At time t=0, a bacterial culture weighs 1 gram. Two hours later, the culture weighs 4
grams. The maximum weight of the culture is 20 grams.
(a) Write a logistic equation that models the weight of the bacterial culture.
(b) Find the culture's weight after 5 hours.
(c) When will the culture's weight reach 18 grams?
(d) Write a logistic dierential equation that models the growth rate of the culture's weight. Then
repeat part (b) using Euler's method with a step size of h=1.
(e) After how many hours is the culture's weight increasing most rapidly? Show work.

Answer:

Step-by-step explanation:

5+ 20= 25

Because when you set them up and add them properly you get 25

(Not sure if that was the question you wanted us to answer..)

The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

1. The integral is given as an area under a graph.

2. The graph has labeled regions.

3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.

4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

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Answer:

c

Step-by-step explanation:

we want that time to be less than equation or equal to 5 minutes start text, m, i, n, u, t, e, s, end text. therefore: 1[tex]5minutes[/tex]

Rate for ZZZ Zambonis × Time ≤ 5 minutes

Time ≤ 5 minutes/Rate for ZZZ Zambonis

To solve for the time needed to resurface one rink, we first need to set up an equation. We know that the number of rinks resurfaced by ZZZ Zambonis is equal to the rate for ZZZ Zambonis multiplied by the time. We want the time for 1 rink to be less than or equal to 5 minutes, so we need to solve for time in the equation. We can do this by dividing both sides of the equation by the rate for ZZZ Zambonis, resulting in the equation Time ≤ 5 minutes/Rate for ZZZ Zambonis. This equation gives us the maximum time needed to resurface one rink.

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given rate r = 5% compounded monthly r = 0.05/12 = 0.0041667

(1) monthly growth factor = 1.0041667 (2) monthly percent change = (1.0041667-1)*100%= 0.0041667*100% monthly percent change = 0.41667%

(B) given rate r = 6.9% compounded quarterly

r = 0.069/4 = 0.01725

(1) Quarterly growth factor = 1.01725

(2) Quarterly percent change = (1.01725-1)*100%= 0.01725*100% monthly percent change =1.725%

(C) given rate r = 3.4% compounded quarterly

r = 0.034/365 = 9.315 * 10 ^ - 5

(1) daily growth factor = 1 + 9.315 * 10 ^ - 5 = 1.00009315

(2) daily percent change = (1.00009315-1)*100%= 0.00009315*100% monthly percent change =0.009315%

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Based on the given information , the proof of triangle RST ≅ triangle VUT is shown below .

In the question ,

two triangles are given where ;

it is given that side  ST ≅ UT

and  ∠SRT ≅ ∠UVT .

we have to prove that ΔRST congruent  ΔVUT .

In triangle RST and triangle VUT .

side ST = side UT              .....given that ST ≅ UT ;

angle SRT = angle UVT    ....given that  ∠SRT ≅ ∠UVT ;

angle RTS = angle VTU    .....because they are vertically opposite angles .

Hence by ASA congruence , triangle RST ≅ triangle VUT .

Therefore , it is proved that triangle RST ≅ triangle VUT  .

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{48, 55, 73} and  {10, 23, 26} do not represent a right angle triangle.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Now,

48² + 53² = 73².

2304 + 2809 = 5329.

5113 ≠ 5329 so do not represents a right-angle triangle.

Similarly,

39² + 80² = 89² represents a right-angle triangle.

42² + 56² = 70² represents a right-angle triangle.

10² + 23² ≠ 26²so do not represent a right-angle triangle.

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Answer:

4k because is right is the best answer

Answer:

4 kilometers is equal to 4000 meters.

Step-by-step explanation:

1 kilometer is equal to 1000 meters, so 4 kilometers is equal to 4 x 1000 = 4000 meters. This is because the prefix "kilo" means 1000, so 1 kilometer is equivalent to 1000 meters.

If a radius is drawn to the point of tangency of a tangent line, then the radius is basically perpendicular to the tangent line.

Given that the radius is drawn to the point of tangency of a tangent line.

We are required to fill the blank with the appropriate word.

Radius is basically the line segment which joins the center to any point on the circumference of the circle.

Tangent line is basically a line which is drawn from an outside point on the circumference of the circle.

When the radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

Hence if a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line.

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The minimum and the maximum values are 0 and 1/27, respectively.

The extreme values of a function are the minimum and the maximum values of the function.

