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4 years ago

Find the constant of variation:

Mathematics

1 answer:

ohaa [14]4 years ago

7 0

Answer:

a. 6

b. 24

Step-by-step explanation:

a and b are both inverse constant variation

a. x * y = K

1 x 6 =6

2 x 3 = 6

3 x 2 = 6

4 x 1.5 = 6

k = 6

b. 1 x 24 = 24

3 x 8 = 24

4 x 6 = 24

24 x 1 = 24

K = 24

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This recipe makes 10 portions of porridge.

tankabanditka [31]

Answer:

245g of oats

980ml of milk

49g of sugar

Step-by-step explanation:

350÷10=35

1,400÷10=140

70÷10=7

35×7=245

140×7=980

7×7=49

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3 years ago

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4 years ago

The proof for the product property of logarithms requires simplifying the expression logb(bx y) to x y. Which property is used t

masya89 [10]

You can use the properties of logarithm to derive the simplified form of the given expression.

The simplification of the given expression requires the given below properties of logarithm

$log_a(b^c) = c \times log_a(b)\\\\$
$log_b(b) = 1$

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

$a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = log_a(c)$

Some properties of logarithm are:

$log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1$

<h3>Using the above properties, to get to the simplified form of the given expression</h3>

The given expression is

$log_b(b^{x+y})$

Using the property $log_a(b^c) = c \times log_a(b)\\\\$ , we get

$log_b(b^{x+y}) = (x+y)\times log_b(b)$

Using the property $log_b(b) = 1$ , we get

$log_b(b^{x+y}) = (x+y)\times log_b(b) = (x+y) \times 1 = x + y$

Thus,

The simplification of the given expression requires the given below properties of logarithm

$log_a(b^c) = c \times log_a(b)\\\\$
$log_b(b) = 1$

Learn more about logarithms here:

brainly.com/question/20835449

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Jobisdone [24]

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Step-by-step explanation

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vekshin1

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