If x varies inversely as y 2, and x = 2 when y = 20, find x when y = 5.

Mathematics

1 answer:

Dominik [7]3 years ago

6 0

Step-by-step explanation:

$x = \frac{k}{y}$

x varies inversely as y. This means that x is equal to the inverse of y which can be translated as x = 1/y but the problem said that x is not exactly equal to the inverse of y. Therefore, we need to introduce a factor k. Factor k will represent the word "varies" in the problem.

To illustrate:

$x = \frac{k}{y}$

Since we don't have the value of k, we have to solve for it by using the first values of x and y which was given as x=2 and y=20.

$x = \frac{k}{y} \\ 2 = \frac{k}{20} \\ k = 2(20) = 40$

Now that we have the value of k, we can now solve for the value of x when y=5.

$x = \frac{k}{y} \\ = \frac{40}{5} \\ = 8$

Therefore, when y is 5, the value of x is 8.

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A welder requires 18 hours to do a job. After the welder and an apprentice work on a job for 6 hours, the welder moves to anothe

Dafna1 [17]

Answer:

the apprentice can complete the job in 30 hours by working alone.

Step-by-step explanation:

Given:

Number of hours required to complete a job by welder = 18 hours

Number of hours welder work on job = 6 hours.

Number of hours required by apprentice to complete the job = 14 hours

We need to find Number of hours required to complete a job by apprentice alone.

Solution:

Let Number of hours required to complete a job by apprentice alone be 'a'.

Also let the job completed be = 1

Now we know that ;

Time required on job is equal to sum of Number of hours welder work on job and Number of hours required by apprentice to complete the job.

framing in equation form we get

Time required on job = $6+14 =20\ hrs$

Now we can say that;

each has done a fraction of the work so we will add to two fraction as number of hours of work done by Total number of hours required to do the work to complete 1 job.

so we can frame the equation as;

$\frac{6}{18}+\frac{20}{a}=1$