The function is given as:

f(x, y, z) = x²y²z²

x² + y² + z² = 1

Subtract 1 from both sides of x² + y² + z² – 1

x² + y² + z²-1=0

Using Lagrange multiplies, we have:

L(xy.z. λ) f(x. y.z) + λ(0)

Substitute f(x.y. z) = x³y²z² and x² + y² + z² − 1 = 0

L(x, y, λ) = x²y²z² + λ(x² + y² + 2² – 1)

Differentiate

Lx = 2xy²z² + 2λx

Ly = 2x²yz² + 2λy

Lz = 2x²y³z + 2λz

Lλ = x² + y² + z²

Equate to 0

2xy²z² + 2λx = 0

2x²yz² + 2λy = 0

2x²y²z+ 2λz = 0

x² + y² + z²-1=0

Factorize the above expressions

2xy²z²+2λx = 0

2x(y²z² + λ) = 0

2x = 0 or y²z²+λ=0

x=0 or y²z² = -λ

2x²yz² + 2λy = 0

2y(x²z² + λ) = 0

2y=0 or x²z²+λ=0

y = 0 or x²z² = -λ

2x²y²z+λz = 0

2z(x²y² + λ) = 0

2z = 0 or x²y² +λ=0

z = 0 or x²y² = -λ

So, we have:

x = 0 or y²z² = -λ

y=0 or x²z² = -λ

z = 0 or x²y² = -λ

Because

-λ= -λ

The above expressions become:

x=y=z=0

x²z² = y²z²

x² = y²

x = ±y

Also, we have:

x²y² = x²z²

y² = z²

y = tz

Also:

y²z² = x²y²

z² = x²

z = ±x

So, we have:

x = ±y

y = ±z

z = ±x

This means that:

x=y=z

Recall that: x² + y² + z² = 1

So, we have:

x² + x² + x² = 1

3x² = 1

Divide through by 3

x² = 1/3

Take square roots of both sides

x=±[tex]\frac{1} \sqrt{3}[/tex]

So, we have:

x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]

So, the critical points are:

x=y=z=0

x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]

Substitute the above values in f(x, y, z)=x²y²z²

f(0,0,0) = 0² × 0² × 0² = 0

f(±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex]) = (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² =[tex]\frac{1}{27}[/tex]

Considering the above values, we have:

Minimum 0

Maximum =      1/27

Hence, the minimum and the maximum values are 0 and 1/27, respectively.

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After solving the logical operations it can be determined that the correct answer is C) FALSE.

Logical operations are phrases that connect expressions to test if they are true or not.

The complement (') sign means that the opposite value of the variable is needed. For example if y is false, y' means true.

Let False = 0 and True = 1

= ((0 OR 0') AND (1' AND 0')) OR ((0 OR 0') AND (1 OR 0)')

= ((0 OR 1) AND (0 AND 1)) OR ((0 OR 1) AND (1)')

= (1 AND 0) OR (1 AND 0)

= 0 OR 0

= 0

Hence, the answer is C) FALSE

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The linear relationship between the number of shirts, n ,it can sell and the price, p is p = (-1/250)x + 79

The linear equation is

y = mx + b

Where m is the slope of the line

b is the y intercept

Here p is the total price

n is the number of shirts

The equation will be

p = mn + b

The price of 6000 shirts = $55

The price of 8000 shirts = $47

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope of the line = (47-55) / (8000-6000)

= -8/2000

= - 1/250

Substitute the point (6000, 55) in the equation

55 = (-1/250)(6000) +  b

55 = -24 + b

b = 55 + 24

b = 79

Substitute the values in the equation

p = (-1/250)x + 79

Therefore, the linear relation in the form of p is p = (-1/250)x + 79

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The missing values for the equivalent ratios in the order that they appear in this table include the following;

In Mathematics, a proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

From column 1, we have:

Let the missing value be represented by x.

1/4/(1/2) = 3/4/x

2/4 = 3/4x

8x = 12

x = 12/8

x = 3/2

From column 2, we have:

Let the first missing value be represented by y.

1/4/(1/2) = y/3

2/4 = y/3

4y = 6

y = 6/4

y = 3/2.

From column 2, we have:

Let the second missing value be represented by z.

1/4/(1/2) = 5/z

2/4 = 5/z

2z = 20

z = 20/2

z = 10.

In conclusion, we can logically deduce that t 10/2, 5/(11/20), and 5/4.

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The probability of the cumulative distribution function  to meet the specification of the components is given by P( X = 0 ) = 0.0304 ,

P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.

