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Lelechka [254]
3 years ago
10

Simplify the cube root in simplest radical form. 9x374 Please help

Mathematics
1 answer:
algol [13]3 years ago
6 0

Answer:

D. xy\sqrt[3]{9y}

Step-by-step explanation:

\sqrt[3]{9x^3y^4}

\sqrt[3]{9}\sqrt[3]{x^3}\sqrt[3]{y^4}

The \sqrt[3]{x^3} cancels out to become x:

\sqrt[3]{9}x\sqrt[3]{y^4}

Split the y^4=y*y^3

\sqrt[3]{9}x\sqrt[3]{y^3}\sqrt[3]{y^1}

\sqrt[3]{y^3} =y

xy\sqrt[3]{9} \sqrt[3]{y}

Put the cube root of y and cube root of 9 together:

xy\sqrt[3]{9y}

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The answer if 7 years, if you multiply 2,000 by .02 it equals 40. so you divide 280 by 40 and get 7
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Solve the equation by multiplying by a power of 10.<br><br><br> 3.1x - 10 = 1.6x + 35
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Simple answer to the equation without the circumstances:
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Step-by-step explanation:

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3 years ago
A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns,
guajiro [1.7K]

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation A=45e^{-0.05t}.

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate A=15 and solve for t as:

15=45e^{-0.05t}

\frac{15}{45}=\frac{45e^{-0.05t}}{45}

\frac{1}{3}=e^{-0.05t}

Now we will switch sides:

e^{-0.05t}=\frac{1}{3}

Let us take natural log on both sides of equation.

\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})

-0.05t\cdot (1)=\text{ln}(\frac{1}{3})

-0.05t=\text{ln}(\frac{1}{3})

t=\frac{\text{ln}(\frac{1}{3})}{-0.05}

t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}

t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}

t=-\text{ln}(\frac{1}{3})\cdot 20

t=-(\text{ln}(1)-\text{ln}(3))\cdot 20

t=-(0-\text{ln}(3))\cdot 20

t=20\text{ln}(3)

Therefore, it will take 20\text{ln}(3) years for area of the glacier to decrease to 15 square kilo-meters.

6 0
3 years ago
The following data give the prices of seven textbooks randomly selected from a university bookstore.
swat32

Answer:

a) Mean = $121

Sum of deviations = $0

b) Standard deviation = 41.19

Variance = 1696.67

Range = $120

Step-by-step explanation:

We are given the following data:

$91 , $176 , $108 , $115 , $56 , $157 , $144

a) Mean and sum of deviations

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{847}{7} = 121

Sum of deviations =

-30 + 55 - 13 - 6 - 65 + 36 + 23 = 0

The sum of deviations is zero dollars.

b) range, variance, and standard deviation

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of square of differences =

900 + 3025 + 169 + 36 + 4225 + 1296 + 529 = 10180

\sigma = \sqrt{\dfrac{10180}{6}} = 41.19\\\\\sigma^2 = 1696.67

Sorted data: 56, 91, 108, 115, 144, 157, 176

Range = Maximum - Minimum

Range = 176 - 56 = 120

5 0
3 years ago
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