All categories

3 years ago

For what interval is the function f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x}) continuous?

Mathematics

1 answer:

konstantin123 [22]3 years ago

5 0

Try this solution:
1. according to the condition
$\left \{ {{x \geq 0} \atop {20+x\ \textgreater \ 0}} \right. \ =\ \textgreater \ \ x \geq 0.$
2. for more details see the attached graph.

Answer: [0;+oo)

You might be interested in

Pair of shoes cost three times as much as a scarf. The total cost of one pair shoes and one scarf is $32. If S represents the co

Mariulka [41]

Let's break down all the information we receive from the question.

One pair of shoes= three times as much as a scarf
One pair of shoes and one scarf= $32

We need to make an equation where 3s= pair of shoes and s=scarf. We then need to put one pair of shoes + one scarf = 32.
3s+s=32
Now add.
4s=32
You could use 4s=32 (or 32÷4=s).

6 0

4 years ago

Item 7

Katyanochek1 [597]

i am sorry i was gonna anwer but i keep getting it wrong mys elf

4 0

3 years ago

1. (a). A police car, approaching right-angled intersection from the north, is chasing a speedmg

tamaranim1 [39]

Answer:

<em>The SUV is running at 70 km/h</em>

Step-by-step explanation:

<u>Speed As Rate Of Change </u>

The speed can be understood as the rate of change of the distance in time. When the distance increases with time, the speed is positive and vice-versa. The instantaneous rate of change of the distance allows us to find the speed as a function of time.

This is the situation. A police car is 0.6 Km above the intersection and is approaching it at 60 km/h. Since the distance is decreasing, this speed is negative. On the other side, the SUV is 0.8 km east of intersection running from the police. The distance is increasing, so the speed should be positive. The distance traveled by the police car (y) and the distance traveled by the SUV (x) form a right triangle whose hypotenuse is the distance between them (d). We have:

$d=\sqrt{x^2+y^2}$

To find the instant speeds, we need to compute the derivative of d respect to the time (t). Since d,x, and y depend on time, we apply the chain rule as follows:

$\displaystyle d\ '=\frac{x.x'+y.y'}{\sqrt{x^2+y^2}}$

Where x' is the speed of the SUV and y' is the speed of the police car (y'=-60 km/h)

We'll compute :

$d=\sqrt{(0.8)^2+(0.6)^2}=\sqrt{0.64+0.36}$

$d=1\ km$

We know d'=20 km/h, so we can solve for x' and find the speed of the SUV

$\displaystyle \frac{x.x'+y.y'}{\sqrt{x^2+y^2}}=20$

Thus we have

$x.x'+y.y'=20$

Solving for x'

$\displaystyle x'=\frac{20-y.y'}{x}$

Since y'=-60

$\displaystyle x'=\frac{20+0.6(60)}{0.8}$

$x'=70\ km/h$

The SUV is running at 70 km/h

7 0

3 years ago

Y= 9x -9 y= 9 substitution method

Aneli [31]

You would plug in the y=9 into the first equation and then have the expression 9=9x-9
. After going through the first steps of solving an expression you would get 18=9x. X=2. Then you would plug in the x value into the first expression to get y=9.

3 0

3 years ago

Evaluate the following expression (-3)^2

Cloud [144]

Answer:

Step-by-step explanation:

negative times a negative is a positive. Negative three squared is 9.

8 0

3 years ago