If a and b are positive numbers, find the maximum value of f(x)=xa(1−x)b, 0≤x≤1 Your answer may depend on a and b.maximum value =________.

Answer:

(m) +  2 (m)  - 7 = 32 is the needed expression.

Points scored by  Pittsburgh Steelers =  13

Points scored by New Orleans Saints = 19

Step-by-step explanation:

Let us assume the points scored by  Pittsburgh Steelers = m

So, the Points scored by New Orleans Saints

 = 2 (Points scored by Pittsburgh Steelers ) - 7

 = 2 (m)  - 7

Also,the total points scored by both teams = 32

So the points scored by( New Orleans Saints + Pittsburgh Steelers) = 32

⇒ (m) +  2 (m)  - 7 = 32

or, 3 m =  32 + 7 =  39

⇒ m = 39/ 3 = 13, or m = 13

So, the points cored by Pittsburgh Steelers = m =  13

and the points scored by  New Orleans Saints  = 2m - 17

                                                                              = 2(13) - 7 = 19

Answer:

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000

Step-by-step explanation:

The total number of alphabet's = 26

The total number of digits  = 10 (0 - 9)

The number plate contains 3 letters followed by 2 digits.

The number of ways the license plates contain no repeated letters and no repeated digits.

The number of ways first letter can be filled in 26 ways.

The number of ways second letter can be filled in 25 ways.

The number of ways third letter can be filled in 24 ways.

The number of ways the first digit can be in 10 ways

The number of ways the second digit can be in 9 ways.

The number of ways the license plates contain no repeated letters and no repeated digits = 26 × 25 × 24 × 1 0 × 9

The number of ways the license plates contain no repeated letters and no repeated digits = 1,404,000

Answer:

x intercept = 15 # of cars to detail if no SUVs

y intercept =  10 # of SUVs to detail if no cars

Hope this helps!

The x-intercept and the y-intercept for the equation 30x + 45y = 450 are 15 and 10 respectively, The x-intercept denotes the number of cars if there is no SUV serviced and the y-intercept represents the number of SUVs if there is no car.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

Awesome autos car detail charges $30 for a full-service detail on SUVs,

The equation 30x + 45y = 450 represents the amount that must be earned each hour to cover expenses,

From this equation, we can determine that the autos car detail charges $45 for a full-service detail on car,

Find the x-intercept as shown below,

30x + 45 × 0 = 450   (For x-intercept y = 0)

30x = 450

x = 450 / 30

x = 15

Find the y-intercept as shown below

30 × 0 + 45y = 450   (For y-intercept x = 0)

45y = 450

y = 10

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Answer:

A. 960

Step-by-step explanation:

Multiply each heart rate by 24 (hours in a day)

Subtract the human's daily heart rate from the elephant's.

30 x 24 = 720

70 x 24 = 1680

1680 - 720 = 960

Answer:

It’s A

Step-by-step explanation:

Answer:the cost of renting one movie is $1.5

the cost of renting one video game is $5.2

Step-by-step explanation:

Let x represent the cost of renting one movie.

Let y represent the cost of renting one video game. One month melissa rented 12 movies and 2 video games for a total of $29. This means that

12x + 2y = 29 - - - - - - -1

The next month she rented 3 movies and 5 video games for a total of 32$. This means that

3x + 5y = 32 - - - - - - - - 2

Multiplying equation 1 by 5 and equation 2 by 2, it becomes

60x + 10y = 145

6x + 10y = 64

Subtracting,

54x = 81

x = 81/54 = 1.5

Substituting x = 1.5 into equation 2, it becomes

3x + 5y = 32

3×2 + 5y = 32

5y = 32 - 6 = 26

y = 26/5 = 5.2

Answer:

0.273

Step-by-step explanation:

Let the number of insured pieces of luggage be i and u be the number of uninsured pieces of luggage, therefore,

i + u = 27

Now,

probability that exactly one of the damaged pieces of luggage is insured = (iC1)(uC3)/(27C4)

probability that none of the damaged pieces are insured = (uC4)/(27C4)

and,

(iC1)(uC3)/(27C4) = 2 (uC4)/(27C4)

=> u − 2i = 3

By solving, i + u = 27 and  u − 2i = 3

i = 8 and u = 19

and,

(8C2)(19C2)/(27C4) = 0.273

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

There is a vertical asymptote at x=3. It is not defined and therefore not included in the domain.

