Direct And Inverse Proportion! Math Trivia Questions Quiz

Explanation
The given information states that "a varies inversely as the square of x." This means that as x decreases, a will increase. We are given that when x = 18, a = 5. Therefore, when x decreases to 6, a will increase. Since we know that a = 5 when x = 18, we can conclude that when x = 6, a will still be 5. Therefore, the answer is 5.

Explanation
The equation for the inverse proportion is g * y = k, where k is a constant. To complete the equation, we can substitute the given values g = 6 and y = 4 into the equation: 6 * 4 = k, which gives us k = 24. Therefore, the complete equation is g * y = 24. To find the value of y when g = 8, we can rearrange the equation to solve for y: y = k / g. Substituting the values k = 24 and g = 8 into the equation, we get y = 24 / 8 = 3. Hence, when g = 8, y = 3.

Explanation
When completing the equation t = [Blank], the missing value is 9. When t = 72, the corresponding value of q is 8.

Explanation
Since w is directly proportional to n, we can use the concept of direct variation to find the value of w when n is 6. We can set up a proportion using the given information: 200/10 = w/6. Cross-multiplying, we get 10w = 1200, and dividing both sides by 10, we find that w = 120. Therefore, when n is 6, w is equal to 120.

Explanation
Since n is inversely proportional to f, it means that as f decreases, n increases. We can use the formula for inverse proportionality, n = k/f, where k is a constant. We can solve for k by substituting the given values of n and f into the equation: 21 = k/12. Solving for k, we get k = 252. Now we can use the value of k to find n when f = 9: n = 252/9 = 28. Therefore, when f = 9, n = 28.

Explanation
In this question, we are given that j varies inversely as h. This means that as j increases, h decreases, and vice versa. We are also given that when h = 2, j = 6. To find the value of h when j = 1.5, we can set up an inverse variation equation: j1 * h1 = j2 * h2, where j1 = 6, h1 = 2, j2 = 1.5, and h2 is what we need to find. Plugging in the values, we get 6 * 2 = 1.5 * h2. Solving for h2, we find that h2 = 8. Therefore, when j = 1.5, h = 8.

Explanation
The value of b is directly proportional to the value of w. When w is 4, b is 16. So, we can find the value of b when w is 8 by using the formula for direct proportionality. We can set up a proportion: 4/w = 16/8. Solving for w, we find that w = 2.

Explanation
The given question states that e is proportional to the square of g. This means that as g increases or decreases, e will increase or decrease by the square of that change. The equation e = 405 when g = 9 tells us that when g is 9, e is 405. Therefore, we can find e when g is 5 by using the proportionality relationship. Since 5 is 4 units less than 9, we square that change (4^2) and apply it to e. 405 - (4^2) = 405 - 16 = 389. Therefore, when g is 5, e is 389.

Explanation
The equation for the inverse variation relationship between p and u can be written as p = k/u^2, where k is a constant. To find the value of k, we can substitute the given values of p and u into the equation. When p = 8 and u = 14, we get 8 = k/14^2. Solving for k, we find k = 1568. To find the value of p when u = 2, we can use the equation p = 1568/2^2, which simplifies to p = 392.

Explanation
In this question, we are given that c is inversely proportional to v. This means that as v increases, c decreases, and vice versa. We are also given that when v = 18, c = 5. To find the value of c when v = 4, we can set up a proportion using the inverse relationship. Since c and v are inversely proportional, we can write the proportion as c1v1 = c2v2, where c1 = 5, v1 = 18, c2 is the value we need to find, and v2 = 4. Solving for c2, we get c2 = (c1v1) / v2 = (5 * 18) / 4 = 22.5. Therefore, when v = 4, c = 22.5.

Explanation
The given statement "a is proportional to the cube of j" means that the value of a is directly related to the cube of j. In other words, if j is multiplied by a certain factor, then a will be multiplied by the cube of that factor.

In the first equation, we are given that when j = 8, a = 4096. Since a is proportional to the cube of j, we can write the equation as a = k * j^3, where k is the constant of proportionality. Plugging in the values, we get 4096 = k * 8^3. Solving for k, we find that k = 8. Therefore, the first equation can be completed as a = 8 * j^3.

In the second equation, we are asked to find the value of a when j = 1. Using the completed equation from the first part, we can substitute j = 1 and find that a = 8 * 1^3 = 8.

Explanation
The equation for the direct variation between h and a is h = ka^2, where k is the constant of variation. Since h = 64 when a = 2, we can substitute these values into the equation to find the value of k. 64 = k(2^2) => 64 = 4k => k = 16. Therefore, the equation is h = 16a^2. To find h when a = 5, we substitute this value into the equation: h = 16(5^2) = 16(25) = 400.

Explanation
When r = 6, y = 1. Therefore, the relationship between r and y can be represented by the equation y = 1/3r. When r = 2, substituting the value into the equation gives y = 1/3(2) = 2/3 = 0.67. However, the given answer is 9, which does not match the equation or the given information. Therefore, the correct answer is not 9.

Explanation
In an inverse variation, the product of the two variables remains constant. To complete the equation, we can write it as f * r = k, where k is the constant. Given that f = 4 when r = 15, we can substitute these values into the equation to find k: 4 * 15 = k, which gives us k = 60. Therefore, the equation is f * r = 60. To find the value of r when f = 60, we can rearrange the equation to solve for r: r = k / f = 60 / 60 = 1. Therefore, when f = 60, r = 1.

Explanation
The relationship between u and c is given as u is proportional to c cubed. This means that u is equal to some constant multiplied by c cubed. We are given that u is equal to 640 when c is equal to 4. By substituting these values into the equation, we can solve for the constant. Once we have the constant, we can use it to find the value of c when u is equal to 3430. The value of c is 7.

Explanation
The given statement "p varies directly as t^2" indicates that p and t^2 are directly proportional. This means that as t^2 increases, p also increases, and vice versa. Using the given information, we can set up a proportion to find the value of t when p = 63. Using the formula for direct variation, we have (p1/t1^2) = (p2/t2^2), where p1 = 700, t1 = 10, and p2 = 63. Solving for t2, we get t2^2 = (10^2 * 63)/700. Simplifying this equation gives us t2^2 = 9, which means t2 can be either 3 or -3.

Explanation
When v = 36 and s = 16, we can use the equation v = s^2 to find the relationship between v and s. Plugging in the given values, we get 36 = 16^2. Simplifying this equation, we find that 36 = 256. Therefore, when v = 9, s must be equal to 256 for the equation v = s^2 to hold true.

Explanation
We can solve this problem by using the concept of direct proportionality. The equation m = kb^3 represents a direct proportionality between m and b^3, where k is a constant. We are given that m = 24 when b = 2, so we can substitute these values into the equation to find the value of k. 24 = k(2^3) = 8k. Solving for k, we find that k = 3. Now, we can use this value of k to find the value of b when m = 2187. 2187 = 3(b^3). Dividing both sides by 3, we get b^3 = 729. Taking the cube root of both sides, we find that b = 9. Therefore, the answer is 27.

Explanation
When m = 6144 and z = 8, we can see that there is a linear relationship between m and z. To find the value of z when m = 12000, we can set up a proportion using the given values: 6144/8 = 12000/z. Cross-multiplying and solving for z, we get z = 10. Therefore, when m = 12000, z = 10.