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3 years ago

Does anyone know away that I maybe able to understand these problems better

Mathematics

1 answer:

avanturin [10]3 years ago

8 0

Answer:

Step-by-step explanation:

Solving for x. Want to solve for f instead?

Step 1 move all terms to one side

fx - 4x² + 100 =0

Step 2 Use the Quadratic Formula

x = -f + √f² + 1600 ÷ -8, -f-√f²+1600 ÷ -8

Done.

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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

Unit of Measurement, a punk/disco band, was signed up to play a benefit

vova2212 [387]

D because they played for two days so that makes you multiply the number of seconds by the same number

7 0

3 years ago

Find the value x2 when x = 5

Bumek [7]

Answer:

The value of x is 25

Step-by-step explanation:

x² when x = 5

So,

(5)² = 5 × 5 = 25

Thus, The value of x is 25

-TheUnknownScientist 72

5 0

2 years ago

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A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the recta

Semenov [28]

1. The formula for calculate the perimeter of a rectangle, is:

P=2L+2W

P is the perimeter of the rectangle (P=320 feet).
L is the lenght of the rectangle.
W is the width of the rectangle.

2. The problem says that the length of the rectangle is three times the width, so you have:

L=3W

3. When you substitute L=3W and P=320, into P=2L+2W, you obtain:

P=2L+2W
320=2(3W)+2W
320=6W+2W
8W=320
W=320/8
W=40 feet

4. The barn forms one end of the rectangle. Therefore the linear feet of fence (x) is:

x=P-W
x=320 feet-40 feet
x=280 feet

How many linear feet of fence must he buy?

The answer is: 280 feet

5 0

3 years ago

If all guitar players are musicians, then all musicians are guitar players.

IrinaVladis [17]

Answer:

This does not make sense.

Step-by-step explanation:

Just because you are a musician does not mean you play the guitar.

You can play the piano and a trumpet, but not be able to play a guitar!

5 0

3 years ago

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