As given in the question,

Let probability of the first component to meet the specification be P (M)

= 0.81

And probability of the second component to meet the specification be P (N)

= 0.84

Probability of the first component do not meet the specification be P ( M' )

= 1 - 0.81

= 0.19

Probability of second component do not meet the specification be P(N' )

= 1 - 0.84

= 0.16

X defined the number of components to the meet the specifications

Here X = 0, 1, 2

P( X = 0 ) represents components do not meet any specifications

= P( M' ∩ N' )

= P(M') P(N')   ( Independent )

= 0.19 × 0.16

= 0.0304

P( X= 1) represents components meet only one specification

= P( M∩N') ∪ P( M'∩N)

= P( M∩N') + P( M'∩N)

=  P(M) P(N')  +  P(M') P(N)  

= 0.81(0.16) + (0.19)(0.84)

= 0.1296 + 0.1596

= 0.2892

P( X=2) represents components meet both the specification

= P( M ∩ N )

= P(M) P(N)

= 0.81(0.84)

= 0.6804

Therefore, the probability of the cumulative distribution function is given by P( X = 0 ) = 0.0304 , P( X = 1 ) = 0.2892 , P( X = 2) = 0.6804.

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In general, the improvements that we can make refer to optimizations that can be applied in a context.

In a particular process or context, the best are optimizations that are done to make something more efficient or to improve the quality of an element.

For example, some improvements that we could make in our community are:

¡Hope this helped!

type of statistical inference should be used to answer each of the questions below.Two-sample t-test is there a difference in the amount of time people spend on social media between genders.

Two-sample t-test is a type of inferential statistic used to determine whether there is a significant difference between the means of two independent groups.

In this case, the two groups would be genders (male and female) and the type of data is the amount of time spent on social media.

Two-sample t-test is there a difference in the amount of time people spend on social media between genders.

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Answer:

Read below

Step-by-step explanation:

The equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality. This constant represents the rate at which water is dripping into the bowl, in milliliters per second.

To find the constant of proportionality, you need to know the rate at which the water is dripping into the bowl. If you know the rate, you can plug it into the formula above to find the equation that represents the volume of water in the bowl over time. For example, if the water is dripping into the bowl at a rate of 1 milliliter per second, the equation would be: y = 1 * x. This means that after 1 second, the bowl would contain 1 milliliter of water, after 2 seconds it would contain 2 milliliters of water, and so on.

It's important to note that the constant of proportionality will change if the rate at which the water is dripping into the bowl changes. For example, if the water is dripping into the bowl at a rate of 2 milliliters per second, the equation would be: y = 2 * x. This means that after 1 second, the bowl would contain 2 milliliters of water, after 2 seconds it would contain 4 milliliters of water, and so on.

In summary, the equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality, which represents the rate at which water is dripping into the bowl. To find the equation, you need to know the rate at which the water is dripping into the bowl, and plug that value into the formula as the value of k.

The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.

We know that two triangles are congruent if and only if they have three pairs of equal sides.

In the case of the LL congruence theorem,

the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).

Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.

Alternatively

If the legs are of equal length then

Their squares would be equal to

Hence, the sum of these squares too would be equal.

Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.

Hence, by SSS congruence criteria

the triangles would be congruent.

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The number of the adult will be 77

The number of the child will be 160.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

237 peoples used the public swimming pool.

And, The daily prices are $1.75 for children and $2 for adult.

Now,

Let The number of the adult = x

The number of the child = y

So, We can formulate;

237 peoples used the public swimming pool.

⇒ x + y = 237 ..(i)

And, The daily prices are $1.75 for children and $2 for adult.

⇒ 2x + 1.75y = 444  ..(ii)

From (i);

⇒ x + y = 237

⇒ x = 237 - y

Substitute above value in (ii), we get;

⇒ 2x + 1.75y = 444

⇒ 2 (237 - y) + 1.75y = 444

⇒ 474 - 2y + 1.75y = 444

⇒ 474 - 444 = 0.25y

⇒ 40 = 0.25y

⇒ y = 160

And, from (i),

⇒ x + y = 237

⇒ x + 160 = 237

⇒ x  = 77

Thus, The number of the adult = 77

The number of the child = 160.

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Let sn be the number of successes in n independent bernoulli trials, the probability of success for each trial is 1/2.

(a) 1 , (b) 0 ,(c) 0

(a) As n approaches infinity, the probability of having 2n - 3n successes in n trials is equal to the probability of having 2n + 3n successes in n trials. Since the probability of success for each trial is 1/2, the probability of having 2n - 3n successes is the same as the probability of having 2n + 3n successes. Therefore, the limit is 1.

