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3 years ago

What are the inequality solutions for 3 ≤ 3 x − 4 < 2 x + 1

Mathematics

1 answer:

krek1111 [17]3 years ago

3 0

Answer:

7/3 ≤ x < 5.

Step-by-step explanation:

3 ≤ 3 x − 4 < 2 x + 1

Split this up into 2 inequalities:

3x - 4 ≥ 3

3x ≥ 7

x ≥ 7/3.

and

3x - 4 < 2x + 1

3x - 2x < 1 + 4

x < 5.

So it's 7/3 ≤ x < 5.

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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$

Then

$\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.$

Answer 2: correct choice is D.

8 0

4 years ago

Read 2 more answers

Justify each step in solving the equation 6x = 3 (x + 4) by writing a reason for each statement.

BaLLatris [955]

First thing is to multiply 3 by x and get 3x,then 3 by 4 equals 12. 3x+12....6x=3x+12...subtract 3x from 6x and get 3x=12..then divide 3 on both sides and 3x crosses out.. and x=4...this is what I have to say about this..

6 0

3 years ago

Solve the following equation. Enter your answer as an integer, decimal or fraction.

Ad libitum [116K]

Answer:

x = 5 or × = -7/2

Step-by-step explanation:

I hope you get it good luck.