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2 years ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y=3/4x-9;(-8,-18)

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

8 0

Answer:

<h2>please make me brainlieast and follow me.....</h2>

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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

Can someone please help me with this problem:(

Flauer [41]

Answer:

x y

-2 4

0 0

1 -2

2 4

Step-by-step explanation:

in the equation replace x with the number from the table in the x colum then complete the equation

7 0

2 years ago

Standard form <br> 0.000085

Tasya [4]

Answer -

i think its $8.5*10^{-5}$

6 0

2 years ago

Ln60-ln4 = ln(x^2 + 2x )

Sliva [168]

The answer you're looking for is, x = 3,-5

3 0

2 years ago

Make the indicated trigonometric substitution in the given algebraic expression and simplify(x-25)/x = Sin y0

Strike441 [17]

Answer:

x = 25 /(1 − sin(y )) and y ≠ π/2 +2πn

Step-by-step explanation:

Let's solve and simplify for x,

(x − 25 )/ x = sin(y)

Let's multiply both sides by x

((x − 25 )/x) *x= sin(y)*x

Then,

x − 25 = sin(y) * x

Let's add 25 to both sides

x − 25 + 25 = sin(y) * x + 25

If simplify again,

x = sin(y) * x + 25

Then we need subtract sin y x from both sides

x − sin(y) * x = sin (y)* x + 25 − sin (y)* x

It will equal:

x − sin (y)* x = 25

Factor x−sin(y) x: x(1−sin(y) ), then we get:

x (1 − sin(y)) = 25

Finally we need divide both sides by 1 − sin(y) ; y ≠π /2 + 2πn

And it will give us this equation:

x = 25 /(1 − sin(y )) and y ≠ π/2 +2πn

3 0

3 years ago