All categories

2 years ago

If y varies inversely as x and y = 8 when x = 9, find x when y = 12.

Mathematics

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

x = 6

Step-by-step explanation:

An inverse variation is

xy = k where k is the constant of variation

8*9 = k

72 = k

xy = k

Let y = 12

x*12 = 72

Divide each side by 12

12x/12 =72/12

x = 6

You might be interested in

Can you define f(0, 0) = c for some c that extends f(x, y) to be continuous at (0, 0)? If so, for what value of c? If not, expla

Ahat [919]

(i) Yes. Simplify $f(x,y)$ .

$\displaystyle \frac{x^2 - x^2y^2 + y^2}{x^2 + y^2} = 1 - \frac{x^2y^2}{x^2 + y^2}$

Now compute the limit by converting to polar coordinates.

$\displaystyle \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = \lim_{r\to0} \frac{r^4 \cos^2(\theta) \sin^2(\theta)}{r^2} = 0$

This tells us

$\displaystyle \lim_{(x,y)\to(0,0)} f(x,y) = 1$

so we can define $f(0,0)=1$ to make the function continuous at the origin.

Alternatively, we have

$\dfrac{x^2y^2}{x^2+y^2} \le \dfrac{x^4 + 2x^2y^2 + y^4}{x^2 + y^2} = \dfrac{(x^2+y^2)^2}{x^2+y^2} = x^2 + y^2$

and

$\dfrac{x^2y^2}{x^2+y^2} \ge 0 \ge -x^2 - y^2$

Now,

$\displaystyle \lim_{(x,y)\to(0,0)} -(x^2+y^2) = 0$

$\displaystyle \lim_{(x,y)\to(0,0)} (x^2+y^2) = 0$

so by the squeeze theorem,

$\displaystyle 0 \le \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} \le 0 \implies \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = 0$

and $f(x,y)$ approaches 1 as we approach the origin.

(ii) No. Expand the fraction.

$\displaystyle \frac{x^2 + y^3}{xy} = \frac xy + \frac{y^2}x$

$f(0,y)$ and $f(x,0)$ are undefined, so there is no way to make $f(x,y)$ continuous at (0, 0).

(iii) No. Similarly,

$\dfrac{x^2 + y}y = \dfrac{x^2}y + 1$

is undefined when $y=0$ .

5 0

1 year ago

NEED HELP WILL GUVE 5 stars

Bumek [7]

Answer:

m=15

Step-by-step explanation:

m/9 + 2/3

x 3 7/3 x 3 = 21/9

m/9 + 6/9 = 21/9

21-6=15

15/9 + 6/9 = 21/9 = 7/3

6 0

2 years ago

Which table represents a linear function?

solniwko [45]

Answer:

Step-by-step explanation:

1 -3

2 -5

3 -7

4 -9

Because it has a constant slope it is increasing x by 1 and decreasing y by -2.

Slope: -2/1 or -2x

3 0

2 years ago

Read 2 more answers

What is the slope of the line that passes through (3, 3) and (-2, -3).

Diano4ka-milaya [45]

Answer:

slope=6/5

Step-by-step explanation:

The formula for finding the slope is y1-y2/x1-x2=slope. So if we substitute in the numbers from you question, it would be (-3-3)/(-2-3)=slope

(-3-3)/(-2-3)=slope

-6/-5=slope

6/5=slope

5 0

2 years ago

Read 2 more answers

Data collected in a survey shows that 60 percent of the buyers are interested in buying a brand of mobile phone and if the total

melisa1 [442]

Answer:

160 not interested and 144*

Step-by-step explanation:

* is the degree sign like the little o

6 0

2 years ago