two concentric circle are of radii 4cm and 3cm find the length of the chord of the larger circle which touches the smaller circle​

[tex]\large\underline{\sf{Solution-}}[/tex]

We know,

Mode of the continuous series is given by

[tex]{\boxed{ \boxed{\sf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}} \\ \\ [/tex]

where,

l is lower limit of modal class.

[tex] \sf{f_1} [/tex] is frequency of modal class

[tex] \sf{f_0} [/tex] is frequency of class preceding modal class

[tex] \sf{f_2} [/tex] is frequency of class succeeding modal class

h is class height.

Now, from given data we concluded that

[tex]\rm \: f_0 = 6 \\ [/tex]

[tex]\rm \: f_1 = f \\ [/tex]

[tex]\rm \: f_2 = 8 \\ [/tex]

[tex]\rm \: l = 65 \\ [/tex]

[tex]\rm \: h = 15 \\ [/tex]

[tex]\rm \: Mode = 75 \\ [/tex]

So, on substituting the values in above formula, we get

[tex]\rm \: 75 = 65 + \bigg[\dfrac{f - 6}{2 \times f - 6 - 8} \bigg] \times 15\\ [/tex]

[tex]\sf \: 75 - 65 = \dfrac{f - 6}{2f - 14} \times 15 \\ \\ [/tex]

[tex]\sf \: 10 = \dfrac{f - 6}{2f - 14} \times 15 \\ \\ [/tex]

[tex]\sf \: 2 = \dfrac{f - 6}{2f - 14} \times 3 \\ \\ [/tex]

[tex]\sf \: 2(2f - 14) = 3(f - 6) \\ \\ [/tex]

[tex]\sf \: 4f - 28 = 3f -18 \\ \\ [/tex]

[tex]\sf \: 4f - 3f = 28 -18 \\ \\ [/tex]

[tex]\bf\implies \:f = 10 \\ \\ [/tex]

[tex]\rule{190pt}{2pt} \\ [/tex]

Additional Information :-

1. Mean using Direct Method

[tex]\boxed{ \rm{ \:Mean = \dfrac{ \sum f_i x_i}{ \sum f_i} \: }} \\ \\ [/tex]

2. Mean using Short Cut Method

[tex]\boxed{ \rm{ \:Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i} \: }} \\ \\ [/tex]

3. Mean using Step Deviation Method

[tex]\boxed{ \rm{ \:Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h \: }} \\ \\ [/tex]

Answer:

• The mode of a grouped frequency distribution is 75 and the modal class is 65 - 80.
• The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8.

• What is frequency of the modal class.

[tex]\clubsuit[/tex] Mode Formula :-

[tex]\bigstar \: \: \sf\boxed{\bold{Mode =\: l + \bigg[\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\bigg] \times h}}\: \: \: \bigstar\\[/tex]

where,

• l = Lower Limit of the Modal Class
• h = Class Size of the Class Interval
• f₁ = Frequency of the Modal Class
• f₀ = Frequency of the Class Preceding the Modal Class
• f₂ = Frequency of the Class Succeeding the Modal Class

Let,

[tex]\mapsto \bf Frequency_{(Modal\: Class)} =\: f_1\\[/tex]

Given :

• Mode = 75
• Lower limit = 65
• Class Size = 15
• Frequency of the class preceding = 6
• Frequency of the class succeeding = 8

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Mode =\: l + \bigg[\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\bigg] \times h}}\\[/tex]

[tex]\implies \sf 75 =\: 65 + \bigg[\dfrac{f_1 - 6}{2f_1 - 6 - 8}\bigg] \times 15\\[/tex]

[tex]\implies \sf 75 =\: 65 + \bigg[\dfrac{f_1 - 6}{2f_1 - 14}\bigg] \times 15\\[/tex]

[tex]\implies \sf 75 =\: 65 + \dfrac{f_1 - 6}{2f_1 - 14} \times 15\\[/tex]

[tex]\implies \sf 75 =\: 65 + \dfrac{15(f_1 - 6)}{2f_1 - 14}\\[/tex]

