a) Defficult to understand and sur plain.
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towards the guest, hespitality
@ A situation that is difficult to understand.
do move to a new place and establish one's home
or business to there.
(0) A ne man kable concahience of events without
appalenf causal connection
Answers
Answer:
BHAIB
Explanation:
Given
\begin{gathered} \to \sf \int \dfrac{9 {r}^{2} }{ \sqrt{1 - {r}^{3} } } dr \\ \end{gathered}
→∫
1−r
3
9r
2
dr
Using Substitution Method ,Let
\to \sf \: 1 - {r}^{3} = u→1−r
3
=u
Now Differentiate on both side wrt r
\sf \to \dfrac{d(1 - {r}^{3} )}{dr} = \dfrac{du}{dr}→
dr
d(1−r
3
)
=
dr
du
\sf \to \: - 3 {r}^{3 - 1} = \dfrac{du}{dr}→−3r
3−1
=
dr
du
\sf \to \: - 3 {r}^{2} = \dfrac{du}{dr}→−3r
2
=
dr
du
\sf \to \: (3 {r}^{2} )dr = - du→(3r
2
)dr=−du
Now we can write as
\begin{gathered} \to \sf3 \int \dfrac{3 {r}^{2} }{ \sqrt{1 - {r}^{3} } } dr \\ \end{gathered}
→3∫
1−r
3
3r
2
dr
Put the value
\begin{gathered} \sf \to \: 3\int \dfrac{ - du}{ \sqrt{u} } \\ \end{gathered}
→3∫
u
−du
\begin{gathered} \sf \to \: - 3\int \dfrac{ du}{ \sqrt{u} } \\ \end{gathered}
→−3∫
u
du
\begin{gathered}\sf \to \: - 3\int \dfrac{ du}{ {u} {}^{ \frac{1}{2} } } \\ \end{gathered}
→−3∫
u
2
1
du
\begin{gathered} \sf \to \: - 3 \int ({u}^{ \frac{ - 1}{2} } )du \\ \end{gathered}
→−3∫(u
2
−1
)du
\sf \to \: - 3 \bigg( \dfrac{u {}^{ \frac{ - 1}{2} + 1 } }{ \dfrac{ - 1}{2} + 1} \bigg) + c→−3(
2
−1
+1
u
2
−1
+1
)+c
\sf \to \: - 3 \bigg( \dfrac{ {u}^{ \frac{ - 1 + 2}{2} } }{ \dfrac{ - 1 + 2}{2} } \bigg) + c→−3(
2
−1+2
u
2
−1+2
)+c
\sf \to - 3 \bigg( \dfrac{u {}^{ \frac{1}{2} } }{ \dfrac{1}{2} } \bigg) + c→−3(
2
1
u
2
1
)+c
\sf \to - 3(2 {u}^{ \frac{ 1 }{2} } ) + c→−3(2u
2
1
)+c
\sf \to \: - 6( \sqrt{u} ) + c→−6(
u
)+c
Now put the value
\to \sf \: 1 - {r}^{3} = u→1−r
3
=u
We get
\sf \to - 6( \sqrt{1 - {r}^{3} } ) + c→−6(
1−r
3
)+c
Answer
\sf \to - 6( \sqrt{1 - {r}^{3} } ) + c→−6(
1−r
3
)+c━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
{ \purple{ \underline{ \boxed{\maltese {\textsf{ \textbf{What \: Are \: Isobars?}}}}}}}
✠ What Are Isobars?
→ Atoms of different elements may have similarity of mass number. Such atoms are called isobars.
Isobars may, thus be defined as atoms of different elements which have different atomic numbers but same mass numbers.
Isobars have different number of sub-atomic particles, electrons, protons and neutrons but they have same number of nucleons.
{ \orange{ \underline{ \boxed{\maltese{ \textsf{ \textbf{Characteristics of Isobars.}}}}}}}
✠ Characteristics of Isobars.
Some Important characteristics of isobars are as follows :
They have same mass number.
They have different atomic numbers.
They are atoms of different elements.
They have different number of protons, electrons and neutrons.
They possess different physical and chemical properties.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━