What would most likely happen if the decomposers were removed from the food web?

A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

Viefleur [7K]

Answer:

The rate of change of the area when the bottom of the ladder (denoted by $b$ ) is at 36 ft. from the wall is the following:

$\frac{dA}{dt}|_{b=36}=-571.2\, ft^2/s$

Explanation:

The Area of the triangle is given by $A=h\times b$ where $h=\sqrt{l^2-b^2}$ (by using the Pythagoras' Theorem) and $b$ is the length of the base of the triangle or the distance between the bottom of the ladder and the wall.

The area is then

$A=\sqrt{l^2-b^2}b$

The rate of change of the area is given by its time derivative

$\frac{dA}{dt}=\frac{d}{dt}\left(\sqrt{l^2-b^2}\cdot b\right)$

$\implies \frac{dA}{dt}=\frac{d}{dt}\left(\sqrt{l^2-b^2}\right)\cdot b+\frac{db}{dt}\cdot\sqrt{l^2-b^2}$

$\implies\frac{dA}{dt}=\frac{1}{2\sqrt{l^2-b^2}}\frac{d}{dt}(l^2-b^2)\cdot b+\sqrt{l^2-b^2}}\cdot \frac{db}{dt}$ Product rule

$\implies\frac{dA}{dt}=-\frac{1}{2\sqrt{l^2-b^2}}\cdot 2\cdot b^2\cdot \frac{db}{dt}+\sqrt{l^2-b^2}}\cdot \frac{db}{dt}$ Chain rule

$\implies\frac{dA}{dt}=-\frac{1}{\sqrt{l^2-b^2}}\cdot b^2\cdot \frac{db}{dt}+\sqrt{l^2-b^2}}\cdot \frac{db}{dt}$

$\implies\frac{dA}{dt}=\frac{db}{dt}\left(-\frac{1}{\sqrt{l^2-b^2}}\cdot b^2+\sqrt{l^2-b^2}}\right)$

In here we can identify $b=36\, ft$ , $l=39$ and $\frac{db}{dt}=8\,ft/s$ .

The result is then

$\frac{dA}{dt}=8\left(-\frac{1}{\sqrt{39^2-36^2}}\cdot 36^2+\sqrt{39^2-36^2}}\right)=-571.2\, ft^2/s$

3 0

3 years ago

What evidence indicates that a chemical change took place when the iron and sulfur combined to form iron sulfide? A. The element

fgiga [73]

Answer:

Explanation:burn the gas

5 0

3 years ago

Read 2 more answers

What increases the ability to see at night?

antiseptic1488 [7]

B is you answer sorry i dont quite know how to explain it in a way that you and anybody else would understand it.

3 0

3 years ago

Read 2 more answers

What aspect of speech sound is the primary factor in determining if one perceives the /ba/ sound or the /pa/ sound?

nignag [31]

The answer is voice onset time. It is a part of the production of stop consonants. Its definition is the length of time that passes between the release of a stop consonant and the start of the voicing and the vibration of the vocal folds.

3 0

3 years ago

9.

mote1985 [20]

Answer:

D. location

Explanation:

The gravitational field strength of Earth is determined by the virtue of the location within the Earth's gravitational field.

That's why all objects regardless of their mass, shape, and size free fall towards the Earth with an acceleration equal to the acceleration at that location in the absence of air resistance.

According to the gravitational force between two bodies, the force experienced by one body due to the other is independent of its own mass.

The gravitational force is given by equation

F = GMm/r²

If F is the force acting on the smaller body of mass 'm', then

F = ma

Therefore, the equation becomes,

ma = GMm/r²

a = GM/r²

The value of 'a' changes with respect to the value of 'r' such that if 'r' is the radius of the Earth, then the acceleration at a height 'h' from Earth surface is given by

a = GM/(r+h)²

Here it is clear that the acceleration at any point is only the inherent property of the Earth itself.

The gravitational field strength of Earth is determined by the virtue of the location within the Earth's gravitational field.

6 0

3 years ago