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3 years ago

Help me prove this trig identity

Mathematics

1 answer:

alexdok [17]3 years ago

3 0

Hello here is a solution:

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PLS TRY TO ANSWER ASAP.

Harrizon [31]

Answer:

0.075 m/min

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

1. Write the equation for the volume of the cone:

$V=\dfrac{1}{3}\pi r^2h$

2. Find the relation between the radius and the height:

r = diameter/2 = 5m/2 = 2.5m

h = 5.2m

h/r =5.2 / 2.5 = 2.08

3. Filling the tank:

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

x/y=r/h

y = x . h / r

The volume of water inside the cone is:

$V=\dfrac{1}{3}\pi x^2y$

$V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3$

4. Find the derivative of the volume of water with respect to time:

$\dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}$

5. Find x² when the volume of water is 8π m³:

$V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\ 11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062$ m²

6. Solve for dx/dt:

$1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}$

$\dfrac{dx}{dt}=0.03596m/min$

7. Find dh/dt:

From y/x = h/r = 2.08:

$y=2.08x\\\\\\\dfrac{dy}{dx}=2.08\dfrac{dx}{dt}\\\\\\\dfrac{dy}{dt}=2.08(0.035964m/min)=0.0748m/min\approx0.075m/min$

That is the rate at which the water level is rising when there is 8π m³ of water.

4 0

3 years ago

The range of the following relation R {(3, -5), (1,2),(-1,-4),(-12)}

lukranit [14]

Answer:

The range of the following relation is(-5,2,-4)

6 0

3 years ago

Which best describes the end behavior of y=-2x^3?

natka813 [3]

Answer:i believ the its the last one

Step-by-step explanation:

For end behaviour, note the leading coefficient and the degree. The degree is odd and the leading coefficient negative, hence it would rise to the left and fall to the right.

3 0

3 years ago

Read 2 more answers

Are these ratios equivalent? Use the proportion method to solve. 18 magazines every 8 months and 9 magazines every 4 months

andreyandreev [35.5K]

Answer:

Yes , those ratios are equivalent, because if you simply 18:8 inti the smpilest form you'll get 9:4.

Step-by-step explanation:

18:8= 18/8

18/8÷2/2=9/4

7 0

3 years ago

if each bag holds 3.75 pounds and they use 0.75 pound of birdseed each each day, for how many will one bag last

aniked [119]

It will last 5 days. That's what I got. :D

4 0

3 years ago