(b) As n approaches infinity, the probability of having 2n - 4n successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 4n successes in n trials is also equal to 0. Therefore, the limit is 0.

(c) As n approaches infinity, the probability of having 2n - 20 successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 20 successes in n trials is also equal to 0. Therefore, the limit is 0.

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I am closing 17 sales opportunities per day.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The total number of sales = 26.

64% of sales are closing.

This means,

The number of closing sales.

= 64% of 26

= 64/100 x 26

= 0.64 x 26

= 16.64

Thus,

The number of closing sales is 17.

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A:

The return from opening the office building under the assumption that it is leased would be the difference between the net income generated by the increase in sales and the expenses associated with opening the new office, including the cost of leasing the office space.

To calculate the net income generated by the increase in sales, we first need to calculate the total cost of goods sold. Since the cost of goods sold is estimated to be 40 percent of sales, the cost of goods sold for the new office would be 40 percent x $2.6 million = $<<40*.01*2.6=1.04>>1.04 million.

Subtracting the cost of goods sold from the increase in sales, we find that the net income generated by the increase in sales would be $2.6 million - $1.04 million = $<<2.6-1.04=1.56>>1.56 million.

Next, we need to calculate the expenses associated with opening the new office, including the cost of leasing the office space. Since the corporate overhead would increase by $306,500, the total up-front costs associated with opening the new office would be $306,500 + $2.6 million = $<<306.5+2.6=2.906>>2.906 million.

To calculate the cost of leasing the office space, we need to multiply the annual lease payment by the number of years in the lease term. Since the annual lease payment is $645,000 and the lease term is 15 years, the total cost of leasing the office space would be $645,000 x 15 years = $<<645000*15=9675000>>9.675 million.

Subtracting the total up-front costs and the cost of leasing the office space from the net income generated by the increase in sales, we find that the return from opening the office building under the assumption that it is leased would be $1.56 million - $2.906 million - $9.675 million = $<<1.56-2.906-9.675=-9.020>>-9.020 million. This means that the corporation would incur a loss of $9.020 million by opening the new office and leasing the office space.

B:

C:

To calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space.

First, let's calculate the cash flow from leasing the office space. We already know that the total cost of leasing the office space would be $9.675 million. To calculate the cash flow from leasing the office space, we need to subtract the real estate operating expenses from the total cost of leasing the office space. Since the real estate operating expenses are estimated to be 50 percent of the lease payments, the real estate operating expenses would be 50 percent x $645,000 = $<<50*.01645=322500>>322,500 per year. Since the lease term is 15 years, the total real estate operating expenses would be $322,500 x 15 years = $<<322.515=4837.5>>4,837,500. Subtracting the real estate operating expenses from the total cost of leasing the office space, we find that the cash flow from leasing the office space would be $9.675 million - $4.837.5 million = $<<9.675-4.837.5=4.837.5>>4,837,500.

Next, let's calculate the cash flow from owning the office space. We already know that the total up-front costs associated with opening the new office would be $2.906 million. To calculate the cash flow from owning the office space, we need to subtract the total annual operating expenses from the net income generated by the increase in sales. Since the net income generated by the increase in sales is $1.56 million and the total annual operating expenses are $217,774.36, the cash flow from owning the office space would be $1.56 million - $217,774.36 = $<<1.56-217774.36=1.34222564>>1,342,225.64.

Finally, to calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space. Therefore, the return on the incremental cash flow from owning versus leasing would be $1,342,225.64 - $4,837,500 = $<<1.34222564-4.837.5=-3.495.5>>-3,495,500. This means that the corporation would incur a loss of $3.495.5 million by choosing to own the office space instead of leasing it.

The number of exams that Gretchen has to take is 4 exams.

From the information illustrated, Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. The total hours that she used will be:

= 5.1 + 3 3/5 + 5 3/10

= 5.1 + 3.6 + 5.3

= 14 hours.

Since she spends 3/1/2 hours studying for each exam, the number of exams that she has to take will be:

= Number of hours / Hours used for each exam

= 14 / 3 1/2

= 4 exams

The number of exams are 4.

