Answer:
3544
Step-by-step explanation:
This is a problem of compound growth. The formula is

Where F is the value in the future (in this case, the population after 13 years)
P is the intial amount (here, the initial population of 2000, so P = 2000)
r is the rate of growth (here, it is 4.5%, in decimal, 0.045)
t is the time frame (here, it is 13 years, so t = 13)
<em>we can plug the numbers into the formula and solve for F:</em>
<em>
</em>
<em>rounded to the nearest whole number, the </em><em>population after 13 years would be 3544</em>
Answer:
The following are the solution to the given points:
Step-by-step explanation:
Given value:

Solve point 1 that is
:
when,







Calculate the sum 


When 


In point 2: 
when,







calculate the sum:

when 


Divide both sides by the numeric factor on the left side then solve x=9
Answer:
729x¹⁵ + 1000
This is a case of a sum of cubes.
729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵
A sum of perfect cubes can be factored into
(a + b) (a² - ab + b²)
(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)
(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION
9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)
729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000
729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000
729x¹⁵ + 1000
Step-by-step explanation:
Jack was planting a tree. He was to dig a hole that was 3 feet deep for every 5 feet of tree height. How deep should he dig the hole for a tree that is 17feet high.
Calculations
Cross multiplication

=
5x = 2 x 13
Divide by 5 to isolate x

=
x = 10.2
Answer = 10.2