All categories

3 years ago

Write a general formula to describe the variation: x varies jointly with the inverse of r and the inverse of the square of the s

um of y and z

Mathematics

1 answer:

pshichka [43]3 years ago

4 0

$\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{"x" varies with}}{x}~~=~~k\stackrel{\textit{inverse of "r"}}{\cfrac{1}{r}}\cdot \stackrel{\stackrel{\textit{inverse of}~\hfill }{\textit{square of a sum}}}{\cfrac{1}{(y+z)^2}}~\hfill x=\cfrac{k}{r(y+z)^2}$

You might be interested in

jackson is going to the movies. he has to pay $7 for his ticket and $2 for each box of candy he buys. write an expression that r

ruslelena [56]

If Jackson went to the movies and payed $7 initially for his ticket and then payed $2 for each box of candy that he buys, then the equation could look like this: y = 2x + 7, where y represents the total cost and x represents the number of boxes of candy Jackson buys.

6 0

4 years ago

Read 2 more answers

Given r(x) = 11/ (x - 42)

julsineya [31]

For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:

g(f(x)) = x = f(g(x))

<u>The restriction is:</u>

x ≠ 4

<u>The inverse is:</u>

$y = 4 + \sqrt{\frac{11}{x} }$

Here our function is:

$f(x) = \frac{11}{(x - 4)^2}$

We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.

(x - 4)^2 = 0

x - 4 = 0

x = 4

So the only value of x that we need to remove from the domain is x = 4.

To find the inverse we try with the general form:

$g(x) = a + \sqrt{\frac{b}{x} }$

Evaluating this in our function we get:

$g(f(x)) = a + \sqrt{\frac{b}{f(x)} } = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)$

Remember that the thing above must be equal to x, so we get:

$g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0$

From the two above equations we find:

b = 11

a = 4

Thus the inverse equation is:

$y = 4 + \sqrt{\frac{11}{x} }$

If you want to learn more, you can read:

brainly.com/question/10300045

3 0

3 years ago

Simplify 2(3x-1)+5.

wlad13 [49]

Answer:

Step-by-step explanation:

4 0

3 years ago

What is the range of the number of minutes that employees commute to work?

Ipatiy [6.2K]

Answer:

Need more information to this question.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

13. How many drinks are in a 2 oz martini made with 100 proof alcohol

pentagon [3]

Answer:

4 drinks.

Step-by-step explanation:

-One drink is defined as having one-half ounce of pure ethyl alcohol; each of the following is considered "one drink." *1 oz of 100 proof distilled spirits at 50% alcohol.

$Drinks=\frac{2oz}{0.5oz}\\\\=4$

Hence, 2 oz martine has 4 drinks

7 0

3 years ago