All other numbers are included in the domain.

Answer:

he age of girl 3 [tex]\frac{1}{2}[/tex] years ago is 8.5 years  .

Step-by-step explanation:

Given as :

The present age of seventh grader girl = 12 years

Let The age of her 3 [tex]\frac{1}{2}[/tex] years ago = x years

So The age of girl [tex]\frac{7}{2}[/tex] years ago = x years

Now, According to question

The age of girl 3.5 years ago = 12 - 3.5

Or,  The age of girl 3.5 years ago = 8.5 years

Hence The age of girl 3 [tex]\frac{1}{2}[/tex] years ago is 8.5 years  . Answer

Answer:

The answer to your question is: Burger = $4.45, Pizza = $2.2

Step-by-step explanation:

Jason = $15.5 for 3 slices of pizza + 2 burgers

Susan = $20 for 1 slice of pizza + 4 burgers

Pizza = p

burger = b

System of equations

Jason                                   3p + 2b = 15.5        (I)

Susan                                     p + 4b = 20           (II)

Solve system by elimination

Multiply (II) by -3

                                          3p + 2b = 15.5

                                        -3p - 12b = -60

                                              -10b = -44.5

                                                   b = -44.5/-10

                                                  b = $4.45

                                             p + 4(4.45) = 20

                                             p + 17.8 = 20

                                             p = 20 - 17.8

                                                 p = 2.2

One slice of pizza costs $2.2 and one burger cost $4.45

The [tex]a_n[/tex] reprsents the nth term where n is some positive whole number {1,2,3,...}

The [tex]a_{n-1}[/tex] represents the term just before the nth term. For example, if n = 22 then [tex]a_{n} = a_{22}[/tex] and [tex]a_{n-1} = a_{21}[/tex]

The +5 at the end means we add 5 to the previous term just before the nth term to get the nth term. In other words, the rule is "add 5 to each term to get the next term".

To get the 9th term [tex]a_{9}[/tex], we need to find the terms before this one because the recursive sequence builds up. The 9th term depends on the 8th term, which depends on the 7th term, and so on. The countdown stops until you reach the first term.

-------

[tex]a_{1} = 3[/tex] (given)

[tex]a_{2} = 8[/tex] (given)

[tex]a_{3} = 13[/tex] (given)

[tex]a_{4} = 18[/tex] (given)

[tex]a_{5} = 23[/tex] (given)

[tex]a_{6} = a_{5}+5 = 23+5 = 28[/tex] (add 5 to the prior term)

[tex]a_{7} = a_{6}+5 = 28+5 = 33[/tex]

[tex]a_{8} = a_{7}+5 = 33+5 = 38[/tex]

[tex]a_{9} = a_{8}+5 = 38+5 = 43[/tex]

So the 9th term is [tex]a_{9} = 43[/tex]

Answer:

The hikers are 5.9 miles apart.

Step-by-step explanation:

Let O represents the base camp,

Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in the line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras theorem,

[tex]BD^2 = BD'^2 + DD'^2[/tex]

[tex]BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9[/tex]

Hence, the hikers are 5.9 miles apart.

The amount increased 4% from last year.

Step-by-step explanation:

Given,

Average cost last year = $625

Average cost this year = $650

Increase amount = Average cost last year - Average cost this year

Increase amount = 650 - 625 = $25

Percent increase = [tex]\frac{Increase\ amount}{Average\ cost\ last\ year}*100[/tex]

[tex]Percent\ increase=\frac{25}{625}*100\\Percent\ increase=\frac{2500}{625}\\Percent\ increase=4\%[/tex]

The amount increased 4% from last year.

Keywords: percentages, subtraction

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Answer:

Step-by-step explanation:

1) 5x(x-2)-2x^2 for x =2

= 5(-2)(-2-2) -2(2)^2

= -10(-4) -2(4)

= 40 - 8

= 36

2) 2x^2 - 5 + 8 for x = 3

= 2(3)^2 - 5(3) + 8

= 2(9) -  15 + 8

= 18 -  15 + 8

= 3 + 8

= 11

Answer:

1. 32.

