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3 years ago

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A spherical balloon with radius r inches has volume defined by the function below. find a function that represents the amount of

air required to inflate the balloon from a radius of r inches to a radius of r + 3 inches. (give the answer in terms of π and r.) v(r) = 4/3 pi r^3

1 answer:

Rashid [163]3 years ago

8 0

The function would be v (r+3)=4/3 π(r+3)^3.

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Two consecutive whole numbers are n-1 and n

Orlov [11]

a. n-(n - 1) = 1

b. n( n - 1) = n² - n

c. (n - 1) + n = 2n - 1

d. (n - 1) + n = 2n - 1

<h3>Solution:</h3>

General Rule for Equation Solving

Remove parentheses and combine like terms to simplify each side of the equation.

To isolate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use multiplication or division.

Given two consecutive numbers , (n - 1) , n

simplifying :

n - (n - 1)

= n -1(n - 1)

= n - n + 1

= 1

multiplying :

n( n -1)

= n² - n

simplifying :

(n-1) + n

= n - 1 + n

= 2n -1

by adding two numbers :

(n - 1) + n

= n -1 + n

= 2n - 1

To learn more about equations refer to :

brainly.com/question/22688504

#SPJ13

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1 year ago

The perimeter of a rectangle is 60 centimeters. The base is 2 times the height. What are the dimensions of the rectangle?

tankabanditka [31]

Licenciado en Letrase (base 20 y altura 10 cm.

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3 years ago

What is the area of the triangle shown below ?3.7mm 4.8mm

Aleks04 [339]

I can’t answer because I don’t have the picture of the triangle

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2 years ago

Calculate the number of subsets and the number of proper subsets for the set.

arlik [135]

A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 <em>proper</em> subsets.

The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.

Just to illustrate the claim, we have

• subsets of size 0 (1 of these):

{ } (empty set)

• subsets of size 1 (4 of these):

{1/6}, {1/7}, {1/8}, {1/9}

• subsets of size 2 (6 of these):

{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}

• subsets of size 3 (4 of these):

{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}

• subsets of size 4 (1 of these):

{1/6, 1/7, 1/8, 1/9}

and the last one is the only subset that is not a proper subset, because that subset = the set.

6 0

2 years ago

67. The line contains the point (4,0) and is parallel<br> to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

<u>1) Determine the slope of the parallel line</u>

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

$y=\frac{3}{2} x+b$

<u>2) Determine the y-intercept</u>

$y=\frac{3}{2} x+b$

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

$y=\frac{3}{2} x-6$

I hope this helps!

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3 years ago