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Tasya [4]
3 years ago
8

The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 3 inches can

hold 81 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 2 inches?
Mathematics
1 answer:
Neporo4naja [7]3 years ago
7 0

Answer:

57 in³

Step-by-step explanation:

Since the volume of gas and the cube of its radius vary directly, we can set up an initial equation to find the constant of variation:

V = kr³, where v=volume, r=radius and k=contant of variation

Given that a balloon with a radius of 3 inches can hold a volume of 81 cubic inches, we can plug these values into the equation and solve for 'k':

81 = k3³ or 81 = 27k or k = 3

Given 'k', now we can find the volume of the balloon with a radius of 2:

V = (3)(2³) = 24 in³

Since the question asked how much gas must be released to reduce the radius, we would find the difference of 81 and 24:

81 - 24 = 57 in³

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Answer:

B. 0.8 meters

Step-by-step explanation:

Divide 2.4 by 3 and you will get 0.8

3 0
3 years ago
3. What are the solutions to the system of equations graphed below?
goldenfox [79]

Answer:

(-1, 5) and (3, -3)

Step-by-step explanation:

The solutions are all the points where the two functions intersect. Since the lines intersect at two different points, there are two solutions.

The two points at which the functions appear to intersect are (-1, 5) and (3, -3).

5 0
2 years ago
Three of the angles of a quadrilateral are 120° 48° and 92° what is the size of the fourth angle
Komok [63]
360-120-48-92=100°

Each <span>quadrilateral has 360</span>° so simply deduct the angles to get your result.
6 0
3 years ago
Read 2 more answers
Can someone please help me with this problem? A fastpitch softball player signs a six year contract. Her agent expects that she
Luba_88 [7]

Answer:

The question is not complete, below is the complete question:

A fastpitch softball player signs a six-year contract. Her agent expects that she will earn $1,000,000 over the next six years. If the agent is right, how many bonus payments, on average, should the pitcher expect each year? Explain

Yearly Salary: $20.000. Bonus for each game that attracts 100+ fans: $8.000.

Answer:

on average, the pitcher expects to earn 18.3 bonuses per year

Step-by-step explanation:

Total amount earned over the next 6 years = $1,000,000

salary per year = $20,000

salary for the next 6 years = 20,000 × 6 = $120,000

Next, let us calculate the amount earned from bonuses:

Total amount earned = amount earned from salaries + amount earned from bonuses

$1,000,000 = 120,000 + Amount earned from bonuses

Amount earned from bonuses = 1,000,000 - 120,000

Amount earned from bonuses = $880,000

Total bonus amount earned over six years = $880,000

Amount of bonus earned per game = $8,000

Number of bonuses received over the next 6 years = (Total bonus earned over six years) ÷ (Amount of bonus earned per game)

Number of bonus received over the next 6 years = 880,000 ÷ 8,000

Number of bonus received over the next 6 years = 110 bonuses

6 years = 110 bonuses

1 year = 110 ÷ 6 = 18.33 bonuses

on average, the pitcher expects to earn 18.3 bonuses per year

5 0
3 years ago
Perform the indicated operation. Simplify the result in factored form. ((x - y)/ (x^2 - 1)) * ((x - 1)/(x^2 - y^2))
Scilla [17]

Answer:

The answer to your question is            \frac{1}{(x + 1)(x + y)}            

Step-by-step explanation:

Real operation

                      \frac{x - y}{x^{2} - 1} \frac{x - 1}{x^{2} - y^{2}}

Process

1.- Factor the denominators

                     \frac{x - y}{(x + 1)(x - 1)} \frac{x - 1}{(x + y)(x - y)}

2.- Simplify like terms

Cancel (x - y) and (x - 1) because they are in numerator and the denominator

                    \frac{1}{(x + 1)(x + y)}            This is the answer or you can expand

3.- Expand

                   \frac{1}{x^{2} + xy + x + y^{2}}                    

3 0
3 years ago
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