 2 is 2x, so the amount removed from that bag is (100-2x). The problem statement tells us the relationship between amounts removed:
... (100 -x) = 3(100 -2x)
... 100 -x -3(100 -2x) = 0 . . . . . . subtract the right side
... 5x -200 = 0 . . . . . . . . . . . . . . eliminate parentheses and collect terms
... x -40 = 0 . . . . . . . . . . . . . . . . .divide by 5
... x = 40 . . . . . . . . . . . . . . . . . . . add 40
- 40 kg is left in the first bag
- 80 kg is left in the second bag
_____
<u>Check</u>
The amount removed from the first bag is 60 kg. The amount removed from the second is 20 kg. The amount removed from the first bag is 3 times the amount removed from the second bag, as described.
Answer:
The HCF is 75
Step-by-step explanation:
Here, we want to get the highest common factors of the two numbers
To do this, we have to write the numbers as the product of their prime factors
We have;
3,000 = 2 * 2 * 2 * 3 * 5 * 5 * 5
525 = 3 * 5 * 5 * 7
now looking at this, we can see that in both numbers, we can have 3 * 5 * 5 taken out as it is common to both numbers
This represents the highest common factor of the two numbers
and that is 75
Answer:
- Center = (3, 0)
- Radius = 3
- Graph = see below
Concept:
Here, we need to know the idea of the circle equation.
Circle equation: (x - h)² + (y - k)² = r²
(h, k) = center
r = radius
x = variable
y = variable
Solve:
<u>Given expression </u>
(x - 3)² + y² = 9
<u>Find the point of the center</u>
(h, k) = 
<u>Find the length of the radius</u>
r² = 9
Hope this helps!! :)
Please let me know if you have any questions
