Answer:
V(w) = 6*w³ [cubic units]
Step-by-step explanation:
h height of the rectangular prism
L the length of the base
w the width of the base
Then the volume of the prism is area of the base times heigth therefore
V(p) = L*w*h [cubic units] (1)
Now the length of the base L = 2*w
And the height of the prism is h = 3*w
If we plugging these values in equation (1) we get olume of a prism as function of w then
V(w) = 2*w* w * 3*w
V(w) = 6*w³ [cubic units]
Slope = 1/3 using slope formula
Answer:
$50
Step-by-step explanation:
$50 would be the payment because it would be 50/50 if you get lower than 50 or higher than 50.
Complete Question
Bacteria culture A culture of the bacterium Rhodobacter sphaeroids initially had 30 bacteria and t hours later increases at a rate of 2e^2t 1 bacteria per hour. Find the population size after four hours
Answer:
3010
Step-by-step explanation:
We were given the rate: 2e^2t
Step 1
We would integrate
P = Population
dP/dt = 2e^2t
dP =( 2e^2t) dt
∫dP = ∫ 2e^2t dt
P(t) = (2e^2t)/2 + C
P(t) = e^2t + C
Step 2
We solve for C
The culture initially has 30 bacteria
When t = 0
P(0) = 30
P(0) = e^2t + C
30 = e^2× 0 + C
30 = 1 + C
C = 30 - 1
C = 29
Step 3
Find the population size after four hours
t = 4, C = 29
P(t) = e^2t + C
P(4) = e^2 × 4 + 29
P(4) = e^8 + 29
P(4) = 3009.957987
Approximately = 3010 bacteria
