6 i belive let me double check
Answer:
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours is
= 89 cells
Step-by-step explanation:
A cell divides into two cells every 20 minutes
In one hour, the cell will divide into 60/20 * 2 = 6 cells
Each cell growth 6 cells per hour
Initial population of a culture = 50 cells
t = time in hours
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours = initial population * growth factor
= 50 * 1.772
= 88.6
= 89 cells
Answer:
-4/5
Step-by-step explanation:
To find the slope of the tangent to the equation at any point we must differentiate the equation.
x^3y+y^2-x^2=5
3x^2y+x^3y'+2yy'-2x=0
Gather terms with y' on one side and terms without on opposing side.
x^3y'+2yy'=2x-3x^2y
Factor left side
y'(x^3+2y)=2x-3x^2y
Divide both sides by (x^3+2y)
y'=(2x-3x^2y)/(x^3+2y)
y' is the slope any tangent to the given equation at point (x,y).
Plug in (2,1):
y'=(2(2)-3(2)^2(1))/((2)^3+2(1))
Simplify:
y'=(4-12)/(8+2)
y'=-8/10
y'=-4/5
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
