Assume that all variables represent positive numbers. Assume that varies directly with . If when , find when .

Question

Assume that all variables represent positive numbers. Assume that  varies directly with  . If  when  , find  when  .

Quizplus · Accepted Answer

If 11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 when 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11, then we can write:

11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 = k * 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11

where k is a constant of proportionality.

Also, we know that 11ec1e8e_2c09_29a6_be9b_dfe174236238_TBX8967_11 varies directly with 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11. So we can write:

11ec1e8e_2c09_29a6_be9b_dfe174236238_TBX8967_11 = m * 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11

where m is a constant of proportionality.

We need to find 11ec1e8e_2c09_29aa_be9b_7950c7064e55_TBX8967_11 when 11ec1e8e_2c09_50bb_be9b_c1303cde95c0_TBX8967_11. If we substitute the given values in the above equations, we get:

11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 = k * 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11

11ec1e8e_2c09_50bb_be9b_c1303cde95c0_TBX8967_11 = m * 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11

We can solve for k and m:

k = 11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 / 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11

m = 11ec1e8e_2c09_50bb_be9b_c1303cde95c0_TBX8967_11 / 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11

Now we can substitute these values to find 11ec1e8e_2c09_29aa_be9b_7950c7064e55_TBX8967_11:

11ec1e8e_2c09_29aa_be9b_7950c7064e55_TBX8967_11 = k * m * 11ec1e8e_2c09_29a6_be9b_dfe174236238_TBX8967_11

= (11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 / 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11) * (11ec1e8e_2c09_50bb_be9b_c1303cde95c0_TBX8967_11 / 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11) * 11ec1e8e_2c09_29a6_be9b_dfe174236238_TBX8967_11

Simplifying this expression gives:

11ec1e8e_2c09_29aa_be9b_7950c7064e55_TBX8967_11 = (11ec1e8e_2c09_29a8_be9b_d1273849166a_TBX8967_11 * 11ec1e8e_2c09_50bb_be9b_c1303cde95c0_TBX8967_11 / 11ec1e8e_2c09_29a9_be9b_e1306c6f56e5_TBX8967_11) * (11ec1e8e_2c09_29a6_be9b_dfe174236238_TBX8967_11 / 11ec1e8e_2c09_29a7_be9b_514302ce0e3f_TBX8967_11)

Therefore, the correct answer is D) 11ec1e8e_2c09_50bf_be9b_0f76536c5018_TBX8967_11.

Assume That All Variables Represent Positive Numbers