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To manufacture ‘𝑥’ number of dolls, a company’s total cost function C(𝑥) is given by C (𝑥) = 100 + 0.025𝑥 2 and the total revenue function R (𝑥) is described as R (𝑥) = 5𝑥. Given that C (𝑥) and R (𝑥) are in thousand rupees, what number of dolls shall be manufactured to maximise the profit of the company? What is the maximum profit?

Posted by Tanushri Bhayani 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 2 years, 1 month ago

Answer is given below:

1Thank You

Tanushri Bhayani 2 years, 1 month ago

This was easy but it made me confusing thank you for helping me always

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ANSWER

An event management company charges ₹ 4,800 per guest, for a bulk booking for 100 guests. In addition, it offers a discount of ₹ 200 for each group of 10 guests over and above 100 guest booking. What is the number of guests that will maximise the amount of money the company receives on a booking? What is the maximum profit on such booking?

Posted by Tanushri Bhayani 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 2 years, 1 month ago

Let the number of guests be x

If x > 100, then the amount received by the company will be-

{4800 - 200/10(x - 100)}x

Now, we need to maximize this amount so let us differentiate with respect to x as follows-

P = 4800x - 20(x - 100)x

P = 4800x - 20x² + 2000x

P = 6800x - 20x²

dP/dx = 6800 - 40x

differentiating again-

d²P/dx² = -40

As d²P/dx² > 0, the maximum value will occur at dP/dx = 0

⇒ 6800 - 40x = 0

40x = 6800

x = 6800/40

x = 170

Now, the amount received will be = 6800(170) - 20(170)²

= 1156000 - 578000

= 578000

Thus, the maximum amount that the company will receive is 5,78,000 when the number of guests are 170.

1Thank You

Tanushri Bhayani 2 years, 1 month ago

Thank you bro

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ANSWER

Milk and water in two vessels A and B are in ratio 5:3 and 5:3 respectively. In what ratio the liquid of both the vessels be mixed to obtain a new mixture of ratio of milk and water 7:5 respectively?

Posted by Vaiharai . 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 1 month ago

2 : 3

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ANSWER

A boat travel 36km upstream in 5hrs. If the speed of the stream is 2.4km/hr, how much time will the boat take to cover a distance of 78km downstream?

Posted by Tanushri Bhayani 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 2 years, 1 month ago

Distance covered by a boat in 5 hours = 36 km
Rate upstream of boat $=\frac{36}{5}$ 7.2 kmph
Speed of the stream = 2.4 kmph
$\therefore$ Speed of the boat in still water
= (7.2 + 2.4) kmph
= 9.6 kmph
$\therefore$ Rate downstream of the boat
= (9.6 + 2.4) kmph
= 12 kmph
$\therefore$ Time taken in covering 78 km distance
$=\frac{78}{12}$
= 6.5 hours or 6 hour 30 minutes.

1Thank You

Tanushri Bhayani 2 years, 1 month ago

Thanks a lot dude 😇

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ANSWER

In a bank, principal increases continuously at the rate of 5% per year. In how many years ₹1000 double itself?

Posted by Tanushri Bhayani 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 2 years, 1 month ago

Let P be the principal at any time t. According to the given problem, $\frac{d p}{d t}=\left(\frac{5}{100}\right) \times \mathrm{P}$
or $\frac{d p}{d t}=\frac{\mathrm{P}}{20}$ ...(i)
separating the variables in equation (i), we get
$\frac{d p}{\mathrm{P}}=\frac{d t}{20}$ ...(ii)
Integrating both sides of equation (ii), we get
log P = $\frac{t}{20}$ + C₁
or P = $e^{\frac{t}{20}} \cdot e^{\mathrm{C}_{1}}$
or P = $\mathrm{C} e^{\frac{t}{20}}$ (where e^C₁= C) ...(iii)
Now, P = 1000, when t = 0
Substituting the values of P and t in (iii), we get C = 1000. Therefore, equation (iii), gives
P = 1000 e^t/20
Let t years be the time required to double the principal. Then 2000 = 1000 e^t/20 $\Rightarrow$ t = 20 log_e2.