2. 11.

Step-by-step explanation:

1.   5x(x-2)-2x^2 for x=-2:

= 5(-2)( -2-2)-2(-2)^2

=  -10*-4 - 2*4

= 40-8

= 32.

2. 2x^2-5x+8 for x=3:

= 2(3)^2 -5(3)+8

=  18 - 15 + 8

= 11.

The coffee's temperature after 15 minutes in the freezer, using Newton's Law of Cooling with a cooling constant [tex]\( k \approx 0.0816 \),[/tex] is approximately [tex]\( 45.57^\circ F \).[/tex]

Newton's Law of Cooling is given by the equation:

[tex]\[ T(t) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

Where:

[tex]\( T(t) \)[/tex]= temperature of the object at time \( t \)

[tex]\( T_0 \)[/tex] = initial temperature of the object

[tex]\( T_a \)[/tex] = ambient temperature

[tex]\( k \)[/tex] = cooling constant

[tex]\( t \)[/tex] = time

Given:

[tex]\( T_0 = 155^\circ F \)[/tex] (initial temperature)

[tex]\( T_a = 0^\circ F \)[/tex] (ambient temperature)

[tex]\( T(5) = 103^\circ F \)[/tex](temperature after 5 minutes)

We need to find the coffee's temperature[tex](\( T(15) \))[/tex] after 15 minutes. First, we need to determine the cooling constant [tex]\( k \)[/tex].

Using the given information, let's rearrange Newton's Law of Cooling to solve for [tex]\( k \)[/tex]:

[tex]\[ T(t) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ T(t) - T_a = (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ \frac{T(t) - T_a}{T_0 - T_a} = e^{-kt} \][/tex]

[tex]\[ -kt = \ln\left(\frac{T(t) - T_a}{T_0 - T_a}\right) \][/tex]

[tex]\[ k = -\frac{1}{t} \cdot \ln\left(\frac{T(t) - T_a}{T_0 - T_a}\right) \][/tex]

Given [tex]\( T(5) = 103^\circ F \)[/tex]:

[tex]\[ k = -\frac{1}{5} \cdot \ln\left(\frac{103 - 0}{155 - 0}\right) \][/tex]

[tex]\[ k = -\frac{1}{5} \cdot \ln\left(\frac{103}{155}\right) \][/tex]

[tex]\[ k \approx -\frac{1}{5} \cdot \ln(0.6645) \][/tex]

[tex]\[ k \approx -\frac{1}{5} \cdot (-0.4081) \][/tex]

[tex]\[ k \approx 0.0816 \][/tex]

Now that we have the cooling constant [tex]\( k \)[/tex], we can find [tex]\( T(15) \)[/tex]:

[tex]\[ T(15) = T_a + (T_0 - T_a) \cdot e^{-kt} \][/tex]

[tex]\[ T(15) = 0 + (155 - 0) \cdot e^{-0.0816 \cdot 15} \][/tex]

[tex]\[ T(15) = 155 \cdot e^{-1.224} \][/tex]

[tex]\[ T(15) \approx 155 \cdot 0.294 \][/tex]

[tex]\[ T(15) \approx 45.57^\circ F \][/tex]

Therefore, the coffee's temperature after 15 minutes in the freezer is approximately [tex]\( 45.57^\circ F \)[/tex].

Answer:

See the answers bellow

Step-by-step explanation:

For 51:

Using the definition of funcion, given f(x) we know that different x MUST give us different images. If we have two different values of x that arrive to the same f(x) this is not a function. So, the pair (-4, 1) will lead to something that is not a funcion as this would imply that the image of -4 is 1, it is, f(-4)=1 but as we see in the table f(-4)=2. So, as the same x, -4, gives us tw different images, this is not a function.

For 52:

Here we select the three equations that include a y value that are 1, 3 and 4. The other values do not have a y value, so if we operate we will have the value of x equal to a number but not in relation to y.

For 53:

As he will spend $10 dollars on shipping, so he has $110 for buying bulbs. As every bulb costs $20 and he cannot buy parts of a bulb (this is saying you that the domain is in integers) he will, at maximum, buy 5 bulbs at a cost of $100, with $10 resting. He can not buy 6 bulbs and with this $10 is impossible to buy 0.5 bulbs. So, the domain is in integers from 1 <= n <= 5. Option 4.

