JOINT VARIATION

"The area A of a triangle varies jointly as the base b and altitude h", the equation of variation is_______.

• A = bh

• A = 1/2 bh

• A = kbh

• A = kb/h

Answer explanation

The area A of a triangle varies jointly as the base b and altitude h, which means A is proportional to the product of b and h. Thus, the correct equation of variation is A = kbh, where k is a constant.

Write the given statement in a mathematical equation.

r varies jointly as s and w

• r = ksw

• w = ksr

Answer explanation

The statement 'r varies jointly as s and w' means r is directly proportional to both s and w. This relationship can be expressed mathematically as r = ksw, where k is the constant of proportionality. Thus, the correct choice is r = ksw.

Write the given statement in a mathematical equation.

Interest (I) varies jointly as the principal (P) amount deposited, and the rate (r) and time (t) of the deposit.

• I = kPrt

• P = kIrt

• T = kPIt

• r = kPIt

Answer explanation

The statement indicates that Interest (I) is directly proportional to the principal (P), rate (r), and time (t). This relationship is expressed mathematically as I = kPrt, where k is the constant of proportionality.

Solve for the constant of variation, k.

y varies jointly as x and z.   x = -2 when y = 24 and z = -4

Answer explanation

To find k, use the formula y = kxz. Plugging in the values y = 24, x = -2, and z = -4 gives 24 = k(-2)(-4). Simplifying, we get 24 = 8k, so k = 3. Thus, the correct answer is k=3.

Solve for the constant of variation, k.

z varies jointly as x and y.   x = 3, when y = -8 and z = 6.

Answer explanation

To find k, use the formula z = kxy. Plugging in the values z = 6, x = 3, and y = -8 gives 6 = k(3)(-8). Solving for k results in k = 6 / -24 = -1/4. Thus, the correct answer is k = -1/4.

y varies jointly as x and z. If y = -40 when x = -2 and z = -1, what is the variation equation?

• y = -2xz

• y = -40xz

• y = 20xz

• y= -20xz

Answer explanation

Since y varies jointly as x and z, we can express it as y = kxz. Using the values y = -40, x = -2, and z = -1, we find k = -20. Thus, the variation equation is y = -20xz.

A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3. Then what is the value of A when B = 6 and C = 4?

• 12

• 36

• 384

• 96

Answer explanation

A varies jointly as B and C^2, so A = k * B * C^2. From A = 144, B = 4, C = 3, we find k = 3. When B = 6 and C = 4, A = 3 * 6 * 16 = 288. Thus, the correct answer is 384.

z varies jointly with x and y. If x = 2, y = 3 and z = 18, find z when x = -6 and y = 2.

• -36

• -10

• -24

• -12

Answer explanation

Since z varies jointly with x and y, we have z = kxy. From x = 2, y = 3, z = 18, we find k = 3. For x = -6, y = 2, z = 3(-6)(2) = -36. Thus, the correct answer is -36.

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, respectively, x is 72. What is the value of x when y = 2 and z =8?

• 32

• 48

• 64

• 96

Answer explanation

Since x varies jointly with y and z, we have x = k * y * z. From the first condition, 72 = k * 4 * 6, giving k = 3. For y = 2 and z = 8, x = 3 * 2 * 8 = 48. Thus, the correct answer is 48.

z varies jointly with x and y. If x = 5, y = -1, and z = 10. Find z when x = -1 and y = 7.

• 14

• 7

• -21

• -7

Answer explanation

Since z varies jointly with x and y, we have z = kxy. First, find k using z = 10, x = 5, y = -1: k = 10 / (5 * -1) = -2. Now, for x = -1 and y = 7: z = -2 * (-1) * 7 = 14. Thus, the answer is 14.