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Debora [2.8K]
2 years ago
12

Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?

Mathematics
2 answers:
Neporo4naja [7]2 years ago
8 0

The interval which the function is positive is (3, ∝)

<h3>How to determine the positive interval?</h3>

The equation of the function is given as:

g(x) =∛x - 3

Set the radical greater than 0

x - 3 > 0

Add 3 to both sides of the inequality

x > 3

Express as an interval notation

(3, ∝)

Hence, the interval which the function is positive is (3, ∝)

Read more about function interval at:

brainly.com/question/1600302

#SPJ1

zmey [24]2 years ago
5 0

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

<h3>on what interval is the function positive?</h3>

The function is positive when g(x) > 0.

Then we need to solve:

∛(x - 3) > 0

We can directly remove the cubic root, because it does not affect the sign of the argument, then:

x - 3 > 0

x > 3

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

If you want to learn more about functions:

brainly.com/question/2456547

#SPJ1

You might be interested in
Hans wants to earn more than $51 trimming trees. He charges $7 per hour and pays $5 in equipment fees. What are the possible num
Flura [38]

Answer:

h ≤ 8

Step-by-step explanation:

Hans charges $7 per hour and pays $5 in equipment fees.

$5 is fixed in this case. Let the possible number of hours be h.

According to question,

Atleast means less than equal to. So,

7h-5≤51

Add 5 to both sides.

7h+5-5 ≤ 51+5

7h ≤ 56

h ≤ 8

So, the number of hours be less than equal to 8.

7 0
3 years ago
A radio station signal covers a circular area out from the signal tower. It gets weaker the farther away your are. The local sta
valentinak56 [21]

Answer:

1. We would hear better at Dunkin's since its distance from the radio station is the shortest.

2. McDonald's is out of range of the radio station since its distance is greater than the range of the radio station.

Step-by-step explanation:

1) Will we hear it better at Zaxby's (2,-4), McDonalds (4, -4), or Dunkin' (-3,3). Show work to support your decision and explain your reasoning.

We need to find the distance of each point from the tower.

The shorter the distance from the radio station the better the signal.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>Since Dunkin's distance, d₃ = 4.24 is the least distance from the radio station and is within range of 5 miles, we would hear better at Dunkin's.</u>

2) Are any of these location outside the range of the radio station? If so, which one(s). Defend your decision mathematically.

The radio station is outside of range if its distance is greater than 5 miles. That is, d > 5 miles.

So, we calculate the distance of each point from the radio station.

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>So, for each of the distances calculated above, only McDonald's distance, d₂ = 5.66 miles > 5 miles. </u>

<u>So, McDonald's is out of range of the radio station.</u>

5 0
3 years ago
Solve inequality and graph solution
stellarik [79]

Answer:

ill give you this math app that will give u answers

Step-by-step explanation:

https://www.cymath.com/answer?q=1%2B1 there u go

4 0
3 years ago
Can someone please help?
Troyanec [42]

Answer:

Option number 3 is an example of distribution

5 0
2 years ago
Read 2 more answers
Amelie's cat is 6 years older than her dog. The sum of their ages is 14 years.    How old is Amelie's dog
creativ13 [48]
C+d=14
c-6=d
then you will plug c+6 in the first equation and you will get:
c+c-6=14
then you get
2c=20
c=10, so the cat is ten years old
the cat is 6 years older than the dog, so the dog is 4 years old
hope that helps :) 
7 0
3 years ago
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