For 54:

As the u values are integers from 8 to 12, having only 5 possible values, the domain of the function will also have only five integers values, With this we can eliminate options 1 and 2 as they are in real numbers. Option C is the set of values for u but not the domain of c(u). Finally, we have that 4 is correct, those are the values you have if you replace the integer values from 8 to 12 in c(u). Option 4.

Answer:

The answer to your question is letter A. [tex]\frac{8}{17}[/tex]

Step-by-step explanation:

Sin C = [tex]\frac{opposite side }{hypotenuse}[/tex]

Opposite side = 8

hypotenuse = 17

Substitution and result

sin C= [tex]\frac{8}{17}[/tex]

Answer:

The average volume of air in the lungs during one cycle is 0.53176 liters.

Step-by-step explanation:

Given : The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex], where t is the time in seconds.

To find : The average volume of air in the lungs during one cycle ?

Solution :

The volume V of air in the lungs during a five-second respiratory cycle is [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex]

Then the average volume of air in the lungs during one cycle [0,5] is

[tex]V_a=\frac{1}{b-a}\int\limits^a_b {V(t)} \, dt[/tex]

[tex]V_a=\frac{1}{5-0}\int\limits^0_5 {0.1729t+0.1522t^2- 0.0374t^3} \, dt[/tex]

[tex]V_a=\frac{1}{5}[\frac{0.1729t^2}{2}+\frac{0.1522t^3}{3}- \frac{0.0374t^4}{4}}]^5_0[/tex]

[tex]V_a=\frac{1}{5}[0.08645t^2+0.05073t^3- 0.00935t^4]^5_0[/tex]

[tex]V_a=\frac{1}{5}[0.08645(5)^2+0.05073(5)^3- 0.00935(5)^4-0.08645(0)^2+0.05073(0)^3- 0.00935(0)^4][/tex]

[tex]V_a=\frac{1}{5}[2.1613+6.3413-5.8438][/tex]

[tex]V_a=\frac{1}{5}[2.6588][/tex]

[tex]V_a=0.53176\ l[/tex]

The average volume of air in the lungs during one cycle is 0.53176 liters.

Final answer:

To find the average volume of air in the lungs during one cycle, calculate the definite integral of V(t) over the interval t = 0 to t = 5 seconds.

Explanation:

The average volume of air in the lungs during one cycle can be approximated by finding the average value of the function V(t) over the interval t = 0 to t = 5 seconds. To do this, we need to find the definite integral of V(t) over the given interval:

∫[0,5] V(t) dt

After calculating the integral, divide the result by the length of the interval (5 seconds) to find the average volume of air in the lungs during one cycle.

Answer:

8

Step-by-step explanation:

Only the innermost 8 1-inch cubes would have no red paint on any face.

The 4 inch cube is divided into 1 inch cubes, and the number of cubes that do not have red on any face is calculated. There are no 1 inch cubes that do not have red on any face.

To find the number of 1 inch cubes that do not have red on any face, we need to consider the number of cubes that have red on at least one face. Since the complete outside of the 4 inch cube is painted red, each face of the cube has a 4x4 square painted red. Therefore, the area of each face is 16 square inches.

Dividing the 4 inch cube into 1 inch cubes, we have a total of 64 smaller cubes (4x4x4 = 64). Each smaller cube has 6 faces.

So, the total area of all the faces of the smaller cubes is 64 x 6 = 384 square inches. Since each face of the smaller cubes has an area of 1 square inch, the number of cubes that have red on at least one face is 384/1 = 384 cubes.

Therefore, the number of 1 inch cubes that do not have red on any face is 64 - 384 = -320. However, since negative numbers do not make sense in this context, we can conclude that there are no 1 inch cubes that do not have red on any face.

To find the athlete's salary for year 7 of the contract, apply a 4% annual increase to the previous year's salary starting from year 2. The athlete's salary for year 7 is approximately $3,836,192.

To find the athlete's salary for year 7 of the contract, we need to calculate the annual increase for each year from year 2 to year 7 and apply it to the starting salary of $3,000,000 for year 1.