1Thank You

Tanushri Bhayani 2 years, 1 month ago

Thames bro 😘

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ANSWER

Integral x

Posted by Praagna Koya 2 years, 1 month ago

CBSE > Class 12 > Applied Maths

1 answers

Tanishka Solanki 2 years, 1 month ago

X^2÷2

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ANSWER

How may I do derivatives and integration if I haven't done them before

Posted by Hardeep Singh 2 years, 2 months ago

CBSE > Class 12 > Applied Maths

1 answers

Tanushri Bhayani 2 years, 1 month ago

You will need to do all coz every formula has its own way of solving the question better start learning all u still hve 13 days for exam to go Best of luck 👍..

1Thank You

ANSWER

Applied mathematics project

Posted by Ri S 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Tanushri Bhayani 2 years, 1 month ago

Need to prepare a spreadsheet presentation on matrix and function separately This project was given in our school And in RKC project was related probability and linear equations Project are given by the school faculty as there no particular viva taken by external faculty and the school faculty itself takes the viva ....

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ANSWER

In year 2000 Mr. Talwar took a home loan of rs. 300000 from state Bank of India at 7.5

Posted by Harrish Kumaran 2 years, 4 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

Please provide complete information.

23Thank You

ANSWER

A company conducted an IQ test for randomly select 50 employees. Volunteer A scored 74 out of the possible 120 points. If the average IQ test score was recorded as 62 and the standard deviation was 11. How well did volunteer A perform on the test compared to the other volunteers?

Posted by Arpit Agrawal 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

4 - 120

= 48

62 ÷ 11

= 5

48 + 5

= 53

therefore, the test compared to the other volunteer

= 53

1Thank You

ANSWER

Find the point of maxima or point of minima of the following:- f(x) = (1-x^2) e^x

Posted by Anushka Kaira 2 years, 4 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

1 divided by x((log x)² -3 log x +2)

Posted by Tamizhiniyan Ganesan 2 years, 5 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

Fine the second derivatives of the following functions x⁵

Posted by Van Thangi 2 years, 5 months ago

CBSE > Class 12 > Applied Maths

2 answers

Tanushri Bhayani 2 years, 1 month ago

f(x)=x^5 f'(x)=5x^4 f"(x)=20x^3. (;5×4=20)

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Kushal Sethi 2 years, 5 months ago

20x^3

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ANSWER

Case study

Posted by Disha Jain 2 years, 6 months ago

CBSE > Class 12 > Applied Maths

4 answers

Tanushri Bhayani 2 years, 1 month ago

Here you go ... they are taken from the sample paper

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Tanushri Bhayani 2 years, 1 month ago

CASE STUDY – III According to an educational board survey, it was observed that class XII students apply at least one to four weeks ahead of colleges application deadline. Let X represent the week when an average student applies ahead of a college’s application deadline and the probability of student to get admission in the college 𝑃(𝑋 = 𝑥) is given as follows: 𝑃(𝑋 = 𝑥) = { 𝑘𝑥 6 𝑤ℎ𝑒𝑛 𝑥 = 0, 1 𝑜𝑟 2 (1 − 𝑘)𝑥 6 𝑘𝑥 2 𝑤ℎ𝑒𝑛 𝑥 = 3 𝑤ℎ𝑒𝑛 𝑥 = 4 0 𝑤ℎ𝑒𝑛 𝑥 > 4 Where k is a real number. Based on the above information, answer the following questions. Show steps to support your answers. a) Find the value of k. 1 b) What is the probability that Sonali will get admission in the college, given that she applied at least 2 weeks ahead of application deadline? 1 c) Calculate the mathematical expectation of number of weeks taken by a student to apply ahead of a college’s application deadline. OR To promote early admissions, the college is offering scholarships to the students for applying ahead of deadline as follows: ₹ 50000 for applying 4 weeks early, ₹ 20000 for applying 3 weeks early, ₹ 12000 for applying 2 weeks early, and ₹ 9600 for applying 1 week early What is the expected scholarship offered by the college?

