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3 years ago

Answer the questions.

Mathematics

1 answer:

Paladinen [302]3 years ago

3 0

Answer:

Objective C

$125x + 200 \geqslant 1200 \\ 125x \geqslant 1000 \\ x \geqslant 8$

$x \: \alpha \: y \\ y = kx \\ 2.00 = k \times 8 \\ k = \frac{2.00}{8} \\ k = 0.25$

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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

4 years ago

Translate into a equation. one subtracted from two times a number is -45.

sleet_krkn [62]

Answer:

2x - 1 = -45.

Step-by-step explanation:

2x - 1 = -45 is the required equation.

x is the number.

3 0

3 years ago

If y varies directly as x, and y=8 when x=3, find y when x=15.

Crank

Answer:

y=40

Step-by-step explanation:

The formula for Direct Variation is y=kx or k=y/x. In this case I would use k=y/x. If you're y is 8 and x is 3, this means that K=8/3. Using this, we know that X=15. We have to find a Y value so that the fraction with an x of 15 simplified is 8/3. To do this you would write 8/3 and y/15. Now cross multiply to get 3y=120. Divide by 3 to get y=40. View my attachment for the work!