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3 years ago

Who was the proprietor of the colony of Pennsylvania?

Mathematics

2 answers:

jeyben [28]3 years ago

6 0

the answer is B william penn

Alex787 [66]3 years ago

4 0

Answer:A William Penn

Step-by-step explanation:

Given to him in 1681 for a debt

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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

Help me plass plaas me

dezoksy [38]

Answer:

it isn't really visible . do it right

Step-by-step explanation:

please mark me brainiest like my answer and follow me on this

3 0

2 years ago

Read 2 more answers

5lb 7oz -11oz need help quick

Aliun [14]

Answer:

76 ounces

Step-by-step explanation:

I'm assuming you meant:

5lb+7oz-11oz=

16 ounces in a pound

5lb+7oz-11oz=

80+7-11=

87-11=

76 ounces

3 0

2 years ago

A driver travels for 2 hours at 80 miles per hour, during

algol [13]

Answer:

$84

Step-by-step explanation:

Find how many miles she traveled by multiplying 80 and 2.

80 × 2 = 160 miles

Next find out how much she gets paid for her mileage by multiply $0.60 and 160.

160 × $0.60 = $96.00

Now find out how much she spent on gas. She gets 40 miles per gallon so solve how many gallons she used by dividing 160 by 40.

160 ÷ 40 = 4 gallons

Then multiply 4 gallons by $3.00

4 × 3 = $12

To find the net rate of pay subtract 96 and 12

$96 - $12 = $84

8 0

2 years ago

Read 2 more answers

A recipe for a loaf of bread calls for 2/3 of a cup of flour. If Milo used 12 cups of flour, how many loafs of bread did he prep

Aloiza [94]

The answer is:

1/2 cups of flour can make 1 loaf.

1 cup would make = 1 /(1/2) = 2 loaves.

12 cups of flour would then make = 12*2 = 24

= 24 loaves.

[Please Mark as Brainliest]

7 0

2 years ago

Read 2 more answers