[tex]\implies \sf 75 =\: 65 + \dfrac{15f_1 - 90}{2f_1 - 14}\\[/tex]

[tex]\implies \sf 75 - 65 =\: \dfrac{15f_1 - 90}{2f_1 - 14}[/tex]

[tex]\implies \sf 10 =\: \dfrac{15f_1 - 90}{2f_1 - 14}[/tex]

By doing cross multiplication we get,

[tex]\implies \sf 15f_1 - 90 =\: 10(2f_1 - 14)[/tex]

[tex]\implies \sf 15f_1 - 90 =\: 20f_1 - 140[/tex]

[tex]\implies \sf 15f_1 - 20f_1 =\: - 140 + 90[/tex]

[tex]\implies \sf {\cancel{-}} 5f_1 =\: {\cancel{-}} 50[/tex][tex]\implies \sf 5f_1 =\: 50[/tex]

[tex]\implies \sf f_1 =\: \dfrac{\cancel{50}}{\cancel{5}}[/tex]

[tex]\implies \sf f_1 =\: \dfrac{10}{1}[/tex]

[tex]\implies \sf\bold{f_1 =\: 10}[/tex]

Hence, the required frequency of the modal class is :

[tex]\dag[/tex] Frequency Of Modal Class :

[tex]\dashrightarrow \sf Frequency_{(Modal\: Class)} =\: f_1\\[/tex]

[tex]\dashrightarrow \sf\bold{\underline{Frequency_{(Modal\: Class)} =\: 10}}\\[/tex]

[tex]\therefore[/tex] The frequency of the modal class is 10 .

• Detour -

The main road was blocked because of which we had to make 3 km detour.

• Formal -

During the meeting with CEO, Rohan behaved in formal manner only.

• Solitary -

She likes to write novels in solitary.

• Take off -

The new Aeroplane's takeoff was very natural without any disturbances.

• Give up -

Even after going through such a big accident, she has decided not to give up her preperation.

Answer:

1. We took a detour to the petrol pump before going to the restaurant.

2. The company sent a formal invitation to all the employees and clients of the stakeholders.

3. It was a solitary verse of the poem that made the judges give them full marks.

4. The flight was gonna take off at the Amsterdam airport.

5. She was taught by her parents, never to give up.

Explanation:

A conjunction is indeed a letter that joins words, phrases, or clauses together. The English language has many conjunctions, but some of the more popular ones include and, for, but, since, for, if, or when.

The set of rules governing the word and sentence constructions in the English language is known as English grammar.

The tense structure refers to the order in which the paragraph's components appear. Verbs, auxiliary verbs, subjects, objects, etc. are all topics of discussion. The way a sentence is put together tells the reader / listener if it is in the past, present, or future tense. The set of grammatical principles governing the English language are known as English grammar. This encompasses the organisation of individual words, sentences, clauses, phrases, and texts as a whole.

#SPJ2

Answer:

proper consideration of the value

Answer:

'Value of Time', will be the suitable title for this passage.

Explanation:

The title is suitable because:

• The passage highlights the importance of time in a person's life.
• The way we value time shows our mutual respect for those we are called upon to meet in the business of life.
• Punctuality is the politeness of the kings,duty of gentlemen and necessity of men at business.
• A person careless about time will be careless with business and should not be trusted upon.
• An appoinment is a contract and he who doesn't keep it, is guilty of breaking faith.

Answer:

See attachment for your answer.

Robin Hood is a mythical fearless outlaw basically described in English folklore and consequently highlighted in literature and film. According to the inscription, he was a profoundly skilled bowman and gladiator. In some accounts of the legend, he is described as signifying of noble birth, and in contemporary time he is sometimes portrayed as having fought in the Crusades before retreating to England to find his lands captured by the Sheriff. In the oldest remembered stories, he is alternately a member of the citizen class. Traditionally portrayed dressed in Lincoln green, he is assumed to have stolen from the rich and distributed to the poo