How much of the circle is shaded? Write your answer as a fraction in simplest form.

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

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negat

CaHeK987 [17]

Answer:

Reflection over the y-axis and rotation of 180°

Step-by-step explanation:

We have,

Rectangle ABCD with co-ordinates A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

It is transformed to a new rectangle A'B'C'D' with co-ordinates A'(-4,-2), B'(-4,-1), C'(-1,-1) and D'(-1,-2).

The graph of both the triangles is shown below.

we see that,

The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

Reflected about y-axis Rotation of 180°

A= (-4,2) (4,2) A'= (-4,-2)

B= (-4,1) (4,1) B'= (-4,-1)

C= (-1,1) (1,1) C'= (-1,-1)

D= (-1,2) (1,2) D'= (-1,-2)

Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.

5 0

2 years ago

Read 2 more answers

Find the value of the following expression:

Greeley [361]

Answer:

25

Step-by-step explanation:

Expression: <em>(2⁸ ⋅ 5⁻⁵ ⋅ 19⁰)⁻² ⋅ (5⁻²/2³)⁴ ⋅ 2²⁸</em>

Inner-most powers: 2⁻¹⁶ • 5¹⁰ • 1 • 5⁻⁸/2¹² • 2²⁸

Combine like terms: 2¹² • 5²/2¹²

Cancel out: 5²

Solve: 25

6 0

3 years ago

Help me out with this equation would be very helpful

Lisa [10]

Answer:

I think its C

Step-by-step explanation:

I could be wrong

3 0

2 years ago

Please help cause I don’t know how to do this

zalisa [80]

Answer:

4 GB

Step-by-step explanation:

Let "g" represent the number of gigabytes of data used. Then the phone bill is computed as ...

bill = 65 + 12g

Aurora's bill is 113, so we can put that value into the equation and solve for g.

113 = 65 + 12g

48 = 12g . . . . . . subtract 65 from both sides of the equation

4 = g . . . . . . . . . divide both sides of the equation by 12

Aurora used 4 gigabytes of data in September.

_____

You can also use your mathematical reasoning to solve this problem. The total bill consists of two charges: a fixed charge of 65 and a charge that depends on data. If you subtract the fixed charge from the bill, you find that the charge that depends on data is 113-65 = 48.

The data charge is 12 times the number of gigabytes. The data charge on the bill is 48, which is 12 times 4. Then the number of gigabytes is 4.

7 0

2 years ago