For the inverse variation equation [tex]xy=k[/tex], what is the value of [tex]x[/tex] when [tex]y=4[/tex] and [tex]k=7[/tex]?
A. [tex]\frac{4}{7}[/tex]
B. [tex]\frac{7}{4}[/tex]
C. 3
D. 28
Answer (2)
The value of x when y = 4 and k = 7 in the equation x y = k is 4 7 . The correct option is B. This is determined by substituting the values into the equation and solving for x .
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Substitute the given values y = 4 and k = 7 into the inverse variation equation x y = k .
Obtain the equation 4 x = 7 .
Solve for x by dividing both sides by 4.
The value of x is 4 7 .
Explanation
Understanding the Problem We are given an inverse variation equation x y = k , where x and y are variables and k is a constant. We are given that y = 4 and k = 7 . Our goal is to find the value of x .
Substituting the Values To find the value of x , we substitute the given values of y and k into the equation x y = k . This gives us x ( 4 ) = 7 .
Solving for x Now, we solve for x by dividing both sides of the equation by 4: x = 4 7 .
Final Answer Therefore, the value of x is 4 7 .
Examples
Inverse variation is a relationship where one variable decreases as the other increases. For example, the time it takes to travel a certain distance varies inversely with the speed you are traveling. If you double your speed, the time it takes to travel the same distance is halved. This concept is useful in many real-world scenarios, such as calculating travel times, understanding the relationship between pressure and volume of a gas, and analyzing the relationship between supply and demand in economics.
