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2 years ago

Find the volume of the figure: a cube with sides of length s with the biggest sphere that fits in it cut out.

Mathematics

1 answer:

garik1379 [7]2 years ago

6 0

Answer:

Volume of cube= a^3

=(2/√3)^3

=8/3√3 cubic units. (~1.5396 cubic units)

Step-by-step explanation:

Such a cube has diagonal lengths (DF, AG, EC & HB)=diameter of sphere=2 units.

Let the sides of the cube (FG, GC, CB, BF, etc.) be 'a'.

Hence facial diagonal of the cube (FC, BG, FH, etc.) will be √2a (Pythagoras' Theorem).

Applying Pythagoras' theorem for △DFC:

FC²+DC²=FD²

⇒(√2a)²+a²=2²

⇒3a²=4

⇒a=2/√3 units

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Need help in this ASAP

Artemon [7]

Answer:

The m∠YXW is 125°.

Addition equation: m∠YXW = m∠YXZ + m∠ZXW = 85° + 40° = 125°

Step-by-step explanation:

To find the m∠YXW you would need to add the m∠YXZ and m∠ZXW together:

m∠YXW = m∠YXZ + m∠ZXW = 85° + 40° = 125°

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3 years ago

Which function is the inverse of f(x)= 3x+5 over 7

Pani-rosa [81]

f(x) = (3x+5)/7

Step 1:

we write f(x) as y

y=(3x+5)/7

Step 2:

switch y by x and x by y

x=(3y+5)/7

Step 3:

solve for y,

x=(3y+5)/7

multiply both sides by 7

7x=3y+5

subtract 5 from left side

3y=7x-5

divide both sides by 3

y= (7x-5)/3

f⁻¹ (x) =(7x-5)/3

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3 years ago

A machine that produces a major part for an airplane engine is monitored closely. In the past, 12% of the parts produced would b

melamori03 [73]

Answer:

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Step-by-step explanation:

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2 years ago

A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.75 , with a standard

bulgar [2K]

Answer:

Following are the solution to the given choices:

Step-by-step explanation:

Using chebyshev's theorem :

$\to P(|(x-\mu)|\leq k \sigma)\geq 1- \frac{1}{k^2}\\\\here \\ \to \mu=28.75\\\\ \to \sigma=4.44$

In point a)

$\to |(x-\mu)|= |20.17-28.75|=8.58 and \sigma=4.44 \\\\so, \\k= \frac{ |(x-\mu)| }{\sigma}$

$= \frac{8.58}{4.44} \\\\ =1.9 \\\\ =2$

$value= (1- \frac{1}{k^2}) \times 100 \% =75\%$

In point b)

$\to (1- \frac{1}{k^2}) \times 100 \% =84\% \\\\\to (1- \frac{1}{k^2})=0.84 \\\\\to \frac{1}{k^2} =0.16 \\\\\to \frac{1}{k}=0.4\\\\ \to k=2.5 \\\\\to |(x-\mu)| \leq k \sigma \\\\= |(x-\mu)|\leq 2.5 \times 4.44 \\\\ = |(x-\mu)|\leq 1.11 \\\\ = (28.75\pm 11.1) \\\\\to \text{fares lies between}(17.65,39.85)$