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Butoxors [25]
3 years ago
11

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

Mathematics
1 answer:
alisha [4.7K]3 years ago
3 0

Answer:

14

Step-by-step explanation:

Steps shown in the image

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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
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3 years ago
Which of the following is in the solution set of y&lt; 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.

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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

4 0
3 years ago
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