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Vaselesa [24]
3 years ago
11

PLZ HELP ASAP!!!! Solve for X: 2X^3 = 54

Mathematics
1 answer:
mariarad [96]3 years ago
6 0
X=3

Divide both sides of the equation by 2
X^3 =27

Write the number in exponential form with an exponent of 3
X^3=3^3

Since the exponents are the same, set the bases equal
X=3
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a) h_0 -u_y t

b) See interpretation below

Step-by-step explanation:

a)

The motion of both balls is a free-fall motion: it means that the ball is acted upon the force of gravity only.

Therefore, this means that the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:

g=32 ft/s^2

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For the ball dropped from the initial height of h_0 = 98 ft, the height at time t is given by

h(t) = h_0 -\frac{1}{2}gt^2 (1)

The ball which is thrown upward from the ground instead is fired with an initial vertical velocity u_y, and its starting height is zero, so its position at time t is given by

h'(t)=u_y t - \frac{1}{2}gt^2 (2)

Therefore, the polynomial that represents the distance between the two balls is:

h(t)-h'(t)=h_0 - \frac{1}{2}gt^2 - (u_y t - \frac{1}{2}gt^2) = h_0 -u_y t

b)

Now we interpret this polynomial, which is:

\Delta h(t) = h_0 -u_y t

which represents the distance between the two balls at time t.

The interpretation of the two terms is the following:

- The constant term, h_0, is the initial distance between the two balls, at time t=0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this problem, h_0 = 98 ft

- The coefficient of the linear term, u_y, is the initial velocity of the second ball; this terms tells us that the distance between the two balls decreases every second by u_y feet.

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