Yes there is actually a formula for this. This is an arithmetic progression with a common difference of 1.
The sum of terms can be solved by using the formula
S = (n/2) * (a1 + an)
where S is the sum of the terms
n is the number of terms
a1 is the first term
an is the last term
we can calculate the number of terms, n by using the formula
an = a1 + (n-1)*d
d is the common difference equal to 1
therefore n = 51
substituting to the first equation
S = 2805
Answer:
Total weight is 150 kg
Step-by-step explanation:
Firstly, we need the weight of the diagonal
To get this, we shall use the Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
The diagonals stand for the hypotenuse
Thus, we have that;
d^2 = 5^2 + 12^2
d^2 = 25 + 144
d^2 = 169
d^2 = 13^2
d = 13
The 6 sides technically includes the whole rectangle sides, then the two diagonals
The total length here is;
2(5 + 12 + 13) = 60 meters
Steel weight is 2.5 kg per meter
Weight of 60 m will be ;
60 * 2.5 = 150 kg
Answer:
24
Step-by-step explanation:
3d
= 3 × 8
= 24
Hope it helps you:)
Due to the symmetry of the paraboloid about the <em>z</em>-axis, you can treat this is a surface of revolution. Consider the curve 
, with 
, and revolve it about the <em>y</em>-axis. The area of the resulting surface is then
But perhaps you'd like the surface integral treatment. Parameterize the surface by
with 
and 
, where the third component follows from
Take the normal vector to the surface to be
The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:
Then the area of the surface is
which reduces to the integral used in the surface-of-revolution setup.
