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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)

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One way to convert from inches to centimeters is to multiply the number of inches by 2.54. How many centimeters are there in 1/4

NikAS [45]

Answer:

0.635

Step-by-step explanation:

1/4 x 2.54 = 0.635

3 0

3 years ago

Read 2 more answers

2. A function g(x) is defined by the diagram shown below.

skad [1K]

Answer:

Step-by-step explanation:

diagram attached represents a function g(x).

Circle (1) (circle on the left) represents the set of domain (input values) and circle (2) represents the range (output values).

a). For input value x = 7, out put value of the function is y = 9.

Therefore, g(7) = 9 will be the answer.

b). Range of the function g(x) is the set of output values.

Range: {12, 9, 9, 17}

c). Inverse of the function g(x) will have,

Domain: {12, 9, 9, 17}

Range: {4, 7, 10, 15}

For input value of x = 9, there are two output values y = 7, 10.

Since, "a function can't have two output values for the same input value".

Therefore, inverse of the function g(x) will not represent a function.

8 0

3 years ago

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 f

krok68 [10]

✰ Concept Used :-

⠀

In this question, we can clearly observer that the diagram shows a right angled triangle. And, we have been provided with the value of base, and the value of hypotenuse, using the pythagoras theorem, now we can easily find out the value of the perpendicular i.e. the value of the side h. According to the pythagoras theorem, square of hypotenuse is equal to the sum of square of perpendicular and square of side respectively. Therefore, square of side is equal to the difference of square of hypotenuse and square of perpendicular.

⠀

✰ Given Information :-

⠀

Hypotenuse = 22 ft.
Base = 10 ft.

⠀

✰ To Find :-

⠀

The value of side or the perpendicular

⠀

✰ Formula Used :-

⠀

$\star \: \underline{ \boxed{ \purple { \sf {Side}^{2} = {Hypotenuse}^{2} - {Base}^{2} }}} \: \star$

⠀

✰ Solution :-

⠀

$\sf \longrightarrow {Side}^{2} = {(22 \: ft)}^{2} - {(10 \: ft)}^{2} \: \: \: \\ \\ \\ \sf \longrightarrow {Side}^{2} = {484 \: ft}^{2} - {100 \: ft}^{2} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow {Side}^{2} = {384 \: ft}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow {Side}^{} = \sqrt{ {384 \: ft}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow {Side}^{} = \underline{ \boxed{ \frak{ \green{19.60 \: ft}}}} \: \star \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\$

Thus, option B. 19.60 ft. is the correct option.

⠀

$\underline{\rule{230pt}{2pt}} \\ \\$

4 0

2 years ago

Which table shows a proportional relationship between a and b? a b 3 9 4 12 5 20 a b 20 25 24 30 32 40 a b 4 12 5 15 6 24 a b 3

umka21 [38]

When the second number is divided by the first, the result is ...

First table
9/3 = 3
12/4 = 3
20/5 = 4 . . . . result is not consistent. NOT a proportional relationship

Second table
25/20 = 1.25
30/24 = 1.25
40/32 = 1.25 . . . . result is consistent. A PROPORTIONAL RELATIONSHIP

Third table
12/4 = 3
15/5 = 3
24/6 = 4 . . . . result is not consistent. NOT a proportional relationship

Fourth table
4/3 ≈ 1.33
9/6 = 1.5
16/12 ≈ 1.33 . . . . result is not consistent. NOT a proportional relationship

8 0

3 years ago

Aaaaaaaaa help me pls.

natita [175]

Answer:B because it shows the base

8 0

3 years ago

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