Solve for x:1/2(x-2)+1/3(x-3)+1/4(x-4)

A ball is dropped from a height of 600 feet. The function describing the height of the ball at t seconds after it dropped is <im

bekas [8.4K]

The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

<h3>What is instantaneous and average velocities?</h3>

Instantaneous velocity is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16 $t^{2}$ + 600

a) Height at t = 0 = 600 feet

Height at t = 3 seconds = f(3) = -16 $(3)^{2}$ + 600 = 456 feet

Distance travelled = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = $\frac{df(t)}{dt}$ = $\frac{d(-16t^{2} + 600) }{dt}$ = -32t

when instantaneous velocity equal average velocity

-32t = -48

t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

Learn more about instantaneous and Average velocity: brainly.com/question/13372043

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7 0

2 years ago

Help<br> -9x + 3.0 > 6.6<br> Group of answer choices<br><br> x 0.4<br><br> x 2.4

Y_Kistochka [10]

Answer:

x 0.4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0

3 years ago

X^2-14x+49 as a graph

Vaselesa [24]

5 0

3 years ago

please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up

babunello [35]

Answer:

$y'' =12x^2 -72=0$

And solving we got:

$x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}$

We can find the sings of the second derivate on the following intervals:

$(-\infty$ Concave up

$x=-\sqrt{6}, y =-180$ inflection point

$(-\sqrt{6}$ Concave down

$x=\sqrt{6}, y=-180$ inflection point

$(\sqrt{6}$ Concave up

Step-by-step explanation:

For this case we have the following function:

$y= x^4 -36x^2$

We can find the first derivate and we got:

$y' = 4x^3 -72x$

In order to find the concavity we can find the second derivate and we got:

$y'' = 12x^2 -72$

We can set up this derivate equal to 0 and we got:

$y'' =12x^2 -72=0$

And solving we got:

$x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}$

We can find the sings of the second derivate on the following intervals:

$(-\infty$ Concave up

$x=-\sqrt{6}, y =-180$ inflection point

$(-\sqrt{6}$ Concave down

$x=\sqrt{6}, y=-180$ inflection point

$(\sqrt{6}$ Concave up

8 0

3 years ago

What is the term used to describe the distance of a complex number from the origin in a complex plane?

IceJOKER [234]

In a rectangular form of a complex number, where a + bi, a and b equates to the location of the x and y respectively in a complex plane. The modulus |z| is the term used to describe the distance of a complex number from the origin. Hence, |z| = √(a²+b²)

3 0

3 years ago