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3 years ago

(9x4 + 3x3y - 5x2y2 + xy3) ÷ (3x3 + 2x2y - xy2)

Mathematics

2 answers:

sattari [20]3 years ago

7 0

Answer:

3x-y

Step-by-step explanation:

This is a polynomial of 4th order.
To obtain the quotient, we use long division method

First step; in using long division method we look for a number which will multiply the first term of the denominator (divisor) to obtain exactly the first term of the numerator (dividend).

In this question, First term of the divisor is 3x³
First term of the numerator is 9x⁴

Hence, 3x³ multiply 3x = 9x⁴

Second step; multiply all the divisor by 3x and subtract the result from the dividend.

3x(3x³ + 2x²y - xy²) = 9x⁴ + 6x³y - 3x²y²

Subtract 9x⁴ + 6x³y - 3x²y² from 9x⁴ + 3x³y - 5x²y² + xy³

= 9x⁴ + 3x³y - 5x²y² + xy³ - (9x⁴ + 6x³y - 3x²y²)

= 9x⁴ + 3x³y - 5x²y² + xy³ - 9x⁴ - 6x³y +3x²y²

= -3x³y - 2x²y² + xy³ (this is the remainder after subtraction and becomes the new dividend)

Third step; note, the first term of the dividend has reduced to -3x³y, again think of a number that will multiply the first term of the divisor to obtain exactly -3x³y.

The number or term is '-y'; -y(3x³) = -3x³y

Fourth step; multiply all the divisor by -y and subtract the result from the dividend.

-y (3x³ + 2x²y - xy²) = -3x³y - 2x²y² + xy³

Subtract -3x³y - 2x²y² + xy³ from -3x³y - 2x²y² + xy³

= -3x³y - 2x²y² + xy³ - (-3x³y - 2x²y² + xy³)

= -3x³y - 2x²y² + xy³ +3x³y + 2x²y²- xy³

= 0

The remainder is now zero (0), we stop dividing

Note: All the terms used in multiplying the divisor before subtracting it from the dividend is the quotient of the long division.

HENCE, $\frac{9x^{4} +3x^{3}y-5x^{2}y^{2} + xy^{3}}{3x^{3} + 2x^{2}y -xy^{2}} = 3x-y$

babunello [35]3 years ago

5 0

We are asked to perform long division of the given problem where the expression 9x4 + 3x3y - 5x2y2 + xy3 is to be divided by the expression 3x3 + 2x2y - xy2

The solution is shown below:
3x + y
--------------------------------------
3x3 + 2x2y -xy2 √ 9x4 + 3x3y - 5x2y2 + xy3
- ( 9x4 + 6x3y - 3x2y2)
-----------------------------------------
0 - 3x3y - 2x2y2 + xy3
+ (3x3y + 2x2y2 - xy3 )
---------------------------------------
0
The answer is 3x + y. No remainder.

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The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer

AlladinOne [14]

Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=100 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$