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Mathematics

1 answer:

Alona [7]3 years ago

6 0

Answer:

<h3>b) A cylinder in which h = 3 and d = 6 has a volume of 27π in^3; therefore, Wilson is correct.</h3>

Step-by-step explanation:

$\text{The formula of a volume of a cone:}\\\\V_{cone}=\dfrac{1}{3}\pi r^2H\\\\r-radius\\H-height\\\\\text{The formula of a volume of a cylinder:}\\\\V_{cylinder}=\pi r^2H}\\\\\text{If the cylinder and the cone have the same diameter,}\\\text{then have the same radius.}\\\\diameter\ d=2r\to r=\dfrac{d}{2}\\\\d=6\ in\to r=\dfrac{6}{2}=3\ in\\\\\text{Substitute:}\\\\V_{cone}=9\pi\ in^3,\ r=3\ in:\\\\9\pi=\dfrac{1}{3}\pi(3^2)(H)\\\\9\pi=3H\pi\qquad\text{divide both sides by}\ 3\pi\\\\3=H\to H=3\ in$

$\text{Calculate the volume of a cylinder:}\\\\V_{cylinder}=\pi(3^2)(3)=27\pi\ in^3$

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3 years ago

Read 2 more answers

A water tank in Stewart's

lara [203]

The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.

Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:

The total leak must be calculated and divided by the 10 minutes duration.
3/5 = 0.6
1 + 0.6 = 1.6
1.6 / 10 = 0.16

Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.

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2 years ago

Fabiano and Sonali's teacher gave them a system of linear equations to solve. They each took a few steps that led to the systems

marin [14]

Question: Which system has the same solution as the teacher's system?

Systems of equations that have the same solution are called equivalent systems.We are given with a system of two equations, we can make an equivalent system by substituting one equation by the sum of the two equations.

Given System:

8x-16y=14→eq.1
−x+5y=−3→eq.2
Teacher's Solution:
From eq.2
x = 5y + 3
Substituting the value of x in eq.1
We get,
 8(5y + 3) - 16y = 14
40y + 24 - 16y = 14
24y + 24 = 14
24y = 14-24
24y = -10
y = -10/24
y = -5/12

Substituting y-value in eq.2,
−x+5(-5/12) = −3
-x -25/12 = -3
-x = -3 + 21/12
-x = 15/12
x = -5/4

Fabiano:
 3x−15y=9
 8x−16y=−7

Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x+7/16

Placing both equations equal to each other,
1/5x - 3/5= 1/2x+7/16
1/5x -1/2x = 7/16 +3/5
-3/5x = 83/80
x = -83×5/80×3
x = -415/240
x = -83/48
This doesnt matches the teachers solution so we will move to sonali.

Sonali
 −x+5y=−3
 −4x+8y=−7
Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x -7/8

Placing both equations equal to each other,
1/5x - 3/5 = 1/2x -7/8
1/5x -1/2x = -7/8 +3/5
-3/10x = -11/40
x = 110/120
x = 11/12

This doesn't match the teacher's solution either, so we will conclude that none of the solutions to the system of equation has the same answer as the teacher.