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2 years ago

The chart below shows the number of students in each grade who are members of the spirit club at Lone Star Middle School.

Mathematics

2 answers:

irina1246 [14]2 years ago

8 0

Answer:

The Answer Is 6

Step-by-step explanation:

frez [133]2 years ago

6 0

Answer:ADD ME ON PS5

crzyjay--

Step-by-step explanation:

Im just cool like that!°

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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

PLEASE HELP ME!!!!!!!

REY [17]

Answer: The right answer is 85.0

Step-by-step explanation: I just did it

Will you mark me brainlyest?

6 0

3 years ago

Michael and Imani go out to eat for lunch. If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the

blondinia [14]

Answer:

The bill total is $27.32

Step-by-step explanation:

how to figure out tax amount: 25.30 x .08 = $2.024

add tax to cost of meal : 25.30 + 2.024 = $27.32

5 0

3 years ago

Expand this question. <br><br> 3(x+2)

irakobra [83]

Answer:

3(x+2)

3x+6

Step-by-step explanation:

We should multiply it by 3

3 0

2 years ago

Read 2 more answers

A cricket team has a 0.25 chance of losing

Westkost [7]

Answer:

a) 0.125

b) 0.015635

c) 0.00000095367431640625‬

Step-by-step explanation:

a) $0.25^2 = 0.125$

b) $0.25^3 = 0.015625$

c) $0.25^{10} = 0.00000095367431640625\\\\$

8 0

3 years ago

Read 2 more answers