2.03 Direct variation
If \left(4, 512\right) is on the curve, P = k Q^{4}, solve for k.
A variable M is directly proportional to the square of N.
Using k as the constant of proportionality, form an equation for M in terms of N.
Given that \left(4, 64\right) satisfies the equation, solve for k.
Consider the relationship where y is directly proportional to the cube of x.
Using k as a constant of proportionality, state the equation relating x and y.
The following table of values shows the relationship between x and y:
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 3 | 24 | 81 | 192 | 375 |
Solve for k, the constant of proportionality.
y is a power function which is directly proportional to x^{n}.
Using k as the proportionality constant, form an equation for y in terms of x.
The table below shows values that satisfy the relationship y = k x^{n}, for the case when n = 2.
| x | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| y | 32 | 128 | 288 | 512 | 800 |
Solve for the constant of proportionality k. Round your answer to the nearest integer.
y is a power function which is directly proportional to x^{n}.
Using k as the proportionality constant, form an equation for y in terms of x.
The table below shows values that satisfy the relationship y = k x^{n}, for the case when n = 3.
| x | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| y | -48 | -384 | -1296 | -3072 | -6000 |
Solve for the constant of proportionality k. Round your answer to the nearest integer.
For the quadratic function pictured here, determine the constant of proportionality k:
For the quadratic shown, determine the constant of proportionality k:
The following graph shows the intersection of the two functions y = m x^{\frac{4}{3}} and y = k x^{\frac{1}{3}}:
Find the value of m.
Find the value of k.
In exchange rate calculations the constant of proportionality is the exchange rate itself. Determine the exchange rate, k, if someone can purchase:
889.00 AUD with 700.00 USD.
553.00 USD with 700.00 AUD.
The heart mass H of a mammal is proportional to its body mass M.
Using k as the constant of proportionality, form an equation relating H and M.
Given that a human with a body mass of 77kg has a heart mass of 0.462kg, determine k, the constant of proportionality.
If a Chimpanzee has a body mass of 57kg, what is the heart mass H?
If a Macaque has a heart mass of 0.084kg, solve for its body mass M.
The blood circulation time C of a mammal is proportional to the fourth root of its body mass B.
Using k as the constant of proportionality, form an equation relating C and B.
Given that an elephant with a body mass of 5290\text{ kg} has a blood circulation time of 148 seconds, determine k, the constant of proportionality. Round your answer to one decimal place.
If a Orangutang has a body mass of 40\text{ kg}, find C, its circulation time. Round your answer to one decimal place.
If a Squirrel has a circulation time of 22 seconds, what is the body mass? Round your answer to one decimal place.