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Mathematics is a branch of study in which we get detailed information from spaces, numbers, and changes. It can also be used in other fields, such as physics. To master this topic, you'll need analytical and methodical skills. However, not everyone is capable of defeating it. Completing mathematical questions is extremely difficult for students. Math assignment help is frequently aimed to help students around the world.

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Mathematics is the study of different topics like quantity, structure, space, and changes, etc. It is present all around us and in everything we do. There are various math formulas that are used in our daily life. Math is the foundation of statistics, accounting, computer science, and the latest technology. You can't imagine the world without it. That is why industries around the world widely use it.

*Different categories of Math*

There are two types of Math

- Pure Mathematics
- Applied Mathematics

Maths is an Art, and Pure math is the backbone of mathematics. It is done without immediate consideration of the direct application. Finance, economics are existing examples of areas to which pure mathematics is applied significantly. It has various branches, and some of them are listed below:

**Algebra****Mathematical analysis****Geometry****Number theory**

It is a mathematical approach to solve different problems, commonly found in fields like Physical science, engineering, computer science, etc. It is the application of mathematics in real-world situations. Statistics or probability theory are examples of applied maths. It involves various branches, and some of them are listed below: -

**Mathematics of engineering****Continuous modeling****Statistics****Game theory**

Addition, subtraction, multiplication, and division consider as the basic elements of mathematics. Without these operations, it is not possible to solve mathematics problems.

Some of the useful tricks to solve math problems quickly are:

**Addition of the large numbers****Subtracting from 1,000****Multiply by 9****Division**

The addition of the larger numbers can be a headache for you. You can simplify the process using the below-mentioned trick.

Example: 678 + 234

Take a round-up value to simplify the problem:

=> 678 -> (680 - 2) -> 678; => 234 -> (230 + 4) -> 234

Add the round-up numbers 680 + 230 = 910

Now subtract/add the number used for round-ups:

910 - (2) + (4) = 912

Directly subtract each number from 9 except the first one.

Example: 1000 - 662

Subtract 6 from 9 = 3

Subtract 6 from 9 = 3

Finally, Subtract 2 from 10 = 8

The answer will be 338.

Suppose you need to multiply 9 with 8, then do it as:

Subtract 1 from the multiplying number;

8 - 1 = 7

Subtract the number from 9 as:

9 - 7 = 2

Combine the answers as 72 that is 9 x 8 = 72.

Divide by 2: When the last digit of the number has an even value, then the number is divisible by 2.

Divide by 4: When the last two digits are divisible by 4, then the number is also divisible by 4.

Complex math problems are not much used in real life. However, the value of mathematics in our daily life cannot be denied. Without recognising it, we use mathematical rules and concepts on a regular basis. It would be tough to live a life without knowing how to solve math problems. The eight factors listed below are sufficient to convince you that math homework and assignments exist for a cause.

- You may use the percentages you have learned in school to get reduced numbers of items when shopping. You can also save a lot of money.
- Nature achieves stability by employing mathematical forms and values. The combs of honey bees are hexagonal. Fibonacci's sequence, a well-known mathematical number system, is used by trees, shrubs, and other plants.
- A fractions calculation can assist in the distribution of a pizza among the persons. Without using a calculator, you can rapidly calculate the bill.
- Every profession in the world necessitates the application of mathematics since you must be able to solve a paycheck and balance a monthly budget.
- People with strong analytical and practical skills can solve mathematical difficulties quickly. Math improves your problem-solving skills by developing the reasoning part of your brain.
- Math improves decision-making abilities, and you become more responsible as a result.
- You can tell time on the clock by knowing fractions.
- The key to creating delicious meals is to use math concepts when preparing the food. You must keep the proportions of the materials in check.

The only language that does not require translation is math. The pie's worth and symbolism will stay throughout the cosmos.

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Suppose 𝑎, 𝑏, and λ be +ve real numbers. P is the endpoint of the parabola's latus rectum 𝑦^2 = 4λ𝑥, and the ellipse {x^{2}}/{a^{2}}+{y^{2}}/{b^{2}} = 1 passes the point 𝑃. If the tangents and the ellipse to the parabola at the point P perpendicular to each other, then the ellipse's eccentricity will be:

- 1/2
- 1/√2
- 2/5
- 1/3

** Solution:**

Answer: b

P(λ, 2λ)

y^{2} = 4λx ⇒ (dx/dy) =1 = p1…….(1)

Now E: = {x^{2}}/{a^{2}}+{y^{2}}/{b^{2}} = 1 Passes the point P

(λ^2/a^2) + (4λ^2/b^2) = 1 ⇒ (dx/dy) = -b/(2a^2) = p2

(2λ/2λ)X − [(λ/a^2) ⋅ (b^2)/2λ] = −1 …….(2)

From eq. (1) & (2)

p1. p2 = -1 ⇒ b^2 = 2a^2

a^2/b^2 = 1/2

for ellipse's eccentricity,

e = √ [1−(a^2/b^2)] = √ [1−(1/2)] = 1/√2

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