In year 2, the salary is 1.04 times the previous year's salary, so the salary for year 2 is $3,000,000 * 1.04 = $3,120,000.

In year 3, the salary is 1.04 times the previous year's salary, so the salary for year 3 is $3,120,000 * 1.04 = $3,244,800.

Following the same pattern, we can calculate the salaries for years 4, 5, 6, and 7:

In year 4: $3,244,800 * 1.04 = $3,379,392

In year 5: $3,379,392 * 1.04 = $3,523,027.68

In year 6: $3,523,027.68 * 1.04 = $3,675,348.11

In year 7: $3,675,348.11 * 1.04 = $3,836,191.72

Therefore, the athlete's salary for year 7 of the contract is approximately $3,836,192.

The athlete's salary for year 7 of the contract is $3,822,736.

To calculate the athlete's salary for year 7, we use the formula for compound interest, which is also applicable to salaries that increase annually at a fixed percentage. The formula is:

[tex]\[ A = P(1 + r)^n \][/tex]

Given that the initial salary (principal amount P is $3,000,000 and the annual increase rate r is 4% (or 0.04 as a decimal), we can calculate the salary for year 7 as follows:

[tex]\[ A = 3,000,000(1 + 0.04)^{7-1} \] \[ A = 3,000,000(1.04)^6 \] \\[ A = 3,000,000 \times 1.26530612 ](after calculating ( 1.04^6 \)) \\\\[A = 3,822,736 \][/tex]

(after rounding to the nearest dollar)

Therefore, the athlete's salary for year 7 of the contract, rounded to the nearest dollar, is $3,822,736.

Answer:

Step-by-step explanation:

The population P of a certain city can be modeled by

P=19000e0.0215t

where T represent the number of years since 2000.

When t=1 the year is 2001

when t =2 the year is 2002. This means that

When t=0 the year is 2000

To determine the year when the population will be 40,000 , we will substitute P = 40,000 and solve for t. It becomes

40000 = 19000e^0.0215t

40000 / 19000 = e^0.0215t

2.105 = e^0.0215t

Take ln of both sides

0.7443 = 0.0215t

t = 0.7443/0.0215

t = 34.62

Approximately 35 years

So the year will be 2035

Answer:

c

Step-by-step explanation:

Answer:

  -tan(73°)

Step-by-step explanation:

The reference angle is the smallest angle between the terminal ray and the x-axis. Here, the terminal ray is in the 4th quadrant, so the reference angle will be ...

  ref∠ = 360° -287° = 73°

In the 4th quadrant, the tangent is negative, so we have ...

  tan(287°) = -tan(73°)

Answer: m<YSH = 35°  

               m<YIH = 20°

              m<SAI =  71°

               m<PAY = 8°

                    PY =  i don' t know

and P.S these answers may all be wrong sorry but hope it helps. :)

Answer:

Step-by-step explanation:

Answer:

P(No blue)=7/9=0.778

Step-by-step explanation:

The sample space of an experiment is "the set of all possible outcomes of that experiment".

The Complement Rule states "that the sum of the probabilities of an event and its complement must equal 1". So for example if A is an event and A' their complement we have this:

[tex]P(A)+P(A')=1[/tex]

[tex]P(A')=1-P(A)[/tex]

The probability of an event is "a number describing the chance that the event will happen".

For this problem we need to find first the sample space and is given by:

[tex]\Omega = [6white,8Black,4Blue][/tex] for a total of 18 socks.

[tex]n(\Omega)=8[/tex]

We can use the definition of probability of an event, and we find the probability that the randomly select sock would be blue we  have:

[tex]P_{blue}=\frac{Favorable outcomes}{Total outcomes}=\frac{4}{18}=\frac{2}{9}[/tex]

And then using the complement rule if we want the probability that the randomly selected sock would be NOT blue we have:

[tex]P'_{blue}=1-P_{blue}=1-\frac{2}{9}=7/9=0.778[/tex]

Answer:

C. 2x^2-7x+7

Step-by-step explanation:

(3x^2-2x+2)-(x^2+5x-5)     Given

From the given you will subtract like terms from both parenthesis.

