Solve 3x^2y z = 7100

Question

Solve the equation

Solve for x

Solve for y

Solve for z

x = \frac{10 213 yz}{3 ∣ yz ∣} x = - \frac{10 213 yz}{3 ∣ yz ∣}

Evaluate

3 x^{2} yz = 7100

Rewrite the expression

3 yz x^{2} = 7100

Divide both sides

\frac{3 yz x ^{2}}{3 yz} = \frac{7100}{3 yz}

Divide the numbers

x^{2} = \frac{7100}{3 yz}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{7100}{3 yz}

Simplify the expression

More Steps

Evaluate

\frac{7100}{3 yz}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{7100}{3 yz}

Simplify the radical expression

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Evaluate

7100

Write the expression as a product where the root of one of the factors can be evaluated

100 \times 71

Write the number in exponential form with the base of 10

1 0^{2} \times 71

The root of a product is equal to the product of the roots of each factor

1 0^{2} \times 71

Reduce the index of the radical and exponent with 2

1071

\frac{10 71}{3 yz}

Multiply by the Conjugate

\frac{10 71 \times 3 yz}{3 yz \times 3 yz}

Calculate

\frac{10 71 \times 3 yz}{3 ∣ yz ∣}

Calculate the product

More Steps

Evaluate

71 \times 3 yz

The product of roots with the same index is equal to the root of the product

71 \times 3 yz

Calculate the product

213 yz

\frac{10 213 yz}{3 ∣ yz ∣}

x = \pm \frac{10 213 yz}{3 ∣ yz ∣}

Solution

x = \frac{10 213 yz}{3 ∣ yz ∣} x = - \frac{10 213 yz}{3 ∣ yz ∣}

Show Solution

Find \frac{\partial z}{\partial x} by differentiating the equation directly

Find \frac{\partial z}{\partial y} by differentiating the equation directly

\frac{\partial z}{\partial x} = - \frac{2 z}{x}

Evaluate

3 x^{2} yz = 7100

Find \frac{\partial z}{\partial x} by taking the derivative of both sides with respect to x

\frac{\partial}{\partial x} (3 x^{2} yz) = \frac{\partial}{\partial x} (7100)

Use differentiation rule \frac{\partial}{\partial x} (f (x) \times g (x)) = \frac{\partial}{\partial x} (f (x)) \times g (x) + f (x) \times \frac{\partial}{\partial x} (g (x))

\frac{\partial}{\partial x} (3 x^{2} y) z + 3 x^{2} y \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (7100)

Evaluate

More Steps

Evaluate

\frac{\partial}{\partial x} (3 x^{2} y)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

3 y \times \frac{\partial}{\partial x} (x^{2})

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

3 y \times 2 x

Multiply the terms

6 x y

6 x yz + 3 x^{2} y \times \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (7100)

Evaluate

6 x yz + 3 x^{2} y \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (7100)

Evaluate

6 x yz + 3 y x^{2} \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (7100)

Find the partial derivative

6 x yz + 3 y x^{2} \frac{\partial z}{\partial x} = 0

Move the expression to the right-hand side and change its sign

3 y x^{2} \frac{\partial z}{\partial x} = 0 - 6 x yz

Removing 0 doesn't change the value,so remove it from the expression

3 y x^{2} \frac{\partial z}{\partial x} = - 6 x yz

Divide both sides

\frac{3 y x ^{2} \frac{\partial z}{\partial x}}{3 y x ^{2}} = \frac{- 6 x yz}{3 y x ^{2}}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 6 x yz}{3 y x ^{2}}

Solution

More Steps

Evaluate

\frac{- 6 x yz}{3 y x ^{2}}

Cancel out the common factor 3

\frac{- 2 x yz}{y x ^{2}}

Reduce the fraction

\frac{- 2 yz}{y x}

Reduce the fraction

\frac{- 2 z}{x}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{2 z}{x}

\frac{\partial z}{\partial x} = - \frac{2 z}{x}

Show Solution