Mathematics, 17.03.2021 23:40 nett4386

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Answer from: amyeileen

$\displaystyle \frac{1}{2}$

General Formulas and Concepts:

Math

Converting to FractionsKCF - Keep Change Flip (Dividing Fractions)

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Step-by-step explanation:

Step 1: Define

$\displaystyle (\frac{(2.7 - 0.8) \cdot 2\frac{1}{3}}{(5.2 - 1.4) \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43$

Step 2: Compute

(Parenthesis) [Fraction] (Parenthesis) Subtract: $\displaystyle (\frac{1.9 \cdot 2\frac{1}{3}}{3.8 \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43$ (Parenthesis) [Fraction] Convert to fractions: $\displaystyle (\frac{\frac{19}{10} \cdot \frac{7}{3}}{\frac{38}{10} \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43$ (Parenthesis) [Fraction] Multiply/Divide: $\displaystyle (\frac{\frac{133}{30}}{\frac{266}{3}} + 0.125) \div 2\frac{1}{2} + 0.43$ (Parenthesis) [Fraction] Divide: $\displaystyle (\frac{1}{20} + 0.125) \div 2\frac{1}{2} + 0.43$ (Parenthesis) Convert to fraction: $\displaystyle (\frac{1}{20} + \frac{1}{8}) \div 2\frac{1}{2} + 0.43$ (Parenthesis) Add: $\displaystyle \frac{7}{40} \div 2\frac{1}{2} + 0.43$ Divide: $\displaystyle \frac{7}{100} + 0.43$ Convert to fraction: $\displaystyle \frac{7}{100} + \frac{43}{100}$ Add: $\displaystyle \frac{50}{100}$ Simplify: $\displaystyle \frac{1}{2}$

Answer from: Quest

-2 is the right

Algebra semester 1 unit4 pretest linear equations

Answer from: Quest

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

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