Answer:
Step-by-step explanation:
Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
d² = 10² + 10² = 200
d = √200 = 14.14cm
Formula for finding the volume of a sphere is expressed as
Volume = 4/3 × π × r³
Radius of sphere = diameter/2 = 14.14/2 = 7.07cm
Volume = 4/3 × π × 7.07³ = 471.19π cm³
Remember
the deritivive of f(x)/g(x)=(f'(x)g(x)-g'(x)f(x))/((g(x))^2)
deritivive of lnx is 1/x
derivitive of t^2=2t
so
=
=
Step-by-step explanation:
45÷11= 4 R 1
between 4 and 5
4 1/11
4 1/11
We want to choose 4 people and we have 6 people to choose from. This is a combination of 6, 4 by 4. Also called <em>six choose four</em>.
The following formula:
Is the combination of 
objects choosen from a total of 
. It's choose .
For our problem, we just need to compute the following:
Thus
Therefore the answer is 15 different combinations
Answer:
Step-by-step explanation:
You know an angle, the side opposite the angle, and the side between them.
Use the Law of Sines.
j3 = arcsin(2.7sin(j1)/4.2) ≅ 27.0°
j2 = 180°-j1-j3 ≅ 108.0°
x = distance from j1 to j2
= 4.2sin(j2)/sin(j1)
≅ 5.7 miles
