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2 years ago

The circumference of a circle is 12π meters. find the circle diameter.

1 answer:

7 0

The circumference of a circle is 2*pi*r=C so plugging in numbers we have
12pi= 2*pi*r so solving for r gives 12pi/2pi=r which gives 6=r so the radius of the circle is 6 meters since diameter is just 2*r this gives 2*r =12 meters so
Diameter = 12meters

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A river flows due east at 1.60 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant v

Citrus2011 [14]

Answer:

part (a) $v\ =\ 10.42\ at\ 81.17^o$ towards north east direction.

part (b) s = 46.60 m

Explanation:

Given,

velocity of the river due to east = $v_r\ =\ 1.60\ m/s.$
velocity of the boat due to the north = $v_b\ =\ 10.3\ m/s.$

part (a)

River is flowing due to east and the boat is moving in the north, therefore both the velocities are perpendicular to each other and,

Hence the resultant velocity i,e, the velocity of the boat relative to the shore is in the North east direction. velocities are the vector quantities, Hence the resultant velocity is the vector addition of these two velocities and the angle between both the velocities are $90^o$

Let 'v' be the velocity of the boat relative to the shore.

$\therefore v\ =\ \sqrt{v_r^2\ +\ v_b^2}\\\Rightarrow v\ =\ \sqrt{1.60^2\ +\ 10.3^2}\\\Rightarrow v\ =\ 10.42\ m/s.$

Let $\theta$ be the angle of the velocity of the boat relative to the shore with the horizontal axis.

Direction of the velocity of the boat relative to the shore. $\therefore Tan\theta\ =\ \dfrac{v_b}{v_r}\\\Rightarrow Tan\theta\ =\ \dfrac{10.3}{1.60}\\\Rightarrow \theta\ =\ Tan^{-1}\left (\dfrac{10.3}{1.60}\ \right )\\\Rightarrow \theta\ =\ 81.17^o$

part (b)

Width of the shore = w = 300m

total distance traveled in the north direction by the boat is equal to the product of the velocity of the boat in north direction and total time taken

Let 't' be the total time taken by the boat to cross the width of the river. $\therefore w\ =\ v_bt\\\Rightarrow t\ =\ \dfrac{w}{v_b}\\\Rightarrow t\ =\ \dfrac{300}{10.3}\\\Rightarrow t\ =\ 29.12 s$

Therefore the total distance traveled in the direction of downstream by the boat is equal to the product of the total time taken and the velocity of the river $\therefore s\ =\ u_rt\\\Rightarrow s\ =\ 1.60\times 29.12\\\Rightarrow s\ =\ 46.60\ m$

7 0

3 years ago

SP1b.

nata0808 [166]

Answer:

2 m/s^2, west

Explanation:

Vf=final velcoity

Vi=initial velocity

t=timw

$a = \frac{vf - vi}{t}$

$\frac{15 - 25}{5}$

= - 2 m/s^2

The - changes direction and makes it opposite

2 m/s, west

3 0

2 years ago

How loudness of a sound wave depends on the intensity of the sound wave?

Anestetic [448]

Loudness of a sound wave is directly proportional to the intensity of the sound wave. In other words, when one increases, other also increases and vice-versa

Hope this helps!

3 0

3 years ago

Newton's Law of Cooling says that the rate of cooling of an object is proportional to the difference between its own temperature

ASHA 777 [7]

Answer:

$\frac{dQ}{dt} =-hA\Delta T(t)$

Explanation:Newton.s law of cooling states that the rate of cooling of an object is proportional to the difference between its own temperatures and temperature of its surroundings. Mathematically,

$\frac{dQ}{dt} =-hA [T(t)-T(s)]\\$