Question

In the following exercises, solve. 465. If y varies directly as x when y=9 and x=3, find x when y=21. 466. If y varies inversely as x when y=20 and x=2, find y when x=4. 467. Vanessa is traveling to see her fiancé. The distance, d, varies directly with the speed, v, she drives. If she travels 258 miles driving 60mph, how far would she travel going 70mph ?

Answer 1

If she drives at 70 mph, she would travel approximately 301 miles.

Explanation:

Consider 465. In a direct variation, the relationship between the variables can be represented by the equation y = kx, where k is the constant of variation.

Given that y = 9 when x = 3, we can substitute these values into the equation to find the value of k:

9 = k * 3

Solving for k:

k = 9 / 3

k = 3

Now that we have the value of k, we can find x when y = 21:

21 = 3x

Solving for x:

x = 21 / 3

x = 7

Therefore, when y = 21, x is equal to 7.

Consider 466.In an inverse variation, the relationship between the variables can be represented by the equation y = k/x, where k is the constant of variation.

Given that y = 20 when x = 2, we can substitute these values into the equation to find the value of k:

20 = k / 2

Solving for k:

k = 20 * 2

k = 40

Now that we have the value of k, we can find y when x = 4:

y = 40 / 4

y = 10

Therefore, when x = 4, y is equal to 10.

Consider 467. In this scenario, the distance, d, varies directly with the speed, v. We can represent this relationship using the equation d = kv, where k is the constant of variation.

Given that she travels 258 miles driving 60 mph, we can substitute these values into the equation to find the value of k:

258 = k * 60

Solving for k:

k = 258 / 60

k ≈ 4.3

Now that we have the value of k, we can find the distance she would travel going 70 mph:

d = 4.3 * 70

d ≈ 301

Therefore, if she drives at 70 mph, she would travel approximately 301 miles.