The formula for the volume of a cone is V = πr²h
÷3
You are solving for the height, h.
V = 338 cm³ and r = 6 cm
338 = π(6)²h÷3
338 = π36h÷3
338 = π12h
28.16 = πh
8.965 = h
The height of the cone is around 9 cm.
Answer:
- P(t) = 100·2.3^t
- 529 after 2 hours
- 441 per hour, rate of growth at 2 hours
- 5.5 hours to reach 10,000
Step-by-step explanation:
It often works well to write an exponential expression as ...
value = (initial value)×(growth factor)^(t/(growth period))
(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...
P(t) = 100·2.3^t
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(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours
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(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t
P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour
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(d) We want to find t such that ...
P(t) = 10000
100·2.3^t = 10000 . . . substitute for P(t)
2.3^t = 100 . . . . . . . . divide by 100
t·log(2.3) = log(100)
t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000
1 more than 9 is 10.
That is because 10-9 = 1.
Answer:
y=2.5
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
1/4 x = -2
You want the value of x. x is being multiplied by 1/4. To get x alone on the left side, you need to divide both sides by 1/4. Dividing by 1/4 is the same as multiplying by 4.
Multiply both sides of the equation by 4.
4 * 1/4 x = -2 * 4
4 * 1/4 = 1, so on the left side you get 1x which is just x.
x = 8
Answer: -8