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3 years ago

Find the third side in simplest radical form:

Mathematics

1 answer:

ryzh [129]3 years ago

7 0

Answer:

I'm pretty sure that this is the answer 41 square root

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Eliza is a chef at a restaurant. she is making spaghetti sauce and put 14 tomatoes and 4 onions in the pot. what is the ratio of

notka56 [123]

Here,
tomato = 14
onion = 4
then,
ratio of tomato to onion = 14/4
= 7/2

7 0

4 years ago

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

2 years ago

Help me pleaseeeeeeeeeeeeeeee

MrMuchimi

The correct answers are

a) 40%

b) 30%

4 0

3 years ago

Read 2 more answers

Hey scale drawing of Jamy’s living room is 4cm in width and 6cm length. If each 2cm on the scale drawing equals 8 feet what are

igor_vitrenko [27]

2 cm = 8 feet.
4 / 2 = 2. 8 * 2 = 16. 16 feet in width.
Now, the length:
6 / 2 = 3. 8 * 3 = 24. 24 feet in length.
The actual dimensions are 16 feet in width and 24 feet in length.

5 0

3 years ago

“Peaches at the Farmer’s Market cost $2.70 per pound.”

koban [17]

Answer:

non-proportional

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers