Evaluate the function 2/3t , when t = 30.

What are the zero(s) of the following function: f(x)= -8X - 4?

ANTONII [103]

0=-8x-4
you then move the variable to the left and you get
8x=-4
you then divide both sides to get the answer
x=-1/2

7 0

3 years ago

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

2 years ago

When dividing the polynomial using synthetic division, which of the following setup boxes would be used?

Galina-37 [17]

The setup boxes in the synthetic division are (b)

<h3>How to determine the setup boxes?</h3>

The dividend is given as:

x^3 + 4x^2 + x - 6

The divisor is given as:

x - 2

Set the divisor to 0

x - 2 = 0

Solve for x

x = 2

Remove the variables in the dividend

1 + 4 + 1 - 6

Remove the arithmetic signs

1 4 1 - 6

So, the setup is:

2 | 1 4 1 - 6

Hence, the setup boxes are (b)

Read more about synthetic division at:

brainly.com/question/12951962

#SPJ1

8 0

1 year ago

Can someone help me with this exempalar? The requirements for this are...

Lyrx [107]

Answer:

I will: Multiply 32 times 20 to get the total cost of the foods and tickets. Then I will add the total cost of the tickets and the total cost of the bus to get the total cost of the trip. Lastly I will divide the total cost of the trip by 2 to find out how much money the class need to earn.

Solution: 32 • 20 = 640 + 900 = 1,540 ÷ 2 = 770

Answer: 770

6 0

3 years ago

Read 2 more answers

81

Rasek [7]

Answer:

2.6

Step-by-step explanation:

7 0

3 years ago