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2 years ago

Solve: 4x+6y+2=0 and 9y=6x+21

Mathematics

2 answers:

AVprozaik [17]2 years ago

6 0

I hope this helps you

user100 [1]2 years ago

5 0

X=-2 and the other variable will be y=1

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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

2 years ago

What is the difference of the rational expressions below? x/x-2 - 3/x

Lera25 [3.4K]

Answer:

x^2-3x+6/x^2-2x

Step-by-step explanation:

5 0

3 years ago

A triangle has sides of lengths 10 24 and 26 is it a right triangle explain?

Romashka-Z-Leto [24]

Yes. For right triangles, the sum of the squares of the shorter sides is equal to the square of the longer side. Thus, this is a right triangle if 10^2+24^2=26^2. Expanding these squares, we have 100+576=676, which is true. Thus, the triangle is right.

6 0

3 years ago

Read 2 more answers

4*7, 5384 divided by 7538

Darya [45]

Answer:40.00212258

Step-by-step explanation:

(4 x 75384) ➗ 7538

301536 ➗ 7538=40.00212258

7 0

3 years ago

You are opening a new checking account. Gringotts Bank has more branches nearby than Tellson’s Bank but charges more fees for ca

Shalnov [3]

Your opening a account

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2 years ago