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3 years ago

Simplify \sqrt{18x^7}

Mathematics

2 answers:

Pie3 years ago

7 0

Answer:

The first answer is B

The second answer is -1

Step-by-step explanation:

on edg.. good luck!!!

Slav-nsk [51]3 years ago

5 0

$\bf \sqrt{18x^7}\qquad 
\begin{cases}
18\\
\qquad 2\cdot 3\cdot 3\\
\qquad 2\cdot 3^2\\
x^7\\
\qquad x^{2+2+2+1}\\
\qquad x^2\cdot x^2\cdot x^2\cdot x^1\\
\qquad (x^2)^3x^1\\
\qquad (x^3)^2x^1
\end{cases}\implies \sqrt{2\cdot 3^2\cdot (x^3)^2\cdot x}
\\\\\\
3\cdot x^3\sqrt{2\cdot x}\implies 3x^3\sqrt{2x}$

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3 years ago

A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da

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Answer:

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Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

$f(x)=mx+b$

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

$c = mx+b$

We must find the values of m and b with the data provided. Substituting the first point:

$79 = 150m+b$

Substituting the second point:

$63.70 = 65m+b$

Both equations form the following system:

$\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.$

Subtracting both equations:

$150m-65m=79-63.70$

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

$85m=15.3$

Solving:

$m=15.3/85=0.18$

From the first equation

$79 = 150m+b$

Solving for b:

$b=79-150m=79-150(0.18) = 52.$

The model for the problem is:

$c=0.18x+52$

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$100=0.18x+52$

Solve for x:

$0.18x+52=100$

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$x=48/0.18=266.67$

Rounding to the closest integer:

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3 years ago

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3 years ago

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Answer:

The estimated amount of metal in the can is 87.96 cubic cm

Step-by-step explanation:

We can find the differential of volume from the volume of a cylinder equation given by

$V= \pi r^2 h$

Thus that way we will find the amount of metal that makes up the can.

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A small change in volume is given by:

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So finding the partial derivatives we get

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Evaluating the differential at the given information.

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Replacing all those values on the differential we get

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That give us

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Thus the volume of metal in the can is 87.96 cubic cm.

6 0

4 years ago