Newton's law of gravitation says that the force due to gravitation between two objects with masses m₁ and m₁ is given by the formula
Where r is the distance between the objects, and G is the gravitational constant (about 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²)
A youth group is setting up camp. Rain is predicted, so the campers decide to build a fly, or rain cover, over their tent. The f
2 answers:
You might be interested in
Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
Note that the left-hand side is a perfect square trinomial pattern. Namely:
If we let <em>a</em> = csc(x) and <em>b</em> = cot(x), we can factor it as such:
Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):
Combine fractions:
Square (but do not simplify yet):
Now, we can make a substitution. Let <em>u</em> = <em>x</em> / 2. So, <em>x</em> = 2<em>u</em>. Substitute:
Recall that cos(2u) = 1 - sin²(u). Hence:
Simplify:
Recall that sin(2u) = 2sin(u)cos(u). Hence:
Square:
Cancel:
Since sin(u) / cos(u) = tan(u):
We can substitute <em>u</em> back for <em>x</em> / 2:
Hence proven.
Im assuming the base of the triangle is 4cm. The volume is 
.
If the dimensions are tripled, the base is 12, the height is 24, and the length is 18. The volume is
, which is 27 times bigger.
If you are increasing each side by a factor of x, you are multiplying the original by
If the dimensions are tripled, the base is 12, the height is 24, and the length is 18. The volume is
If you are increasing each side by a factor of x, you are multiplying the original by