All categories

3 years ago

Angel jogged around the park in 1 1/4 hr chris jogged same distance in 5/6 hrs how much longer did angel take then chris in hr??

1 answer:

6 0

You will have to get the difference and get a common denominator but first combine the mixed number:
$1 \: \frac{1}{4} - \frac{5}{6} = \frac{5}{4} - \frac{5}{6} = \frac{15}{12} - \frac{10}{12}$
Then subtract the numbers
$\frac{15}{12} - \frac{10}{12} = \frac{5}{12}$
Angel took 5/12 hours longer than Chris

You might be interested in

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

Four expressions are shown below:

Alina [70]

The answer is A and C, because 4(7x + 2 + x) simplifies to 32x + 8, and expressions A and C also simplify to 32x + 8. I hope this helps!

8 0

3 years ago

What is the sum of5 + 4 +

Nadusha1986 [10]

Answer:

Step-by-step explanation:

5+4=9

6 0

3 years ago

Read 2 more answers

Simplify: (3x2 - 4x + 6) + (7x - 2)

V125BC [204]

Answer:

11x-2

Step-by-step explanation:

(3x2 - 4x + 6) + (7x - 2) This is the breakdown. (6 4x + 6)= 4x. + (7x-2) = 11x-2

8 0

3 years ago

GIVING 100 POINTS!!!!

IrinaK [193]

Answer:

As per dot plots we see the distribution of prices is close but majority of prices are concentrated in different zones. So MAD would be more similar by the look.

<u>Let's verify</u>

<h3>Neighborhood 1</h3>

55, 55, 60, 60, 70, 80, 80, 80, 90, 120

(55*2+ 60*2+ 70+ 80*3 + 90+ 120)/10 = 75

(20*2+15*2+5+5*3+15+45)/10 = 15

<h3>Neighborhood 2</h3>

100, 110, 110, 110, 120, 120, 120, 140, 150, 160

(100 + 110*3+ 120*3+ 140 + 150+ 160)/10 = 124

(24+14*3+4*3+16*3+16+26+36)/10 = 20.4

As we see the means are too different (75 vs 124) than MADs (15 vs 20.4).

7 0

3 years ago

Read 2 more answers