2. "If a varies directly as b and inversely as c, and a = 8 when b = 4 and c = 2. Find a when b = 4 and c =8?

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Ivanjaytananghatulango Ivanjaytananghatulango

Math

Answered

2. "If a varies directly as b and inversely as c, and a = 8 when b = 4 and c = 2. Find a when b = 4 and c =8?

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Ajamheago Ajamheago · Answer 1

Ajamheago Ajamheago

Answer:

A=xB

B=C/y

6=2x

x=3

2=3/y

y=3/2

So when B=8,

8=6/y

y=3/4

As y=x/2

x/2=3/4

x=3/2

S0, A is

3/2*8

12

Step-by-step explanation:

Answer Link

Hanimeyago Hanimeyago · Answer 2

[tex]\sf{\underline{{Problem:}}}[/tex]

If a varies directly as b and inversely as c, and a = 8 when b = 4 and c = 2. Find a when b = 4 and c =8?

[tex]\sf{\underline{{Answer:}}}[/tex]

'As a varies directly with b and inversely with c, we have: "a = kb/c" as our guide to find the constant k variation

[tex] \tt{a = \frac{kb}{c}} [/tex]
[tex] \tt{8 = \frac{k(4)}{2}} [/tex]
[tex] \tt{8 = \frac{4k}{2} }[/tex]
[tex] \tt{16=4k}[/tex]
[tex] \tt\green{k = 4}[/tex]

Hence, the equation of variation is [tex] \frac{a = 4b}{c}[/tex]

Substitute the values b = 4 and c = 8 to the equation [tex] \frac{a = 4b}{c}[/tex]

[tex] \tt{a = \frac{4(4)}{8}} [/tex]
[tex] \tt{a = \frac{16}{8}} [/tex]
[tex] \tt\green{a = 2}[/tex]

Hence, a = 2 when b = 4 and c = 8

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