Easy
equation is
f(x)=2ˣ
where x=number of hours elapsed
after 6 hours
f(6)=2⁶=64 bacteria
to solve for 1024
1024=2ˣ
take ln of both sides
ln(1024)=ln(2ˣ)
ln(1024)=x(ln(2))
divide both sides by ln(2)
ln(1024)/ln(2)=x
using calculator
10=x
or you could recognize that
1024=2¹⁰
or keep divising 1024 by 2
10 hours for 1024 bacteria
Answer:
θ = 49.4584°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cosθ = adjacent over hypotenuse
- Inverse Trig
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
Angle θ = ?
Adjacent Leg = 13
Hypotenuse = 20
<u>Step 2: Find Angle</u>
- Substitute in variables [cosine]: cosθ = 13/20
- Inverse Trig: θ = cos⁻¹(13/20)
- Evaluate: θ = 49.4584°
Inverse variation is of the form y=k/x (direct variation is of the form y=kx)
We are given that x=2 when y=1 so using the inverse form y=k/x we can solve for the constant of variation...
1=k/2
k=2
so the equation is:
y=2/x now they want us to find y when x=-1 so
y=2/-1
y=-2
Three hundred- fifty- five
Reason; number words refer to the alphabetical form of numbers.
Regroup terms
Add 2x to both sides
Simplify 4 - x + 2x to 4 + x
subtract 4 from both sides
subtract -6 - 4.
Answer: x = -10
