Question

10. By what number should (3)-2 be divided to get (9)
$3^{ - 2} \div x = 9^{ - 3}$
​

Answer 1

Answer:

9

Step-by-step explanation:

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Answer 2

Answer:

6. Construct a quadrilateral ABCD, when AB=5 cm. , BC = 6 cm , DC=5.5 cm. AC=4 cm. and BD = 4.5 cm\large\underline{\sf{Solution-}}

Solution−

Given that,

In a new year, Reenu saved ₹50 in the first week and then increased her weekly savings by ₹17.50. If in the nth week, her weekly savings become ₹207.50.

So,

Savings in first week = ₹ 50

Savings in second week = ₹ 50 + 17.50 = ₹ 67.50

Savings in third week = 67.50 + 17.50 = ₹ 85

.

.

.

.

.

Savings in nth week = 207.50

So, the savings

\begin{gathered}\rm \: 50, \: 67.50, \: 85, \: \cdots \cdots, \: 207.50 \: forms \: an \: AP \: with \\ \\ \end{gathered}

50,67.50,85,⋯⋯,207.50formsanAPwith

\begin{gathered}\rm \: First \: term, \: a \: = \: 50 \\ \end{gathered}

Firstterm,a=50

\begin{gathered}\rm \:Common \: difference, \: d \: = \: 17.50 \\ \end{gathered}

Commondifference,d=17.50

\begin{gathered}\rm \: {n}^{th} \: term \: = \: 207.50 \\ \\ \end{gathered}

n

th

term=207.50

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

\begin{gathered}\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}\end{gathered}

★

a

n

=a+(n−1)d

Wʜᴇʀᴇ,

aₙ is the nᵗʰ term.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

Tʜᴜs,

\begin{gathered}\rm \: 207.50 = 50 + (n - 1) \times 17.50 \\ \end{gathered}

207.50=50+(n−1)×17.50

\begin{gathered}\rm \: 207.50 - 50 = (n - 1) \times 17.50 \\ \end{gathered}

207.50−50=(n−1)×17.50

\begin{gathered}\rm \: 157.50 = (n - 1) \times 17.50 \\ \end{gathered}

157.50=(n−1)×17.50

\begin{gathered}\rm \: 9 = n - 1 \\ \end{gathered}

9=n−1

\begin{gathered}\bf\implies \:n \: = \: 10 \\ \\ \end{gathered}

⟹n=10

\rule{190pt}{2pt}

{ \red{ \mathfrak{Additional\:Information}}}AdditionalInformation

↝ Sum of n terms of an arithmetic sequence is,

\begin{gathered}\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}\end{gathered}

★

S

n

=

2

n

(2a+(n−1)d)

Wʜᴇʀᴇ,

Sₙ is the sum of n terms of AP.

a is the first term of the sequence.

n is the no. of terms.

d is the common difference.

Step-by-step explanation:

hope it will helps you