Integrate both sides with respect to <em>t</em> :
∫ d<em>y</em>/d<em>t</em> d<em>t</em> = ∫ -12<em>t</em> ² d<em>t</em>
<em>y(t)</em> = -4<em>t</em> ³ + <em>C</em>
Use the initial condition to solve for <em>C</em> :
5 = -4•0³+ <em>C</em>
<em>C</em> = 5
So
<em>y(t)</em> = -4<em>t</em> ³ + 5
and the answer is D.
Alternatively, you can directly apply the fundamental theorem of calculus:
Identify a3 of this sequence: 0.25, 0.5, 0.75, 1, 1.25, 1.5,...a3=
<h3><u>Answer:</u></h3>The third term of sequence is 0.75
Given that, sequence is:
0.25, 0.5, 0.75, 1, 1.25. 1.5
Let us find the difference between terms
This is a arithmetic sequence
Because the difference between any term and its immediately preceding term is always 0.25
In a arithmetic sequence,
Thus, in the sequence 0.25, 0.5, 0.75, 1, 1.25. 1.5
Thus the third term of sequence is 0.75
Answer
Find out the volume of a cylinder .
To prove
Formula
Where r is the radius and h is the height.
As given
Diameter of 12 in. and a height of 7 in.
Radius = 6 in
put all the values in the formula
= 791.28 in³
Therefore the volume of the cylinder is 791 .28 in³ .