Question Find $a$ when $a \propto b$ and $a=12$ when $b=2$ , given $b=7$ .

Studdy Solution

STEP 1

Assumptions1. $a \propto b$ means $a$ is directly proportional to $b$ . . The constant of proportionality can be found using the given values of $a$ and $b$ .
3. The value of $a$ when $b=$ is $12$ .

STEP 2

To find the constant of proportionality, we use the formula $k = \frac{a}{b}$ where $k$ is the constant of proportionality.

STEP 3

Plug in the given values for $a$ and $b$ to calculate $k$ .
$k = \frac{12}{2}$

STEP 4

Calculate the constant of proportionality.
$k = \frac{12}{2} =6$

STEP 5

Now that we have the constant of proportionality, we can find the value of $a$ when $b=7$ . We use the formula $a = k \cdot b$

STEP 6

Plug in the values for $k$ and $b$ to calculate $a$ .
$a =6 \cdot$

STEP 7

Calculate the value of $a$ .
$a =6 \cdot7 =42$ The value of $a$ when $b=7$ is42. So, the correct answer is (c)42.

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Question Find $a$ when $a \propto b$ and $a=12$ when $b=2$ , given $b=7$ .

Studdy Solution

STEP 1

Assumptions1. $a \propto b$ means $a$ is directly proportional to $b$ . . The constant of proportionality can be found using the given values of $a$ and $b$ .
3. The value of $a$ when $b=$ is $12$ .

STEP 2

To find the constant of proportionality, we use the formula $k = \frac{a}{b}$ where $k$ is the constant of proportionality.

STEP 3

Plug in the given values for $a$ and $b$ to calculate $k$ .
$k = \frac{12}{2}$

STEP 4

Calculate the constant of proportionality.
$k = \frac{12}{2} =6$

STEP 5

Now that we have the constant of proportionality, we can find the value of $a$ when $b=7$ . We use the formula $a = k \cdot b$

STEP 6

Plug in the values for $k$ and $b$ to calculate $a$ .
$a =6 \cdot$

STEP 7

Calculate the value of $a$ .
$a =6 \cdot7 =42$ The value of $a$ when $b=7$ is42. So, the correct answer is (c)42.

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Question Find aaa when a∝ba \propto ba∝b and a=12a=12a=12 when b=2b=2b=2, given b=7b=7b=7.

Studdy Solution

STEP 1

Assumptions1. a∝ba \propto ba∝b means aaa is directly proportional to bbb. . The constant of proportionality can be found using the given values of aaa and bbb.3. The value of aaa when b=b=b= is 121212.

STEP 2

To find the constant of proportionality, we use the formulak=abk = \frac{a}{b}k=ba​where kkk is the constant of proportionality.

STEP 3

Plug in the given values for aaa and bbb to calculate kkk.k=122k = \frac{12}{2}k=212​

STEP 4

Calculate the constant of proportionality.k=122=6k = \frac{12}{2} =6k=212​=6

STEP 5

Now that we have the constant of proportionality, we can find the value of aaa when b=7b=7b=7. We use the formulaa=k⋅ba = k \cdot ba=k⋅b

STEP 6

Plug in the values for kkk and bbb to calculate aaa.a=6⋅a =6 \cdota=6⋅

STEP 7

Calculate the value of aaa.a=6⋅7=42a =6 \cdot7 =42a=6⋅7=42The value of aaa when b=7b=7b=7 is42. So, the correct answer is (c)42.

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Question Find $a$ when $a \propto b$ and $a=12$ when $b=2$ , given $b=7$ .

Assumptions1. $a \propto b$ means $a$ is directly proportional to $b$ . . The constant of proportionality can be found using the given values of $a$ and $b$ .
3. The value of $a$ when $b=$ is $12$ .

To find the constant of proportionality, we use the formula $k = \frac{a}{b}$ where $k$ is the constant of proportionality.

Plug in the given values for $a$ and $b$ to calculate $k$ .
$k = \frac{12}{2}$

Calculate the constant of proportionality.
$k = \frac{12}{2} =6$

Now that we have the constant of proportionality, we can find the value of $a$ when $b=7$ . We use the formula $a = k \cdot b$

Plug in the values for $k$ and $b$ to calculate $a$ .
$a =6 \cdot$

Calculate the value of $a$ .
$a =6 \cdot7 =42$ The value of $a$ when $b=7$ is42. So, the correct answer is (c)42.