A hydraulic device has two pistons, one with a small cross-section area and another piston with a larger cross-section area. If a given force is applied to the small piston, the output force on the larger-area piston will be

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A hydraulic device has two pistons, one with a small cross-section area and another piston with a larger cross-section area. If a given force is applied to the small piston, the output force on the larger-area piston will be

1. area = 3.14 x 3.5^2 = 38.46 = 38.5 cm^2

2. circumference = 2 x 3.14 x r = 21.98 = 22.0 cm

3. area = 3.14 x 6^2 = 113.04 = 113.0 ft^2

4. area = (8*5) + (.5x 3.14*4^2) = 90.24 = 90.2 cm^2

5. area = (4*4) - (3.14x 2^2) = 3.44 = 3.4 in^2

[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=\textit{length of a side}\\ ----------\\ perimeter=s+s+s\\ perimiter=3s\\ 36=3s\\ \frac{36}{3}=s\\ 12=s \end{cases} \\\\\\ A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}[/tex]

ok.. .based on a side of 12, that's the area of the equilateral triangle, now, the hexagon has the same area... so... let's use the area of a polygon to see what's the length of a side

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\ cot\left( \frac{180}{n} \right)\qquad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of one side}\\ ----------\\ n=6\\ A=36\sqrt{3} \end{cases} \\\\\\ 36\sqrt{3}=\cfrac{1}{4}\cdot 6\cdot s^2\cdot cot\left( \frac{180}{6} \right)\implies 36\sqrt{3}=\cfrac{1}{4}\cdot 6\cdot s^2\cdot \sqrt{3} \\\\\\ 36\sqrt{3}=\cfrac{6s^2\sqrt{3}}{4}\implies \cfrac{4\cdot 36\sqrt{3}}{6\sqrt{3}}=s^2 \\\\\\ 24=s^2\implies \sqrt{24}=s\implies 2\sqrt{6}=s[/tex]

now, in case you want to check how much is the cot(30°), check your Unit Circle, recall, cotangent is cosine/sine

sweeps out equal areas in equal times.

Explanation:

As we know that there is no torque due to Sun on the planets revolving about the sun

so we will have

[tex]\tau_{net} = 0[/tex]

now we have

[tex]\frac{dL}{dt}= 0[/tex]

now we also know that

[tex]Area = \frac{1}{2}r^2d\theta[/tex]

so rate of change in area is given as

[tex]\frac{dA}{dt} = \frac{1}{2}r^2\frac{d\theta}{dt}[/tex]

so we will have

[tex]\frac{dA}{dt} = \frac{1}{2}r^2\omega[/tex]

[tex]\frac{dA}{dt} = \frac{L}{2m}[/tex]

since angular momentum and mass is constant here so

all planets sweeps out equal areas in equal times.

The output force on the larger area piston ( F ) = [tex]\frac{F_{1} }{A_{1} }[/tex] × A

Explanation:

Let

Area of the smaller cross section piston = [tex]A_{1}[/tex]

Force of the smaller cross section piston = [tex]F_{1}[/tex]

Area of the larger cross section piston = A

Force of the larger cross section piston = F

So the Pressure on the smaller cross section piston [tex]P_{1}[/tex] = [tex]\frac{F_{1} }{A_{1} }[/tex] ----------- (1)

And the Pressure on the larger cross section piston [tex]P_{}[/tex] = [tex]\frac{F}{A}[/tex] -------------(2)

When a given force is applied to the small piston the pressure on the smaller piston is equal to pressure on the larger piston. i.e. equation (1) is equal to equation (2)

⇒ [tex]P_{1}[/tex] = [tex]P_{}[/tex]

⇒ [tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F}{A}[/tex]

⇒ F = [tex]\frac{F_{1} }{A_{1} }[/tex] × A ------------(3)

This is the output force on the larger area piston.

B

Explanation:

B is the right answer that you're looking for 😉

Climate does describe the conditions in an area over a long period of time; weather does describe the day to day conditions in an area at a given time.

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL 🙂

1) Area = πr² = π × 3.5² = 38.48451, to the nearest tenth = 38.5 (option B)

2) Circumference = πd = π × (3.5 + 3.5) = π × 7 = 21.991... = 22.0 (option D)

3) Area = πr² = π × (12 ÷ 2)² = π × 6² = 113.097... = 113.0 (option A)

4) Area (semi-circle) = πr² ÷ 2. (π × (8 ÷ 2)²) ÷ 2 = 25.1327412287 (Area (rectangle) = l × w. 8 × 5 = 40. 40 + 25.1327412287 = 65.1327412287, to the nearest tenth = 65.1 (option C)

5) Area (circle) = πr² = π × 2² = 12.5663706144. Area (square) = l² = (2 × 2)² = 16. 16 - 12.5663706144 = 3.4336293856, to the nearest tenth = 3.4 (option C)

The correct answer is letter "C": New strict laws in the area require buildings in the industrial areas to reduce their emissions by 60% in the next 5 years.

Explanation:

According to the point of view of the author, the mild winters are caused due to high concentration of vehicle exhaust emitted in the region. However, from the research of the scientists, the mild winters are caused because of the increase in the rate of the commercial areas being changed into industrial areas. The idea that reinforces the scientists' point of view must blame the industrial workforce for the mild winters in the region. Out of the 5 options we have, letter "C" matches with the scientists position because if the new laws are already forcing industrial areas to reduce their emissions, it is because it has been proved that industrial areas are the main cause of the pollution in that region, not the concentration of vehicle exhaust as the author states.

A-B-A-B-A-A-C-C-D-A

Step-by-step explanation

10 might be different on some ppls keep that in mind 🙂

b. Climate describes the conditions in an area over a long period of time; weather describes the day to day conditions in an area at a given time.

Explanation:

Basically, weather corresponds to the atmospheric state in a given location momentarily. Therefore, the weather is subject to several variations. For example: in the morning, it can be cold; in the afternoon, it can be hot, with a temperature change in a short period of time. These changes are not just limited to temperature, but can also happen with respect to air humidity, the occurrence or not of rain, etc. Factors such as rainfall (rain), relative humidity, clouds and solar radiation act directly on the atmospheric conditions of a given place, thus influencing the weather.

To characterize a climate, an analysis over a long period is necessary. It can then be said that the climate is a set or succession of the types of weather and their elements. These times are observed over the seasons in a given location, over a period of approximately 30 years. Now, it is worth mentioning that if someone says: “The city of Belem, in Brazil, is very hot and very dry”, that person does not refer to the momentary state, because, to make this observation, it needed an analysis of a long period. Thus, the climate of the region in which the city of Belem is located is hot and dry, characterizing the climate known as dry tropical.

In summary, climate describes the conditions in an area over a long period of time; weather describes the day to day conditions in an area at a given time.

1.A

2.C

3.A

I am sorry i couldnt solve the rest.