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Verdich [7]
3 years ago
5

A particular type of mold is growing 9.7% per hour. Assuming that mold growth continues at this rate and there were 14,000 spore

s at 12:00am, estimate the expected number of mold spores at 9:30am.
Mathematics
1 answer:
nydimaria [60]3 years ago
7 0

Total mold spores at end of 9.30 am is 26901.

Step-by-step explanation:

Number of molds = 14000

Rate = 9.7% per hour

Number of hours = 12 am to 9.30 am =  9\frac{1}{2} hours

Growth of mold = 14000 * 9.7% * 9\frac{1}{2}

                            = 12901

Total mold spores at end of 9.30 am = 14000 + 12901

                                                                = 26901

Hence, the expected number of mold spores at 9.30 am is 26901.

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What are the types of roots of the equation below?<br> - 81=0
Tju [1.3M]

Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0. This can be obtained by finding root of the equation using algebraic identity.    

<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

  • the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,  

⇒ x⁴ - 81 = 0                      

⇒ (x² +  9)(x² - 9) = 0

⇒ (x² + 9)(x² - 9) = 0

  1. (x² -  9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
  2. x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

⇒ [x² - 3x + 3x - 9][x² - 3xi + 3xi - 9i²] = 0

⇒ (x² +0x - 9)(x² +0xi - 9(- 1)) = 0

⇒ (x² - 9)(x² + 9) = 0

⇒ x⁴ - 9x² + 9x² - 81 = 0

⇒ x⁴ - 81 = 0

Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

#SPJ9

5 0
1 year ago
What is 40% equivalent to?
olga_2 [115]

Answer:0.4

Step-by-step explanation:

3 0
4 years ago
2,3,5,9,17,33 what are the next three terms?
stich3 [128]

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<em><u>Solution:</u></em>

<em><u>Given sequence is:</u></em>

2, 3, 5, 9, 17, 33

We have to find the next three terms in sequence

<em><u>Let us find the logic used in this sequence</u></em>

2 + 2^0 = 2 + 1 = 3\\\\3 + 2^1 = 3 + 2 = 5\\\\5 + 2^2 = 5 + 4 = 9\\\\9 + 2^3 = 9 + 8 = 17\\\\17 + 2^4 = 17 + 16 = 33

Thus the sequence is increasing by 2 raised to power 0, 1, 2 and so on

<em><u>Thus the next three terms are found by:</u></em>

33 + 2^5 =33 + 32= 65\\\\65 + 2^6 = 65 + 64 = 129\\\\129 + 2^7 = 129 + 128 = 257

Thus the next three terms of sequence are 65, 129 and 257

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Answer:

d

Step-by-step explanation:

It is a 1/13 chance but even if you shuffle and replace it, its still a 1/13 chance.

4 0
3 years ago
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Equation is (x+2)^2 - x^2 = 7676
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you'll end up with 4x + 4 = 7672
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5 0
3 years ago
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