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4 years ago

What will be the remainder when 6x ^5+ 4x^4 -27x^

Mathematics

1 answer:

Furkat [3]4 years ago

6 0

Answer:

Remainder = (3145/8)x - 408

Step-by-step explanation:

We want to find the remainder when 6x^(5) + 4x⁴ - 27x³ - 7x² + 27x + 3/2 is divided by (2x² - 3)²

Let's expand (2x² - 3)² to give ;

(2x - 3)(2x - 3) = 4x² - 6x - 6x + 9 = 4x² - 12x + 9

So,we can divide now;

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

First of all, we'll divide the term with the highest power inside the long division symbol by the term with the highest power outside the division symbol. This will give;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

We now subtract the new multiplied term beneath the original one from the original one to get;

3/2x³

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x²

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

(3/2)x³ + (11/2)x² + (159/8)x

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

We'll now divide the term in new polynomial gotten with the highest power by the term with the highest power outside the division symbol. This gives;

(3/2)x³+(11/2)x²+(159/8)x+(91/2)

______________________

4x²-12x+9 |6x^(5)+4x⁴-27x³-7x²+27x+3/2

6x^(5)-18x⁴-(27/2)x³

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

22x⁴+(27/2)x³-7x²+27x +3/2

22x⁴-66x³ + (99/2)x²

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

(159/2)x³-(113/2)x²+27x+(3/2)

(159/2)x³-(477/2)x²+(1431/8)x

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

182x²-(1215/8)x + (3/2)

182x²-545x + 819/2

We now subtract the new multiplied term beneath the immediate one from the immediate one to get;

182x² - (1215/8)x + (3/2) - 182x² + 545x - 819/2 = (3145/8)x - 408

Remainder = (3145/8)x - 408

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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a

lutik1710 [3]

The number of classes Anna can take so the total cost for the month will be the same is 5.

The monthly cost would be $37.50.

<h3>When would the total cost be the same?</h3>

When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms: 7.5x - 5.5x = 10
Add similar terms: 2x = 10
Divide both sides by 2 : 10 /2 = 5

Monthly cost when the cost is the same: 7.5 x 5 = $37.50

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2 years ago

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solut

Mars2501 [29]

Answer:

Option (4)

Step-by-step explanation:

An ordered pair (x, y) represents,

x = number of days that a library book is late

y = Total fee for the delay

Late fee of a library book = $0.30 per day

Then late fee of a book for the delay of 'x' days,

y = per day fee × number of days delayed

y = $0.30\times x$

Option (1). For (-3, -0.90)

Since number days can't be negative so not the answer.

Option (2). For (-2.5, -0.75)

Number of days are negative so can't be the answer.

Option (3). For (4.5, 1.35)

Fee for 4.5 days will be,

y = 0.30(4) [Since fee is charged after completion of one day or in the midnight]

Fee for 4.5 days will be the same as fee for 4 days.

y = $1.20

Therefore, this option will not be the answer.

Option (4). For (8, 2.40)

y = 0.30x

y = 0.30(8)

y = 2.40

Therefore, option (4) will be the answer.

3 0

3 years ago

Someone please help me anyone ?

pishuonlain [190]

The answer in this question is 14.5.

Just add those numbers together and divide it by the amount of students

7 0

4 years ago

The formula for an arithmetic series is shown below, where n = 1, 2, 3 ...

lisov135 [29]

Answer:

4th term = 28

5th term = 37

6th term = 45

Step-by-step explanation:

f(n + 1) = f(n) + 8

f(1) = 5

f(1 + 1) = f(1) + 8 = 5+8 = 13

f(2) = 13

f(2 + 1) = f(2) + 8 = 13+8 = 21

Thus, series is 5, 13, 21......

In arithmetic series

Nth term is given by

n th term = a + (n-1)d

where a is the first term

and d is the common difference.

common difference d = nth term - (n-1)th term

For this series

a = 5

lets take nth term as 2nd term and 1st term as (n-1)th term

d = 13-5 = 8

n th term = a + (n-1)d

using the formula for nth term

4th term = 5 + (4-1)8 = 29

5th term = 5 + (5-1) 8= 37

6th term = 5+ (6-1)8 = 45

Thus, 4th term = 28

5th term = 37

6th term = 45

Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.

5 0

3 years ago

Consider rolling a fair die thrice and tossing a fair coin sixteen times. Assume that all the tosses and rolls are independent.

Trava [24]

The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Given a fair dice and tossing a fair coin sixteen times.

We have to find the probability that the total number of heads in all the coin tosses equals 12.

The probability lies between 0 and 1.

Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.

Let X shows the sum of heads while tossing.

P(X=12)=?

We can find the probability using binomial theorem.

= $16C_{12} (0.5)^{12} (0.5)^{2}$

We have to toss sixteen times and out of 16 times we need head 12 times.

=16!/12!4!*0.00024*0.0625

=1820*0.000015

=0.0273

Hence the probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Learn more about probability at brainly.com/question/24756209

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8 0

2 years ago