Answer:
4 x^(3/2) + 5x -32
Step-by-step explanation:
This problem involves definite integration (anti-derivatives).
If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.
(1/2) + 1
This integrates to y = 6x
----------------
(1/2) + 1 x^(3/2)
= 6 ------------ + C
3/2
or: 4 x^(3/2) + C
and the ∫5dx term integrates to 5x + C.
The overall integral is:
4 x^(3/2) + C + 5x + C. better expressed with just one C:
4 x^(3/2) + 5x + C
We are told that the curve represented by this function goes thru (4, 20).
This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:
20 = 4 · 4^(3/2) + 5·4 + C, or:
20 = 4 (8) + 20 + C
Then 0 = 32 + C, and so C = -32.
The equation of the curve is thus 4 x^(3/2) + 5x -32
(1/2 + 1)
Answer:
1st Blank: 5
2nd Blank: 3
3rd Blank: -8
4th Blank: -8
5th Blank: 12
Step-by-step explanation:
15x+35y=-100
-15x+9y=-252
___________
44y=-352
___ ___
44 44
y=-8
3x+7(-8)=-20
3x-56=-20
+56 +56
__________
3x=36
__ __
3 3
x=12
Answer:
177
Step-by-step explanation:
This scenario can be modeled as an <u>exponential function</u>.
General form of an exponential function: 
where:
- a is the initial value (y-intercept)
- b is the base (growth/decay factor) in decimal form
- x is the independent variable
- y is the dependent variable
If b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
If the number of trees <u>increase</u> by <u>10% each year</u>, then the number of trees each year will be 110% of the number of trees the previous year. Therefore, the <u>growth factor is 110%</u>.
Given:
- a = 100 trees
- b = 110% = 1.10 (in decimal form)
- x = time (in years)
- y = number of trees in the orchard
Substituting the given values into the function:

(where x is time in years and y is the number of trees in the orchard)
To find how many trees are in the orchard in the 6th year, input x = 6 into the found equation:

Therefore, Martin had 177 trees in his orchard in the sixth year.