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jenyasd209 [6]
3 years ago
15

3. Growth of Cholera bacteria. Suppose that the cholera bacteria in a colony grows unchecked according to the Law of Exponential

Change. The colony starts with 1 bacterium and doubles in number every half hour. a. How many bacteria will the colony contain at the end of 24 h
Mathematics
1 answer:
Elza [17]3 years ago
6 0

Answer:

2.814 * 10^14

Step-by-step explanation:

For exponential growth:

A = A0*e^kt

A = final amount ; A0 = initial amount ; t = time

Since bacterium doubles ever half hour ;

In 1 hour number of bacterium will be 2² = 4

Hence

Final amount after 1 hour

4 = 1*e^k*1

4 =e^k

Take In of both sides

In(4) = k

Number of bacterium in 24 hours

A = 1*e^In4 * 24

A = e^24In4

A = e^33.271064

A = 281474976710656

A = 2.814 * 10^14

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p is a constant so the answer is D.

Step-by-step explanation:

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Round 12.335 to the place named.<br> hundreds <br> The rounded number is
mafiozo [28]

Answer: 12.3

Step-by-step explanation: It's 12.3 because the other 3 is in the hundredths place and the rule says 5 or more round,4 or less stays the same

7 0
3 years ago
A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the top of
-Dominant- [34]

Answer:

63.6 feet

Step-by-step explanation:

  • sin (45)=\frac{x}{90}
  • x=90 sin (45)
  • x=45\sqrt{2}
  • x = 63.6 feet
6 0
2 years ago
For each part, give a relation that satisfies the condition. a. Reflexive and symmetric but not transitive b. Reflexive and tran
Vesnalui [34]

Answer:

For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.

(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .

Step-by-step explanation:

Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.

Given a relation R on a set X,

R is said to be reflexive if for every a \in X, (a,a) \in R.

R is said to be symmetric if for every (a, b) \in R, (b, a) \in R.

R is said to be transitive if (a, b) \in R and (b, c) \in R, then (a, c) \in R.

(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.

Reflexive: (a, a), (b, b), (c, c) \in R

Therefore, R is reflexive.

Symmetric: (a, b) \in R \implies (b, a) \in R

Therefore R is symmetric.

Transitive: (a, b) \in R \ and \ (b, c) \in R but but (a,c) is not in  R.

Therefore, R is not transitive.

Therefore, R is reflexive and symmetric but not transitive .

(b) R = {(a, a), (b, b), (c, c), (a, b)}

Reflexive: (a, a), (b, b) \ and \ (c, c) \in R

Therefore, R is reflexive.

Symmetric: (a, b) \in R \ but \ (b, a) \not \in R

Therefore R is not symmetric.

Transitive: (a, a), (a, b) \in R and (a, b) \in R.

Therefore, R is transitive.

Therefore, R is reflexive and transitive but not symmetric .

(c) R = {(a,a), (a, b), (b, a)}

Reflexive: (a, a) \in R but (b, b) and (c, c) are not in R

R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.

Therefore, R is not reflexive.

Symmetric: (a, b) \in R and (b, a) \in R

Therefore R is symmetric.

Transitive: (a, a), (a, b) \in R and (a, b) \in R.

Therefore, R is transitive.

Therefore, R is symmetric and transitive but not reflexive .

4 0
3 years ago
A line passes through the points (-3,-4) and (6,2)
Zanzabum

Answer: x - int : (3,0)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = -4-2/-3-6

   =-6/-9

   = 2/3

y1 = 2

x1 =6

y - 2 = 2/3(x-6)  

x -int: when y = 0, what is x?

0-2 = 2/3(x-6)

-2 = 2/3x - 4

2 = 2/3x

x=3

~Hope this helps!~

5 0
1 year ago
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