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The equation of line that passes through the given point and is (a) parallel  to given line is 4x + y - 16 =0

(b) perpendicular to given line is 4x - y -8 =0

According to the question,

The required line is passing through given points and is

(a) parallel (b) perpendicular to given line

Let the equation of required line be (y - y') = m'(x - x')

(a) Parallel

If two lines are parallel to each other then their slopes are equal

Slope of given line : m = y2 - y1 / x2-x1

This line passes through (2,2) and (1,6)

=> m = 6 - 2 / 1 - 2

=> m = -4

Therefore , the slope of required line will be -4 also,

Required line passes through (4,3)

Equation of required line = (y - 4) = -4(x - 3)

=> y - 4 = -4x + 12

=> 4x + y - 16 =0

(b) Perpendicular

If two lines are perpendicular to each other then the product of their slope is -1

So, m × m' = -1

=> -4 × m' = -1

Dividing by -4

=> m' = 4

Therefore , equation of required line =>  (y - 4) = 4(x - 3)

=> y - 4 = 4x - 12

=> 4x - y -8 =0

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Answer:

a) ending inventory:     11,850,000

  cost of goods sold: 25,200,000

 gross profit               25,200,000

b)

ending inventory:     1,800,000

cost of goods sold:  23,100,000

gross profit  50,400,000 - 23,100,000 =  27,300,000

5,200 at $600

4,100 at $700

6,200 at $800

purchase 29,000 at $900

-sold 28,000 grills

As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account

ending inventory

5,200 at $  600

4,100 at $   700

6,200 at $  800

1,000  at $  900

Total    $ 11,850,000

cost of good sold:

28,000 x $900 = $25,200,000

sales revenue

28,000 x 900 x 200% = $50,400,000

gross profit sales revenue less COGS

b) 5,200 at $600

4,100 at $700

6,200 at $800

purchase 15,500 at $900

-sold 28,000 grills

we check how many layer deep we go:

28,000 - 15,500 at 900= 12,500

12,500  -  6,200  at 800=  6,300

6,300 - 4,100 at 700      =  2,200  at 600

Ending Inventory

3,000 at $600 = $ 1,800,000

COGS:

15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000

Step-by-step explanation:

At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e^-0.1 t - e^-0.20 t) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was 0 mg.

A limit is a value that a function or sequence approaches as the input or index approaches a certain value. Limits are a fundamental concept in calculus, and they are used to define important ideas such as derivatives and integrals. They are also used in other areas of mathematics, such as real analysis and mathematical analysis.

The rate at which the drug is being eliminated is the derivative of the amount of drug present at time t. We can write this as:

r(t) = dA(t)/dt = 50(e^-0.1 t - e^-0.20 t) mg/hr

If we integrate both sides of this equation with respect to t, we get:

A(t) = ∫r(t) dt = ∫50(e^-0.1 t - e^-0.20 t) dt

This integral can be evaluated using integration by parts. Let u = e^-0.1 t and dv = e^-0.20 t. Then du = -0.1 e^-0.1 t and v = -1/(0.2) * e^-0.20 t = -5e^-0.20 t. We can then write:

A(t) = -5 ∫e^-0.1 t * e^-0.20 t dt + (1/0.2) ∫e^-0.1 t dt

The first integral on the right-hand side can be evaluated using the substitution y = -0.3t, which gives:

A(t) = -5 ∫e^y dy + (1/0.2) ∫e^-0.1 t dt

The first integral is simply -5e^y, and the second integral is -5e^-0.1 t. Substituting these results back into the expression for A(t) gives:

A(t) = -5(-5e^-0.3 t) + (1/0.2)(-5e^-0.1 t)

Combining constants and simplifying gives:

A(t) = 25e^-0.1 t - 25e^-0.3 t

We are told that all the drug is eventually eliminated, so A(t) approaches 0 as t approaches infinity. This means that the original dose A(0) must be equal to the limit of A(t) as t approaches 0.

Taking the limit as t approaches 0 gives:

A(0) = lim t → 0 [25e^-0.1 t - 25e^-0.3 t]

This limit is equal to 25 - 25 = 0, so the original dose was 0 mg.

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Answer:

$368 per week

Step-by-step explanation:

[tex]8 \times 40 \times 1.15 = 368[/tex]

The differentiation of y = logx - cosecx + 5ˣ + 3/(x^(3/2)) with respect to x is cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))

In mathematics, differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how the function changes as its input (or independent variable) change

Given: y = logx - cosecx + 5ˣ + 3/(x^(3/2))

Thus, the derivative will be:

d/dx [logx - cosecx + 5ˣ + 3/(x^(3/2))]

= d/dx [logx] -  d/dx [logx]  +  d/dx [5ˣ]  +  3d/dx[(x^(3/2))]

= 1/x -  (-cotx)cosecx + log(5).5ˣ + 3(-3/2)x^((3/2) -1)

=  cotx.cosecx + log(5).5ˣ + 1/x - 9/(2x^(5/2))

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