17Thank You

Tanushri Bhayani 2 years, 1 month ago

CASE STUDY – I An overhead water tank has three pipes A, B and C attached to it (as shown in figure (II)). The inlet pipes A and B can fill the empty tank independently in 15 hours and 12 hours respectively. The outlet pipe C alone can empty a full tank in 20 hours. Based on the above information, answer the following questions. a) For a routine cleaning of the tank, the tank needs to be emptied. If pipes A and B are closed at the time when the tank is filled to two-fifth of its total capacity, how long will pipe C take to empty the tank completely? 1 b) How long will it take for the empty tank to fill completely, if all the three pipes are opened simultaneously? 1 c) On a given day, pipes A, B and C are opened (in order) at 5 am, 8 am and 9 am respectively, to fill the empty tank. In how many hours will the tank be filled completely? OR Given that the tank is half-full, only pipe C is opened at 6 AM, to empty the tank. After closing the pipe C and an hour’s cleaning time, tank is filled completely by pipe A and B together. What is the total time taken in the whole process?

2Thank You

Tanushri Bhayani 2 years, 1 month ago

When observed over a long period of time, a time series data can predict trend that can forecast increase or decrease or stagnation of a variable under consideration. Such analytical studies can benefit a business for forecasting or prediction of future estimated sales or production. Mathematically, for finding a line of best-fit to represent a trend, many methods are available. Methods like moving-averages and least-squares squares are some of the techniques to predict such trends. Mrs. Shamita runs a bread factory and the record of her sales of bakery items for the period of 2015 - 2019 is as follows: Year 2015 2016 2017 2018 2019 Sales (in ₹ thousands) 35 42 46 41 48 Based on the above information, answer the following questions. Show steps to support your answers. a) By taking year 2017 as origin, use method of least-squares to find the best-fit trend line equation for Mrs. Shamita’s business. Show the steps of your working. OR Demonstrate the technique to fit the best-suited straight-line trend by the method of 3-years moving averages. Also draw the trend line. 2 b) What are the estimated sales for Mrs. Shamita’s business for year 2022? 1 c) Mrs Shamita wishes to grow her business to yearly sale of ₹ 67400. In which year will she be able to reach her target?

18Thank You

ANSWER

f(x)=2x³-6x²+6x+5 find local maxima and local minima

Posted by Manisha Behera 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

We have
f (x) = 2x³ – 6x² + 6x + 5
or f ′(x) = 6x² – 12x + 6 = 6 (x – 1)²
Now, f ′(x) = 0
$\Rightarrow$ x = 1
Thus, x = 1 is the only critical point of f . We shall now examine this point for local maxima and/or local minima of f. Observe that f ′(x) $\ge$ 0, for all x $\in$ R and in particular f ′(x) > 0, for values close to 1, to the left and to the right of 1. Therefore, by first derivative test, the point x = 1 is neither a point of local maxima nor a point of local minima. Hence x = 1 is a point of inflexion.

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ANSWER

Second derivative of log x/x

Posted by Deep Chakraborty 2 years, 6 months ago

CBSE > Class 12 > Applied Maths

1 answers

Tanushri Bhayani 2 years, 1 month ago

-3x+logx/x^4 is the ans

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ANSWER

Find the anti derivative of 1/(x+1)^2(x^2 +1)

Posted by Saloni Dwivedi 2 years, 6 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

Find the points on the curve y = x^3 -3x + 2x

Posted by Sudhanshu Suman 2 years, 7 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

Integral x by (x+2)² dx

Posted by Seitinngam Singson 2 years, 7 months ago

CBSE > Class 12 > Applied Maths

1 answers

Tanushri Bhayani 2 years, 1 month ago

(x+2)^3/3+c is the answer

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ANSWER

X=a(1+t^2/1-t^2), y=2t/1-t^2

Posted by Deep Chakraborty 2 years, 7 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

A man can robot 8 km per hour and still water is the speed of the current istwent 2 km per hour and he takes 4 hours to row a place and written back how far is a place

Posted by Pravee Na 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

Speed of the man in still water =8 kmph.
Speed of the river =2 kmph
Downstream =8+2=10 kmph
Upstream =8−2=6 kmph
$\Rightarrow \frac{x}{10}+\frac{x}{6}=\frac{48}{60}$
⇒8x=24
⇒x=3 km

1Thank You

ANSWER

A stationery company manufactures 'x units of pen in a given time, if the cos square of the pens produced, cost of transportation is twice the number of pens property tax costs 5000. Then, (1) Find the cost function C(x). Differentiation and its Applications (ii) Find the cost of producing 21pen. (iii) The marginal cost of producing 50 pens.

