Answer:
The number of bacteria at initial = 187
Step-by-step explanation:
Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.


Integrating both side we get
㏑ N = k t + C ------- (1)
Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.
⇒ ㏑ 500 = 3 k + C -------- (2)
⇒ ㏑ 5000 = 10 k + C ------ (3)
⇒ ㏑ 5000 - ㏑ 500 = 7 k
⇒ ㏑
= 7 k
⇒ ㏑ 10 = 7 k
⇒ k = 0.329
Put this value of k in equation (2),
⇒ ㏑ 500 = 3 × 0.329 + C
⇒ C = 5.23
Put this value of C in equation 1 we get,
⇒ ㏑ N = k t + 5.23
Initially when t = 0 , then
⇒ ㏑ N = 5.23
⇒ N = 187
Thus the number of bacteria at initial = 187
Answer:
5 81/100
Step-by-step explanation:
Let x = cost of desktop computer; then x - 250 = cost of laptop computer
converting % to decimals, 9% = 0.09 and 6% = 0.06
Then, 0.09x + (x - 250)0.06 = $300
0.09x + 0.06x - 15 = $300
0.15x = $315
x = $2100
then x - 250 = $1850
Proof: $2100•0.09 + 1850•0.06 = $189 + $111 = $300
Answer:
3x^2−13x+4
Step-by-step explanation:
(x−4)(3x−1)
=(x+−4)(3x+−1)
=(x)(3x)+(x)(−1)+(−4)(3x)+(−4)(−1)
=3x^2−x−12x+4
=3x^2−13x+4
Answer:
60 units
Step-by-step explanation:
Ratio of the perimeter = ratio of sides
Sides are in the ratio:
6 : 24
1 : 4
Perimeter of the first triangle:
4+5+6 = 15
Perimeter of the second triangle:
4(15) = 60