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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This is a correlation as it describes the relationship of Marcus's running speed with the time of day. The cause of the increase in speed is not elaborated.
For this case we have by definition that the area of a parallelogram is given by:
Where:
b: It's the base
h: It's the height
According to the data we have:
Substituting in the formula:
The area of the parallelogram is 
Answer:
Answer:
7/15
Step-by-step explanation:
Determine how much she has watched.
1/3 + 1/5 The common denominator of 3 and 5 is 15. Multiply each fraction by an amount that will make the denominator 15
1/3 = 1*5/(3*5) = 5 / 15
1/5 = 1*3 / (5*3) = 3/15
Now add the two fractions together.
5/15 + 3/15 = 8/15
What is left of the movie? The whole movie = 1 so that which is left is
1 - 8/15
15/15 - 8/15
7 / 15
She has just a bit under 1/2 to go.
By <span>(x + 5/x^2 + 9x + 20) you apparently meant the following:
x+5
----------------------
x^2 + 9x + 20
and by
</span><span>(x^2-16/x-4)
x^2-16
you apparently meant ---------------
x - 4
Please use additional parentheses for clarity.
Dividing,
</span> x+5 (x-4)(x+4)
---------------------- * ---------------
x^2 + 9x + 20 x-4
Now, x^2 + 9x + 20 factors into (x+4)(x+5), so what we have now is
(x+5)(x+4)
------------------------- = 1 This is true for all x, so there are no exclusions.
(x+4)(x+5)
