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3 years ago

It is given that yvaries directly as x. If y= 5 when x= 4 determine the constant of variation,

Mathematics

1 answer:

aivan3 [116]3 years ago

3 0

Answer:

$k=\dfrac{5}{4}$

Step-by-step explanation:

Given that,

y varies directly as x. It means,

y = kx

Where

k is the constant of variation

$k=\dfrac{y}{x}\\\\k=\dfrac{5}{4}$

So, the constant of variation is $\dfrac{5}{4}$ .

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3 years ago

All points from which of the following patterns would be contained on the given graph?

NeX [460]

Answer:

Step-by-step explanation:

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4 years ago

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4 years ago

Read 2 more answers

Which of the following describes the end behavior of f(x) = 2x 3x2 − 3 ? The graph approaches 0 as x approaches infinity. The gr

Arada [10]

1) An operator is missing in your statement. Most likely the right expression is:

 2x
f(x) = -------------
 3x^2 - 3

So, I will work with it and find the result of each one of the statements given to determine their validiy.

2) Statement 1: The graph approaches 0 as x approaches infinity.

Find the limit of the function as x approaches infinity:

 2x
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 3x^2 - 3

Start by dividing numerator and denominator by x^2 =>

 2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2

 2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
 3 - 3/∞ 3 - 0 3

Therefore the statement is TRUE.

3) Statement 2: The graph approaches 0 as x approaches negative infinity.

Find the limit of the function as x approaches negative infinity:

 2x
Limit when x → - ∞ of ------------
 3x^2 - 3

Start by dividing numerator and denominator by x^2 =>

 2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2

 2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
 3 - 3/(-∞) 3 - 0 3

Therefore, the statement is TRUE.

4) Statement 3: The graph approaches 2/3 as x approaches infinity.

FALSE, as we already found that the graph approaches 0 when x approaches infinity.

5) Statement 4: The graph approaches –1 as x approaches negative infinity. 

FALSE, as we already found the graph approaches 0 when x approaches negative infinity.

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4 years ago

Read 2 more answers

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trapecia [35]

Answer:

option A

Step-by-step explanation:

given,

sample of tritium, ³H

$t_{1/2} = 12.32 years$