Which of the following statements best describes energy conservation in heat engines?

the half-life of carbon-14 is 5,730 years. After 11,460 year, how much of original carbon-14 remains?

Inessa [10]

Via the half-life equation:

$A_{final}=A_{initial}(\frac{1}{2})^{\frac{t}{h}}$

Where the time elapse is 11,460 year and the half-life is 5,730 years.

$A_{final}=A_{initial}(\frac{1}{2})^\frac{11460}{5730} \\\\A_{final}=A_{initial}\frac{1}{4} \\\\A_{final}=\frac{1}{4}A_{initial}$

Therefore after 11,460 years the amount of carbon-14 is one fourth (1/4) of the original amount.

6 0

3 years ago

what is the dot product and cross product of of two vectors if the angle is between them is 90 degree?

DaniilM [7]

$\sf{\pink{\underline{\underline{\blue{GIVEN:-}}}}}$

The angle between the two vectors is 90° .

$\sf{\pink{\underline{\underline{\blue{TO\: FIND:-}}}}}$

The dot product of two vectors .
The cross product of two vectors .

$\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}$

⚡ Let $\rm{\vec{a}}$ and $\rm{\vec{b}}$ are the two vectors .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:ab\cos{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\cos{90^{\degree}}\:}$

cos 90° = 0

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\times{0}\:}$

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:0\:}$

$\rm{\red{\therefore}}$ [1] The dot product of two vectors is “ 0 ” .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:\times\:\vec{b}\:=\:ab\sin{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\sin{90^{\degree}}\:}$

sin 90° = 1

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\times{1}\:}$

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\:}$

$\rm{\red{\therefore}}$ [2] The cross product of two vectors is “ ab ” .

3 0

3 years ago

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When an object is balanced about a pivot, the total clockwise moment must be equal to the total __________ __________. What two

Keith_Richards [23]

Answer:

When an object is balanced, about a pivot, the total clockwise moment must be equal to the total anticlockwise moment about that pivot.

Hope that helps.

5 0

2 years ago

The process by which the nuclei of radio active atoms are split into 2 or more smaller nuclei is called what

Andreas93 [3]

Are there multiple choice?

3 0

3 years ago

What is the Kinetic Energy of a 120 kg object that is moving with a velocity of 15 m/s

gizmo_the_mogwai [7]

Answer:

Kinetic Energy:120 x 15=1800

Explanation:

8 0

3 years ago

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