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:
1. C
2.A
Hope this helps, good luck :D
Accordingly the answer is Nineteen Fourths.
Answer:
x = 6
y = 4
Step-by-step explanation:
Let the two numbers be x and y
<u><em>Condition 1:</em></u>
7x+3y = 54 -----------(1)
<u><em>Condition 2:</em></u>
x = 2+y -----------------(2)
<em>Putting (2) in (1)</em>
=> 7(y+2)+3y = 54
=> 7y+14+3y = 54
=> 10y = 54-14
=> 10y = 40
<em>Dividing both sides by 10</em>
=> y = 4
<em>Now putting y = 4 in eq(2)</em>
=> x = 2+4
=> x = 6
