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Paladinen [302]
2 years ago
14

Find the modulus of -2-6i A. 40 B. -40 C. 6.3 D. -6.3

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
8 0

Answer:

Option C.  6.3

Step-by-step explanation:

we know that

To find the modulus of a complex number, apply the Pythagoras theorem

Let

c-----> the modulus

c=\sqrt{(-2)^{2}+(-6)^{2}}

c=\sqrt{4+36}

c=\sqrt{40}=6.3

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3 years ago
3 2/3 divided by 2 2/3
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1 3/8

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3 2/3 = 11/3

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3 /min and its coarseness is such that it forms a pile in the shap
pantera1 [17]

Answer:

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

i.e \dfrac{dV}{dt}= 20 \ ft^3/min

we know that radius r is always twice the   diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

V = \dfrac{\pi r^2 h}{3}

V = \dfrac{\pi (h/2)^2 h}{3}

V = \dfrac{1}{12} \pi h^3

V = \dfrac{ \pi h^3}{12}

Taking the differentiation of volume V with respect to time t; we have:

\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}

\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}

we know that:

\dfrac{dV}{dt}= 20 \ ft^3/min

So;we have:

20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}

20= 56.25 \pi \times \dfrac{dh}{dt}

\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

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