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3 years ago

How many 7 digit numbers have6 9 s and no 9 in ones place

Mathematics

1 answer:

Daniel [21]3 years ago

5 0

Answer:

1062882

Step-by-step explanation:

Seven digits numbers, with repetition of digits, having 6 or 9 at the last one's place :

The first six digits can be filled with 9 options each (numbers 1 to 9) , & the last digit can be filled with 2 options (number 6 & 9)

So, total 7 digit numbers as per given condition = 9 x 9 x 9 x 9 x 9 x 9 x 9 x 2 = 1062882

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−10 = −0.4k<br><br> this is probably easy but can someone find k

azamat

Answer: k = 25

hope this helped :)

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2 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

1 year ago

The model represents the equation x - 1 < -4. What is the solution for the inequality?

Step2247 [10]

Answer:

any number equal to or less than -4

Step-by-step explanation:

x - 1 < -4

< represents that -4 is a larger number than x - 1. we know that -4 is a negative number, so anything below -4 would be less. x = -4 would be a good solution, but the reality is that any number equal to or less than -4 is the correct answer. I hope this helps!

7 0

2 years ago

I don’t know how to divide 3 and 2 digits

Varvara68 [4.7K]

3.5 think of it as 3.0
C. ——
2.0

8 0

3 years ago

Plz help I will make you brainliest!Thanks

STatiana [176]

Use the formula V=AbH and 48=16h will be the second step and then divide by 16 and then you get the answer

7 0

3 years ago

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