Suppose that y varies inversely with x and that y = 2 when x = 8. What is an equation for the inverse variation?
What would the answer be?
What is the factored form of the expression?
s^2 – 81
(s – 9)(s – 9)
(s – 9)(s + 11)
(s – 9)(s + 9)
(s + 9)(s + 9)
I think that it is B. Is that right?
y = k/x
2 = k/8
k = 16
y = 16/x
a^2-b^2 = (a-b)(a+b) always
For the first question, we are given that y varies inversely with x. Inverse variation can be represented by the equation y = k/x, where k is the constant of variation.
To find the specific equation for this inverse variation, we can use the given information that when x = 8, y = 2. Substituting these values into the inverse variation equation, we get:
2 = k/8
To find the value of k, we can rearrange the equation:
2 * 8 = k
k = 16
Therefore, the equation for the inverse variation is y = 16/x.
For the second question, we are given the expression s^2 - 81 and are asked for its factored form. To factor this expression, we need to find two binomials that, when multiplied together, give us s^2 - 81.
Since 81 is a perfect square, we can factor it using the difference of squares formula: a^2 - b^2 = (a + b)(a - b). In this case, a = s and b = 9. Applying the formula, we can rewrite the expression as:
s^2 - 9^2 = (s + 9)(s - 9)
So, the factored form of the expression s^2 - 81 is (s + 9)(s - 9). Therefore, your answer is C, (s - 9)(s + 9).