IM USING 20 POINTS FOR THIS PLS HELP AND SHOW WORK

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

Answer:

the object is in the air on the time interval (0.24 sec, 6.51 sec)

Step-by-step explanation:

The object is 'in the air' for all t such that h> 0. We need to find the roots of h = -16t^2 + 108t - 25 = 0. From the graph we see that both t values are positive. Once we find them, we subtract the smaller t from the larger t, which results in the length of time the object is in the air.

Use the quadratic formula to find the roots of h(t). The coefficients of t are {-16, 108, -25}, and so the discriminant b^2 - 4ac is

108² - 4(-16)(-25) = 11664 - 1600 = 10064, whose square root is 100.32.

Then the quadratic formula x = (-b ± √[b² - 4ac)/(2a) becomes

-108 ± 100.32 108 ± 100.32

t = ---------------------- = --------------------- = 3.375 ± 3.135

2(-16) 32

or t = 6.51 or t = 0.24 (both times expressed in seconds).

So, again, the object is in the air on the time interval (0.24 sec, 6.51 sec)

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Tomtit [17]

Answer:

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Step-by-step explanation:

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3 years ago

Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4

ad-work [718]

Answer:

$f''(x)=36x^2+4$

Step-by-step explanation:

Let's start by finding the first derivative of $f(x)= 3x^4+2x^2-8x+4$ . We can do so by using the power rule for derivatives.

The power rule states that:

$\frac{d}{dx} (x^n) = n \times x^n^-^1$

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

$\frac{d}{dx} (3x^4+2x^2-8x+4)$

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)$

Simplify the equation.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)$
$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)$

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)$
$f'(x)=12x^3+4x-8$

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).