3x^2-x^2=2x^2

-2x-5x=-7x

2-(-5)=7                      

To simplify the given expression, distribute the negative sign through the second parentheses, combine like-terms, which results in 2x^2 - 7x + 7, corresponding to option (c).

To simplify the expression (3x2−2x+2)−(x2+5x−5), you'd start by distributing the negative sign through the second parentheses.

Doing so gives us 3x^2 - 2x + 2 - x^2 - 5x + 5.

Upon combining like-terms, the expression becomes 2x^2 - 7x + 7.

So, the simplified form of the original expression is 2x^2 - 7x + 7.

In the given options,

c) 2x²-7x+7 is right

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Answer:

The number of leaves are 10648

Step-by-step explanation:

By the given information,

number of leaves be= z

height of tree= y

hours of sunlight= x

by the given conditions,

[tex]z = (k)(y)(x^{3})[/tex]

,where k is portionality constant.

now, z=6048, y=7 and x=6,

evaluating value of k using above conditions,

k=4

thus, using this value of k,

[tex]z=(4)(2)(11^{3})[/tex]

z= 10648.

The number of leaves on a tree of 2 yards tall receiving 11 hours of sunlight is predicted to be approximately 8712 based on the given relation.

The number of leaves z on a tree varies directly with the height of the tree y in yards and directly with the cube of the hours x of direct sunlight that the tree receives. Let's represent this relationship as z = kyx³ , where k is a constant of proportionality.

From the information provided, we know that a tree that is 7 yards tall and receives 6 hours of direct sunlight has 6048 leaves. Therefore, we can substitute these values into the equation and solve for k. Thus, if we replace z = 6048, y = 7, and x = 6, we find that k is approximately equal to 3.

With k approximately equal to 3, we can then predict the number of leaves on a tree that is 2 yards tall and receives 11 hours of sunlight. If we replace k = 3, y = 2, and x = 11 into our equation, we find that the predicted number of leaves is approximately 8712.

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its B. on ed :)  

Hope this helps

Answer:

  c.  an algorithm

Step-by-step explanation:

Most math problems are best solved using an algorithm. Certainly, converting numbers from one form to another is easily done that way.

_____

The integer part is the whole-number quotient of the division. The fractional part is the remainder divided by the denominator:

  39/8 = 32/8 + 7/8 = 4 7/8

Answer:

Light intensity = L =1

Step-by-step explanation:

The given function is:

[tex]P = \frac{120L}{L^{2}+L+1 }[/tex]                    (Equation.1)

Taking derivative of the whole equation:

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{d}{dL}[/tex] [tex](\frac{120L}{L^{2}+L+1 } )[/tex]

[tex]\frac{dP}{dL}[/tex] =120 [tex]\frac{1 (L^{2}+L+1) - (\frac{d}{dL}L^{2} +\frac{d}{dL} L+\frac{d}{dL}1)L}{(L^{2}+L+1)^{2} }[/tex]

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L^{2}-1)}{L^{2}+L+1 }[/tex]

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L+1)(L-1)}{L^{2}+L+1 }[/tex]

For first derivative test, there is a maxima. for that , we need to take:

L+1 =0 and L-1 =0

we get:

L= -1

or L=1

Since light intensity cannot be negative so, L=1

put this in equation 1:

[tex]P(1) = \frac{120}{1^{2}+1+1 }[/tex]

P = [tex]\frac{120}{3}[/tex]

P= 40  which is the maximum value of P (At L=1)

To find the light intensity that maximizes photosynthesis, you must differentiate the function P = 120I/(I^2 + I + 1) with respect to I, equate it to zero and solve for I. Then, use these values to examine the second derivative and verify whether these are local maxima or minima.

To find the light intensity (I) that maximizes photosynthesis rate (P), we should analyze the function P = 120I/(I2 + I + 1) using calculus concepts. This type of problem is looking for a maximum value, so we need to find where the derivative of the function equals zero.

First, differentiate the function P regarding I, using quotient rule: P' = (120(I² + I + 1) - 120I (2I + 1))/ (I² + I + 1)² = 0.

Then, solve this equation for I to find the values for which the rate of change of P with respect to I is zero. These are the points where P is at a maximum or a minimum. Finally, check the second derivative of the function P on these values to determine whether these correspond to a local maximum, a local minimum, or a saddle point.

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