Mathematics, 30.07.2019 22:00, nikejenkins18

Apaper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top. if water is poured into the cup at a rate of 2cm3/s, how fast is the water level rising when the water is 5 cm deep?

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answered: bluebabyyy

Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 centimetres per second.

The volume of a cone of radius r and height h is given by:

$V = \frac{\pi r^2h}{3}$

Applying implicit differentiation, the rate of change is given by:

$\frac{dV}{dt} = \frac{2\pi r}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}$

In this problem:

The radius is constant, thus $\frac{dr}{dt} = 0$ .Height of 5 cm and radius of 3 cm, thus h = 5, r = 3

.Water poured at a rate of 2 cm³/s, thus $\frac{dV}{dt} = 2$

Then

$\frac{dV}{dt} = \frac{2\pi r}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}$

$2 = \frac{25\pi}{3}\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{6}{25\pi}$

$\frac{dh}{dt} = 0.0764$

The water level is rising at a rate of 0.0764 centimetres per second.

A similar problem is given at link

answered: floressavanna15

Let
h: height of the water
r: radius of the circular top of the water
V: the volume of water in the cup.
We have:
r/h = 3/10
So,
r = (3/10)*h
the volume of a cone is:
V = (1/3)*π*r^2*h
Rewriting:
V (t) = (1/3)*π*((3/10)*h(t))^2*h(t)
V (t) =(3π/100)*h(t)^3
Using implicit differentiation:
V'(t) = (9π/100)*h(t)^2*h'(t)
Clearing h'(t)
h'(t)=V'(t)/((9π/100)*h(t)^2)
the rate of change of volume is V'(t) = 2 cm3/s when h(t) = 5 cm.
substituting:
h'(t) = 8/(9π) cm/s

the water level is rising at a rate of:
h'(t) = 8/(9π) cm/s

answered: Guest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

answered: Guest

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126