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3 years ago

I would like to know what the answer to this is (-2x^2y^7)^2

Mathematics

1 answer:

satela [25.4K]3 years ago

6 0

Answer:

4x⁴y¹⁴

Step-by-step explanation:

When you have an expression in parentheses that is being raised to a power of any value where n ≠ 0, you distribute the exponent to every number enclosed.

(-2x²y⁷)²

Distributing to a number that is not already being raised by an exponent will be raised to the given power:

-2² = 4

4(x²y⁷)²

When distributing an exponent to a number that is already being raised to a given power, multiply the two exponents:

(x²)² = x²ˣ² = x⁴

(y⁷)² = y⁷ˣ² = y¹⁴

4x⁴y¹⁴

The simplified expression of (-2x²y⁷)² is 4x⁴y¹⁴.

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In a sewage treatment plant, a large concrete tank initially contains 440,000 liters of liquid and 10,000 kg of fine suspended s

viva [34]

Answer:

$Concentration = 8.26kg/m^3$

Step-by-step explanation:

Given

$V = 440000L$ --- volume of tank

$m = 10,000 kg$ --- solid mass

$r = 40000L/hr$ --- outflow rate

Required

Determine the concentration at the end of 4 hours

First, calculate the amount of liquid that has been replaced at the end of the 4 hours.

$Amount = r * Time$

$Amount = 40000L/hr * 4hr$

$Amount = 40000L * 4$

$Amount = 160000L$

This implies that, over the 4 hours; The tank has 160000 liters of liquid out of 440000 liters were replaced

Calculate the ratio of the liquid replaced.

$Ratio = \frac{Amount}{Volume}$

$Ratio = \frac{160000L}{440000L}$

$Ratio = \frac{16}{44}$

$Ratio = \frac{4}{11}$

Next, calculate the amount of solid left.

$Amount (Solid)= Ratio * m$

$Amount (Solid)= \frac{4}{11} * 10000kg$

$Amount (Solid)= \frac{40000}{11}kg$

$Amount (Solid)= 3636kg$

Lastly, the concentration is calculated as:

$Concentration = \frac{Amount (Solid)}{Volume}$

$Concentration = \frac{3636kg}{440000L}$

Convert L to cubic meters

$Concentration = \frac{3636kg}{440000* 0.001m^3}$

$Concentration = \frac{3636kg}{440m^3}$

$Concentration = 8.26kg/m^3$

3 0

3 years ago

Find the volume of a triangle prism with the following dimensions triangle base: 5ft

Andrews [41]

Hey there :)

We know the volume formula of a triangular prism
Volume = base area × height of prism

We are given:
Base of triangle = 5 ft
Height of triangle = 3 ft
Height of prism = 7.5 ft

Apply the formula
V = $\frac{1}{2}$ ( 5 )( 3 ) × 7.5
= 7.5 × 7.5
= 56.24 ft³