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:
Answer:
B. 1
Step-by-step explanation:
they only cross at one point... look below
Answer:
A. (1, -2)
Step-by-step explanation:
We can substitute the variables of x and y into the inequality of .
Let's start with A, -2 being y and 1 being x.
The absolute value of 1 is 1, and negating that gets us -1.
Indeed, -2 is less than -1! So A is a solution to the inequality.
Let's test the rest of them, just in case.
For B:
Absolute value of 1 is 1, negating it is -1.
-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.
Let's try C.
Absolute value of 1 is 1, negating it is -1.
0 is GREATER than -1, so that is not a solution to the inequality.
Hope this helped!