Posted by Moorthi Maths 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

Cost of raw material = x²

Cost of transportation = 2x

Property tax = 5,000

Therefore ,

(i) C(x) = x² + 2x + 5000

(ii) MC = 2x + 2

Now, x = 21,

MC = 2(21) + 2 = 42 + 2 = 44

(iii) x = 50,

MC. = 2(50) + 2 = 100+2 = 102

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ANSWER

A man borrows Rs 30000 at 12% per annum compound interest from a bank and promises to pay off the loans in 20 installments beginning at the end of first year. What is the annual payment necessary?

Posted by Tejasni Somasundaram 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

$\begin{aligned} & \text { We know } \mathrm{V}=\frac{\mathrm{A}}{\mathrm{r}}\left[1-(1+\mathrm{r})^{-\mathrm{n}}\right] \\ & \text { Thus } 30000=\frac{\mathrm{A}}{0.12}\left[1-(1+0.12)^{-20}\right] \\ & \Rightarrow \mathrm{A}=\frac{30000 \times 0.12}{\left[1-(1+0.12)^{-20}\right]} \\ & \Rightarrow \mathrm{A}=\frac{3600}{\left[1-(1.12)^{-20}\right]} \\ & \Rightarrow \mathrm{A}=\text { Rs. } 4016.76 \end{aligned}$

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ANSWER

If you need 20000 for your daughter's education how much must you set aside each your quarter for 10 years to accumulate

Posted by Krishna Goswami Xii B 3 years, 1 month ago

CBSE > Class 12 > Applied Maths

2 answers

Tanushri Bhayani 2 years, 1 month ago

P=R/I; R=20000 and I=10years×4=40 P=20000÷40 P=500 Therefore, he must keep ₹500 every quarterly for 10 years to accumulate the actual amount.

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Husan Preet 3 years ago

20000 N=10*4=40 So 20000÷40 = 5000

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ANSWER

We have 4 white and 3 blue balls in a bowl. Accidentally we pull out two balls. What is the probability that: a) both of the pulled out balls are white b) one ball is white and the other one is blue?

Posted by Shruti Thakur 3 years, 1 month ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

If you need 20000 for your daughter education how much must you set aside each quarter for 10 years

Posted by Joel Dawson G 3 years, 3 months ago

CBSE > Class 12 > Applied Maths

0 answers

ANSWER

Find the slope of a line making inclination of 60 degree with positive direction of x axis

Posted by Sonia Sharma 3 years, 4 months ago

CBSE > Class 12 > Applied Maths

1 answers

Aseem Mahajan 3 years, 4 months ago

√3

0Thank You

ANSWER

Acompany conducted a iq test for randomly selected 50 employees . Volunteer A scored 74 out of the possible 120 points .If the average IQ test score was recorded as 62 and the standard deviation was 11 ,how well did Volunteer A perform on the test compared to other volunteers?

Posted by Sushma Mittal 2 years, 3 months ago

CBSE > Class 12 > Applied Maths

1 answers

Preeti Dabral 2 years, 3 months ago

74 - 120

= 48

62 ÷ 11

= 5

48 + 5

= 53

therefore, the test compared to the other volunteer

= 53

0Thank You

ANSWER

A can run 40 metres while B run 50 metres in the same time in a 1000m race find by how much distance b beats a

Posted by Khushi Thakur 3 years, 5 months ago

CBSE > Class 12 > Applied Maths

1 answers

Gembali Harsha Vardhan 3 years, 5 months ago

When B runs 50 m, then A runs 45 m. When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m ∴ B beats A by 100 m.

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ANSWER

A lady’s bag contains 2 black and 1 red pens. One pen is drawn at random and then put back in the box after noting its colour. The process is repeated again. If X denotes the number of red pens recorded in the two draws. Describe X.

Posted by Deepansh Jayara 3 years, 6 months ago

CBSE > Class 12 > Applied Maths

1 answers

Gembali Harsha Vardhan 3 years, 5 months ago

Let 2 white ball be denoted by W₁, W₂ & red ball by r We draw two balls, one after the other Sample space = S = {(W₁, W₁), (W₂, W₂), (W₁, W₂), (r, W₂), (W₂, r), (W₂, W₁), (r, w₁), (W₁, r), (r, r)} Let X: Number of red balls in two draws We can see there are 0 red, 1 red and 2 red balls So, X = 0 or X = 1 or X = 2

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ANSWER

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