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3 years ago

Look at the image to see the question

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

6 0

9514 1404 393

Answer:

1385.4 yd³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

V = πr²h . . . . radius r and height h

For the given radius and height, the volume is ...

V = π(7 yd)²(9 yd) = 441π yd³ ≈ 1385.4 yd³

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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

3 years ago

Find 2 positive real numbers that differ by 1 and have a product of 1

velikii [3]

A) x -y =1
B) x * y =1
B) y = 1/x

A) x -(1/x) = 1
Multiplying both sides by "x"
A) x^2 -1 = x
A) x^2 -x -1 = 0

Solving by the quadratic formula
x = 1.618 and
y = .618

Interestingly, the number 1.6180339... is called the "phi ratio" or the "golden ratio".
https://en.wikipedia.org/wiki/Golden_ratio

6 0

3 years ago

3(4x−2)=2(5x+3) what is the answer pls asap

Paha777 [63]

Answer:

Step-by-step explanation:

1. get rid of parentheses: 12x -6 = 10x +6

2. group like terns together: 12x-10x = 6+6

3. simplify: 2x = 12

4. divide both sides by 2: x=6

7 0

3 years ago

Read 2 more answers

I WILL GIVE YOU BRAINLIEST, AND 30 POINTS SO PLEASE HELP ME, IT'S URGENT!

evablogger [386]

Answer:

The answer is 6

Step-by-step explanation:

The answer is 6

5 0

3 years ago

Please help worth 20 points will mark brainliest

ddd [48]

Answer:

P(t)= 100t + 150

Step-by-step explanation:

If the price for 6 hours of studio time is 600 dollars, that means every hour the studio is used it costs 100 dollars. Since the fixed fee is 150 dollars, that is added to the cost of how many hours the studio is used.

I hope this helped you. If it did Brainilest is appreciated.

3 0

4 years ago