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2 years ago

Name the angle relationship. Find the measure of angle b.

Mathematics

2 answers:

icang [17]2 years ago

8 0

<h3><u>Answer:</u></h3>

Vertically opposite angle b = 86 °

<h3><u>Step-by-step explanation:</u></h3>

Angle b and angle 86° both are equal because they are vertical opposite of each other.

yarga [219]2 years ago

5 0

Answer:

vertical angles b= 86

Step-by-step explanation:

b is equal to 86 since the angles are vertical angles

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sp2606 [1]

Answer:

The volume is decreasing at a rate 20π cubic meter per hour.

Step-by-step explanation:

We are given the following in the question:

The radius is increasing at a rate 1 meter per hour.

$\dfrac{dr}{dt} = 1\text{ meter per hour}$

The height is decreasing at a rate 4 meter per hour

$\dfrac{dh}{dt} = -4\text{ meter per hour}$

At an instant time t,

r = 5 meter

h = 8 meters

Volume of cylinder =

$\pi r^2 h$

where r is the radius and h is the height of the cylinder.

Rate of change of volume is given by:

$\dfrac{dV}{dt} = \dfrac{d(\pi r^2 h)}{dt}\\\\\dfrac{dV}{dt} = 2\pi rh\dfrac{dr}{dt} + \pi r^2\dfrac{dh}{dt}$

Putting all the values we get,

$\dfrac{dV}{dt} = 2\pi (5)(8)(1) + \pi (5)^2(-4)\\\\\dfrac{dV}{dt} = 80\pi - 100\pi = -20\pi \approx -62.8$

Thus, the volume is decreasing at a rate 20π cubic meter per hour or 62.8 cubic meter per hour.

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