The most general antiderivative of the given function g(t) is (8t + t³/3 + t²/2 + c).
The antiderivative of a function is the inverse function of a derivative.
This inverse function of the derivative is called integration.
Here the given function is: g(t) = 8 + t² + t
Therefore, the antiderivative of the given function is
∫g(t) dt
= ∫(8 + t² + t) dt
= ∫8 dt + ∫t² dt + ∫t dt
= [8t⁽⁰⁺¹⁾/(0+1) + t⁽²⁺¹⁾/(2+1) + t⁽¹⁺¹⁾/(1+1) + c]
= (8t + t³/3 + t²/2 + c)
Here 'c' is the constant.
Again, differentiating the result, we get:
d/dt(8t + t³/3 + t²/2 + c)
= [8 ˣ 1 ˣ t⁽¹⁻¹⁾ + 3 ˣ t⁽³⁻¹⁾/3 + 2 ˣ t⁽²⁻¹⁾/2 + 0]
= 8 + t² + t
= g(t)
The antiderivative of the given function g(t)is (8t + t³/3 + t²/2 + c).
Learn more about antiderivative here: brainly.com/question/20565614
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2h + 6 = 3h -19
collect like terms
2h - 3h = -19 - 6
-h = -25
Divide both sides by -1
-h/-1 = -25/-1
h = 25
Hope this helps.
Answer:
Step-by-step explanation:
log3^(2x+3) = log243
(2x+3)log3 = log243
2x+3 = log243/log3
2x = (log243/log3)-3
x = [(log243/log3)-3]/2
x = (5-3)/2
x = 2/2
x = 1
Check:
3^2(1)+3 = 243
3^2+3 = 243
3^5 = 243
3×3×3×3×3 = 243
9×9×3 = 243
81×3 = 243
243 = 243
Answer:
see explanation
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
22 - 18 < x < 22 + 18
4 < x < 40
3rd side can be any value from 5 to 39
All 12 months have 28 days in it.
because every month has 28 days ( February) or more number of days like the other months(Jan, Mar..)
