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3 years ago

Solve for x. -1/5(x-4)= -2

Mathematics

1 answer:

alisha [4.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

Steps shown in the image

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Need help with 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12

kobusy [5.1K]

Do oz so oz. Top oz so off.

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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

F(x)=2x – x(2) - 2 Can you also solve it for me

evablogger [386]

Look at the attached picture⤴

Hope this will help u....:)✌

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3 years ago

Which of the following is in the solution set of y< 8 x− 3? Select one: (7, 46) (7, 60) (10, 89) (9, 82)

navik [9.2K]

Answer:

(7, 46)

Step-by-step explanation:

The offered answer choices have x-values of 7, 9, 10. The corresponding upper limit of y-value is ...

x=7 : y < 8·7 -3 = 53 . . . . . 46 is in the solution set, 60 is not

x=9 : y < 8·9 -3 = 69 . . . . 82 is not in the solution set

x=10 : y < 8·10 -3 = 77 . . . . 89 is not in the solution set

Of the choices offered, only (7, 46) is in the solution set.

3 0

3 years ago

henry and his brother each start a savings account. henry begins with $200 and deposits $25 each month. his brother begins with

zlopas [31]

Answer:

Henry after 2 months: 250

His brother after 2 months: 220

Step-by-step explanation:

Henry started with $200 so add $25 twice (for 2 months) and get $250 dollars after 2 months.

His brother started with $150 so add $35 twice and get $220 dollars after 2 months

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3 years ago