Which cone has a greater volume: a circular cone that is 3in. wide and 4in. tall or a second circular cone that is 4in. wide and 3in. tall? What is the difference in thier volume?

The volume of a right circular cone is 22.11 in³.

What are algebraic expressions?

• In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

• Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a right circular cone that has a height of 2.6 in and a base with a diameter of 5.7 in.

The volume of a right circular cone is -

V = {πr²h/3}

V = {π(d/2)²h/3}

V = {πd²h/12}

V = {3.14 x 5.7 x 5.7 x 2.6}/12

V = 22.11 in³

Therefore, the volume of a right circular cone is 22.11 in³.

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Answer:

22.12 cubic inch rounded to the nearest tenth is 22.1 cubic inch.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the formula for calculating the distance between two points as shown;

D = √(x2-x1)²²+(y2-y1)²

Given the coordinates  (-2, 4) and (10,2)

x1 = -2, y1 = 4, x2 = 10 and y2 = 2

substitute into the formula;

D = √(10+2)²+(2-4)²

D = √(12²+(-2)²

D = √144+4

D = √148

D = 12.17 units

Hence the distance of Mac,s house from Nate's house is 12.17 units

Final answer:

To find the coordinates of Mac's house, we use the section formula in mathematics. By substitifying the given locations of Nate's house and the park into the formula, we conclude that Mac's house is located at approximately (2, 3.33) which is one third the distance from Nate's house to the park.

Explanation:

In this math problem, we are dealing with points in a 2D cartesian coordinate system. Nate's house is at (-2, 4) and the park is at (10, 2). Mac's house is located one third of the distance between these two points. Following the formula for the coordinates of a point dividing a line segment in a given ratio, we can find Mac's house location.

Let the coordinates of Mac's house be (x, y). We use the formula for section formula which is:

x = [(m*x2 + n*x1) / (m+n)] and y = [(m*y2 + n*y1) / (m+n)]

Here, x1, y1 (-2, 4) are the coordinates of Nate's house, x2, y2 (10, 2) are the coordinates of the park and the ratio m:n is 1:2 since it's one third of the distance from Nate's house to the park.

By substituting these values in the formula, we get x = [(1*10 + 2*-2) / (1+2)] = 2 and y = [(1*2 + 2*4) / (1+2)] = 3.33

So, the coordinates of Mac's house are approximately (2, 3.33).

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The algebraic expression "8 minus the quotient of 15 and y" can be written as:

8 - (15 / y)

Given that a verbal expression we need to convert it in algebraic form,

The given algebraic expression is "8 minus the quotient of 15 and y."

To understand this expression, let's break it down step by step:

Quotient: The quotient refers to the result of dividing one number by another.

In this case, we are dividing 15 by y. The expression "15 divided by y" can be written as 15/y.

Minus: The word "minus" indicates subtraction. It means we need to subtract the value obtained in the previous step from 8.

Putting it all together, the algebraic expression "8 minus the quotient of 15 and y" can be represented as:

8 - (15/y)

This expression represents the difference between 8 and the result obtained by dividing 15 by y.

The expression represents the result of subtracting the quotient of 15 and y from 8.

The value of y will determine the specific numerical result when you substitute it into the expression.

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