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Marat540 [252]
3 years ago
11

Solve for n: c= 6n−5g /11t

Mathematics
1 answer:
qwelly [4]3 years ago
3 0

Answer: \frac{11tc+5g}{66t}=n

Step-by-step explanation:

You have the equation c=6n-\frac{5g}{11t}.

Then, to solve for the variable n from the equation you need:

Make the subtraction of the right side of the equation:

(As the denominators are 1 and 11t, the least common denominator is 11t)

c=\frac{(6n)(11t)-5g}{11t}\\\\c=\frac{66nt-5g}{11t}

Multiply  11t to both sides:

(11t)c=(\frac{66nt-5g}{11t})(11t)\\\\11tc=66nt-5g

Add 5g to both sides:

11tc+5g=66nt-5g+5g\\\\11tc+5g=66nt

And finally divide both sides by 66t:

\frac{11tc+5g}{66t}=\frac{66nt}{66t}\\\\\frac{11tc+5g}{66t}=n

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Hello I would really appreciate if someone could help me with this math question. I’m so confused
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Answer:

  a. f = 17.5/c

  b. 8.75 N

Step-by-step explanation:

<h3>(a)</h3>

Inverse variation means one variable is proportional to the inverse of the other. The equation for that is ...

  f = k(1/c) . . . . . . force (f) is proportional to the inverse of distance (c)

We find the value of k using data given for a specific instance.

  3.5 N = k(1/(5 cm)) . . . . use the given values

  17.5 N·cm = k . . . . . . multiply by the denominator

Then the equation of interest is ...

  f = 17.5/c . . . . . . . where c is in cm, and f is in newtons

__

<h3>(b)</h3>

Using the above equation, we find the force to be ...

  f = 17.5/2 = 8.75 . . . . newtons

_____

<em>Additional comment</em>

We often look at several different kinds of proportionality:

  • y = kx . . . . direct
  • y = k(1/x) . . . . inverse
  • y = kx² . . . . proportional as the square
  • y = kx·z . . . . jointly proportional to x and z

and there are combinations of these, such as ...

  • y = kr²h . . . . jointly proportional to h and the square of r

You may have noticed that when x and y are inversely proportional, their product is a constant. y = k/x  ⇒  xy = k

__

We have left off the units of k in the problem above. Sometimes it is a good idea to retain them, or to pay close attention to what they are. This can avoid using the wrong measures for the variables.

  f = (17.5 N·cm)/(2 cm) = 8.75 N . . . . . units of cm cancel

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