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3 years ago

What is clairouts equation

1 answer:

8 0

In mathematical analysis, Clairaut's equation is a differential equation of the form where f is continuously differentiable. It is a particular case of the Lagrange differential equation

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A type of bacteria has a very high exponential growth rate of 80% every hour. If there are 10 bacteria, determine how many will

Lana71 [14]

<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are $10(1.8)^{168}$ bacteria in 1 week</h3>

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

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

<em><u>The increasing function is given as:</u></em>

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

$r = 80 \5 = \frac{80}{100} = 0.8$

<em><u>Determine how many will be in 5 hours</u></em>

Substitute t = 5

$y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96$

y = 189

Thus, there are 189 bacteria in 5 hours

<em><u>Determine how many will be in 1 day ?</u></em>

1 day = 24 hours

Substitute t = 24

$y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588$

Thus, there are 13382588 bacteria in 1 day

<em><u>Determine how many will be in 1 week</u></em>

1 week = 168

Substitute t = 168

$y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}$

Thus there are $10(1.8)^{168}$ bacteria in 1 week

6 0

3 years ago

You want to paint the walls of your bedroom. Two walls measure 15 ft by 9 ft, and the other two walls measure 18 ft by 9 ft. The

sertanlavr [38]

Answer:

The total amount you will spend on the paint=$34

Step-by-step explanation:

Step 1: Determine total area of walls

The total area of walls=Area of wall 1+area of wall 2+area of wall 3+area of wall 4

where;

area of wall 1=(15×9)=135 ft²

area of wall 2=(15×9)=135 ft²

area of wall 3=(18×9)=162 ft²

area of wall 4=(18×9)=162 ft²

replacing;

Total area of walls=(135×2)+(162×2)=594 ft²

Total area of walls=594 ft²

Step 2: Number of gallons of paint needed

Use the expression;

Total area of walls=area per gallon cans×number of gallon cans needed

where;

total area of walls=594 ft²

area per gallon=400 ft²

number of gallons=n

replacing;

594=400×n

n=594/400

n=1.485

Total number of gallon cans=1.485=2 gallon cans

Step 3: Total cost

The total cost of painting can be expressed as;

Total cost=cost per gallon can×number of gallon cans needed

where;

Cost per gallon=$17

number of gallon cans needed=2

replacing;

Total cost=(17×2)=$34

The total amount you will spend on the paint=$34

8 0

3 years ago

If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 <

Darina [25.2K]

The answer would be B, because in order for the function to have two values of x where the function value is the same, it must have a point in the function where it is a max or min. Because it has a max or min, at that point, the slope of the function is 0, meaning that B is the correct answer because B states that at that point that is a max or min, the slope of the function is 0.

4 0

3 years ago

In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x?

mojhsa [17]

Similar triangles are triangles that has all sides and angles to be equal. The value of x if , ΔGEF and ΔHEF are congruent is 28

<h3>Similar triangles</h3>

Similar triangles are triangles that has all sides and angles to be equal. From the given diagram;

<GFE = <EFH

Given

<GFE = 60 degrees

<EFH = 2(x+2)

Substitute

2(x+2) = 60
2x + 4 = 60

2x = 60 - 4

2x = 56

x = 28

Hence the value of x if , ΔGEF and ΔHEF are congruent is 28

Learn more on congruent shapes here: brainly.com/question/2644832

#SPJ1

8 0

2 years ago

H/7 =27 can some one answer this pls

Lesechka [4]

Answer:

h=189

Step-by-step explanation:

solve for H by simplifying both sides of the equation, then isolating the variable.

hope this helped

3 0

3 years ago

What is clairouts equation​

What is clairouts equation