Question

show your solution.

need help​

Answer 1

Answer:

1.y= 20

2.y=4

Step-by-step explanation:

1. 3x5=15

4x5=20

2. 5x3 =15

4 x3=12

Answers

Answer 2

Question 1 :

• If y varies directly as x and y = 15 when x = 3, find y when x = 4.

‎

Given :

• y varies directly as x
• y = 15 when x = 3

‎

To find :

• The value of y when x = 4.

‎

Solution :

$\sf\curvearrowright\:y∝x$

$\sf\triangleright\:$[ from the given ]

$\bf\curvearrowright\:y=kx$ ⠀⠀⠀⠀⠀$\small\red{\tt\pmb{--(i)}}$

$\sf\triangleright\:$[ k = constant of proportionality]

‎

From the given, y = 15 when x = 3.

Using equation (i) and substituting the respective values

$\sf\nrightarrow\:y=kx$

$\sf\nrightarrow\:15=k\times3$

$\sf\nrightarrow\:k=\cancel{\frac{15}{3}}$

$\small{\underline{\boxed{\mathrm{\nrightarrow\:k= 5}}}}$

‎

Now, when x = 4

Using equation (i) and substituting the known values

$\sf\nrightarrow\:y=kx$

$\sf\nrightarrow\:y=5 \times 4$

$\small{\underline{\boxed{\mathrm{\nrightarrow\:y= 20}}}}$ ⋆

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Question : 2

If y varies inversely as x and y = 12 when x = 5, find y when x = 15.

‎

Given :

• y varies inversely as x
• y = 12 when x = 5

‎

To find :

• The value of y when x = 15.

‎

Solution :

$\sf\curvearrowright\:y∝\frac{1}{x}$

$\sf\triangleright\:$[ from the given ]

$\bf\curvearrowright\:y=\frac{k}{x}$⠀⠀⠀⠀ $\small\red{\tt\pmb{--(i)}}$

$\sf\triangleright\:$[ k = constant of proportionality]

‎

From the given, y = 12 when x = 5.

Using equation (i) and substituting the respective values

$\sf\nrightarrow\:y=\frac{k}{x}$

$\sf\nrightarrow\:12=\frac{k}{5}$

$\sf\nrightarrow\:k=12 \times 5$

$\small{\underline{\boxed{\mathrm{\nrightarrow\:k= 60}}}}$

‎

Now, when x = 15

Using equation (i) and substituting the known values

$\sf\nrightarrow\:y=\frac{k}{x}$

$\sf\nrightarrow\:y=\cancel{\frac{60}{15}}$

$\small{\underline{\boxed{\mathrm{\nrightarrow\:y= 4}}}}$ ⋆

⠀⠀⠀⠀

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