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2 years ago

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

Mathematics

1 answer:

Katarina [22]2 years ago

4 0

Answer:

a. f = 17.5/c

b. 8.75 N

Step-by-step explanation:

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

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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3 years ago

Tickets that cost $88 for a professional women’s championship soccer game are offered at a 15% discount. What is the sale price?

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3 years ago

There are nickels, dimes, quarters in a large piggy bank, for every 2 nickels there are 3 dimes, for every 2 dimes there are 5 q

Alex

There are 80 nickels and 120 dimes and 300 quarters in piggy bank

<em><u>Solution:</u></em>

Given that,

For every 2 nickels there are 3 dimes ,

So, ratio of nickel to dime will be 2 : 3

Also for every 2 dimes there are 5 quarters

So, ratio of dime to quarters is 2 : 5

Let us first find the ratio of nickles to dimes to quarters

nickel : dime = 2 : 3

dime : quarters = 2 : 5

$\frac{nickel}{dime} = \frac{2}{3}$

$nickel = \frac{2}{3} dime$

$\frac{dime}{quarter} = \frac{2}{5}$

$quarter = \frac{5}{2}dime$

So,

$nickel : dime : quarter = \frac{2}{3}dime : dime : \frac{5}{2}dime\\\\nickel : dime : quarter = \frac{2}{3} : 1 : \frac{5}{2}\\\\nickel : dime : quarter = 4 : 6 : 15$

Thus nickel : dime : quarters = 4 : 6 : 15

Now, let the number of nickel be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

From given question,

There are 500 coins in all.

number of nickel + number of dimes + number of quarters = 500

4x + 6x + 15x = 500

25x = 500

x = 20

Thus,

number of nickel = 4x = 4(20) = 80

number of dimes = 6x = 6(20) = 120

number of quarters = 15x = 15(20) = 300

Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank

3 0

3 years ago