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2 years ago

the value of a varies directly as the square of the value of b, and b=3 when a=10. Find the value of a when b=9.

Mathematics

1 answer:

Charra [1.4K]2 years ago

4 0

Answer:

answer = 90

Step-by-step explanation:

General equation: a = k*b^2

Specifically: 10 = k*(3)^2 = 9 k

Solving for k: k = 10/9

Then a = (10/9)b^2. If b = 9, then a = (10/9)(9)^2 = 90 (answer)

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Hi! I'm happy to help!

To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:

15 $\frac{1}{6}$ ÷ $\frac{1}{6}$

This problem is hard to do with mixed numbers, so we need to turn 15 $\frac{1}{6}$ into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra $\frac{1}{6}$ .

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So, our improper fraction would be $\frac{91}{6}$ , now, let's solve.

$\frac{91}{6}$ ÷ $\frac{1}{6}$

It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.

$\frac{91}{6}$ × $\frac{6}{1}$

Now, we just multiply the top by the top, and bottom by the bottom.

$\frac{546}{6}$

We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.

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Therefore, the recipe should require 91 uses of the 1/6 cup.

I hope this was helpful, keep learning! :D

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