Which statement shows how two polynomials 3x + 6 and 5x2 - 4x demonstrate the closure property when multiplied?

A ball is thrown vertically in the air with a velocity of 95 ft/s. The ball is at a height of 120 ft.

sattari [20]

Answer:

The ball is at a height of 120 feet after 1.8 and 4.1 seconds.

Step-by-step explanation:

The statement is incomplete. The complete statement is perhaps the following "A ball is thrown vertically in the air with a velocity of 95 ft/s. What time in seconds is the ball at a height of 120ft. Round to the nearest tenth of a second."

Since the ball is launched upwards, gravity decelerates it up to rest and moves downwards. The position of the ball can be determined as a function of time by using this expression:

$y = y_{o} + v_{o}\cdot t +\frac{1}{2}\cdot g \cdot t^{2}$

Where:

$y_{o}$ - Initial height of the ball, measured in feet.

$v_{o}$ - Initial speed of the ball, measured in feet per second.

$g$ - Gravitational constant, equal to $-32.174\,\frac{ft}{s^{2}}$ .

$t$ - Time, measured in seconds.

Given that $y_{o} = 0\,ft$ , $v_{o} = 95\,\frac{ft}{s}$ , $g = -32.174\,\frac{ft}{s^{2}}$ and $y = 120\,ft$ , the following second-order polynomial is found:

$120\,ft = 0\,ft + \left(95\,\frac{ft}{s} \right)\cdot t +\frac{1}{2}\cdot \left(-32.174\,\frac{ft}{s^{2}} \right) \cdot t^{2}$

$-16.087\cdot t^{2} + 95\cdot t -120 =0$

The roots of this polynomial are, respectively:

$t_{1} \approx 4.075\,s$ and $t_{2} \approx 1.831\,s$ .

Both roots solutions are physically reasonable, since $t_{1}$ represents the instant when the ball reaches a height of 120 ft before reaching maximum height, whereas $t_{2}$ represents the instant when the ball the same height after reaching maximum height.

In nutshell, the ball is at a height of 120 feet after 1.8 and 4.1 seconds.

8 0

3 years ago

Please help me!!!!! How do you get 67.3 and 112.7 from .9228

antoniya [11.8K]

Answer and Step-by-step explanation:

You are correct in that we need to use the Law of Sines: $\frac{c}{sinC} =\frac{b}{sinB}=\frac{a}{sinA}$ .

Here, when we use the Law of Sines, we have: $\frac{28}{sin(63)}=\frac{29}{sinB}$ .

Cross multiply:

(sinB) * 28 = (sin63) * 29

28sinB ≈ 25.839

sinB ≈ 0.9228

Now, in order to solve for B, we need to use inverse sin ( $sin^{-1}$ ):

$sin^{-1}(sinB)=sin^{-1}(0.9228)$

The sines on the left cancel out, and we're left with:

B ≈ 67.3 degrees

Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:

180 - 67.3 = 112.7 degrees.

Hope this helps!

7 0

3 years ago

Read 2 more answers

7) I am saving up for a video game. I currently have $28. If this is 30% of the

Snezhnost [94]

Answer:

93.3333333333 I think

7 0

2 years ago

Can anyone tell me what is 2/5 x 3/2 ?