Question

please give me the answer quickly​

Answer 1

QUESTION :–

• If y is directly proportional to x² and the difference in the values of y when x = 1 and x = 3 is 32, find the value of y when x =-2.

ANSWER :–

GIVEN :–

• y is directly proportional to x².

• Difference in the values of y when x = 1 and x = 3 is 32.

TO FIND :–

• Value of y when x = -2 .

SOLUTION :–

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$\bf \implies y \propto {x}^{2}$

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• We should write this as –

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$\bf \implies y = k {x}^{2} \: \: \: \: \: \: \{ where \: \: k \to constant\}$

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• When x = 1 :–

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$\bf \implies y_1= k {(1)}^{2}$

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$\bf \implies y_1= k$

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• When x = 3 :–

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$\bf \implies y_2= k {(3)}^{2}$

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$\bf \implies y_2= k(9)$

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$\bf \implies y_2= 9k$

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▪︎According to the question –

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$\bf \implies y_1 - y_2= 32$

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$\bf \implies k - 9k= 32$

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$\bf \implies -8k= 32$

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$\bf \implies k= - \cancel \dfrac{32}{8}$

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$\bf \implies \large{ \boxed{ \bf k= -4}}$

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• So that given function is –

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$\bf \implies y= - 4{x}^{2}$

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• Now let's find the value of 'y' at x = -2 ,

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$\bf \implies y= - 4{( - 2)}^{2}$

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$\bf \implies y= - 4(4)$

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$\bf \implies \large{ \boxed{ \bf y= -16}}$

Answer 2

${\sf{\underline{\underline{\pink{Question:-}}}}}$

ɪꜰ ʏ ɪꜱ ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ x² ᴀɴᴅ ᴛʜᴇ ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ɪɴ ᴛʜᴇ ᴠᴀʟᴜᴇꜱ ᴏꜰ ʏ ᴡʜᴇɴ x = 1 ᴀɴᴅ x = 3 ɪꜱ 32, ꜰɪɴᴅ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ ʏ ᴡʜᴇɴ x =-2.

${\sf{\underline{\underline{\pink{Answer:–}}}}}$

$\sf\pink{Given:-}$

• ʏ ɪꜱ ᴅɪʀᴇᴄᴛʟʏ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ x².

• ᴅɪꜰꜰᴇʀᴇɴᴄᴇ ɪɴ ᴛʜᴇ ᴠᴀʟᴜᴇꜱ ᴏꜰ ʏ ᴡʜᴇɴ x = 1 ᴀɴᴅ x = 3 ɪꜱ 32.

$\sf\pink{To \ FIND :–}$

• ᴠᴀʟᴜᴇ ᴏꜰ ʏ ᴡʜᴇɴ x = -2 .

${\sf{\underline{\underline{\pink{SOLUTION :–}}}}}$

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$\bf \implies y \propto {x}^{2}$

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• ᴡᴇ ꜱʜᴏᴜʟᴅ ᴡʀɪᴛᴇ ᴛʜɪꜱ ᴀꜱ –

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$\bf \implies y = k {x}^{2} \: \: \: \: \: \: \{ where \: \: k \to constant\}$

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• ᴡʜᴇɴ x = 1 :–

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$\bf \implies y_1= k {(1)}^{2}$

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$\bf \implies y_1= k$

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• ᴡʜᴇɴ x = 3 :–

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$\bf \implies y_2= k {(3)}^{2}$

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$\bf \implies y_2= k(9)$

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$\bf \implies y_2= 9k$

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★︎ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ Qᴜᴇꜱᴛɪᴏɴ –

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$\bf \implies y_1 - y_2= 32$

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$\bf \implies k - 9k= 32$

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$\bf \implies -8k= 32$

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$\bf \implies k= - \cancel \dfrac{32}{8}$

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$\bf \implies \large{ \boxed{ \bf k= -4}}$

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★ꜱᴏ ᴛʜᴀᴛ ɢɪᴠᴇɴ ꜰᴜɴᴄᴛɪᴏɴ ɪꜱ –

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$\bf \implies y= - 4{x}^{2}$

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ɴᴏᴡ ʟᴇᴛ'ꜱ ꜰɪɴᴅ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ 'ʏ' ᴀᴛ x = -2 ,

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$\bf \implies y= - 4{( - 2)}^{2}$

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$\bf \implies y= - 4(4)$

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$\bf \implies \large{ \boxed{ \bf y= -16}}$