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3 years ago

The population of a particular type of bacteria is known to triple in 22 days. What is the daily growth rate

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer: ∛(3)

Step-by-step explanation:

Suppose that at day 0 the population was A.

at day 3, the population will be: 3*A

at day 6, the population will be 3*(3*A) = A*3^2

then, at day N = 3*n (where n = 0, 1, 2.....) the population will be:

P(N) = A*3^n

Particularly, if we take n = 1/3 we will have:

N = 3*1/3 = 1

This means that this is the first day after the day 0.

P(1) = A*3^(1/3)

(then in day one, the population grow by a factor of 3^(1/3))

N = 2 is when n = 2/3, then:

P(2) = A*3^(2/3)

The quotient between P(2) and P(1) is equal to the growth between day one and day two, this should be the same as the growth between day zero and day one.

A*3^(2/3)/(A*3^(1/3)) = 3^( 2/3 - 1/3) = 3^(1/3)

So we found that the daily growth rate is 3^(1/3) or ∛(3)

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Please help!!! it would be much appreciated

AveGali [126]

Answer:

12/13, or answer choice B

Step-by-step explanation:

Ok first lets find the lengths of this triangle. We know 2 lengths already, 5 and 12. By using the pythagorean theorem, a^2+b^2=c^2, we can figure out that the third side is 13 units long.

Math:

5^2+12^2=169

25+144=169

And the square root of 169 is 13, meaning that the hypotenuse of the right triangle is 13.

To remember what SIN TAN and COS mean, you can use this helpful phrase: SOH CAH TOA

SOH: It means that SIN is OPPOSITE OVER HYPOTENUSE

CAH: it means that COS is ADJACENT OVER HYPOTENUSE

TOA: It means that TAN is OPPOSITE OVER ADJACENT

because it asks for SIN B, we need to do OPPOSITE OVER HYPOTENUSE.

Because the side opposite to angle B is 12 units, and the hypotenuse is 13 units, the answer is 12 over 13 units, or 12/13.

I hope my answer helped!

If this helped you, please vote brainliest. Thanks!

8 0

1 year ago

Read 2 more answers

A circle with radius 3 has a sector with a central angle of 1/9 pi radians

Art [367]

The area of sector is 1.57 m²

Explanation:

Given:

Radius, r = 3 m

Central angle of a sector = 1/9π radians

Area of sector, A = ?

We know:

Area of sector, A = $\frac{1}{2} r^2 \alpha$

where,

α is the central angle in radians

On substituting the value we get:

$A = \frac{1}{2} X(3)^2 X \frac{1}{9}X 3.14\\ \\A = 1.57 m^2$

Therefore, the area of sector is 1.57 m²

5 0

3 years ago

List 3 values that would make this inequality true. 10≥2n 10 0 5 8 6 7 2

GuDViN [60]

Answer:

0, 2, 5

Step-by-step explanation:

10 ≥ 2n

Divide both sides by 2

5 ≥ n

Flip

n ≤ 5

Values less than or equal to 5

0, 2, 5

7 0

3 years ago

Can the set of lengths be the side lengths of a right triangle?

andreyandreev [35.5K]

Answer:

B. No.

Step-by-step explanation:

We have been given 3 side lengths 7 ft, 12 ft, 17 ft. We are asked to determine, whether the given set of lengths can form a right triangle or not.

We will use Pythagoras theorem to solve our given problem, which states that the square of hypotenuse of a right triangle is equal to the sum of squares of two legs of right triangle.

$17^2=12^2+7^2$

$289=144+49$

$289>193$

Since the sum of squares of both legs is less than square of hypotenuse, therefore, the given set of lengths can not be the side lengths of a right triangle.

4 0

3 years ago

Read 2 more answers

For women at hartford college, times to run 400 meters are normally distributed with a mean of 84 seconds and a standard deviati

pashok25 [27]

z=(63-84)/3= -21/7= -3
P(x>63)=p(z > -3) = .9987 or 99.87%

4 0

3 years ago