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2 years ago

Review the equation used in writing a partial fraction decomposition.

Mathematics

1 answer:

Aleksandr [31]2 years ago

5 0

Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:

5A = -15.

-2A + B = 10.

<h3>What is the partial fraction?</h3>

The partial fraction is given as follows:

$\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}$

Applying the least common multiple at the right side, we have that:

$\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}$

$\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}$

Hence, comparing both sides of the equality:

5A = -15.

-2A + B = 10.

More can be learned about partial fractions at brainly.com/question/24594390

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Which expression is a sum of cubes?

erik [133]

we know that

A polynomial in the form $a^{3} +b^{3}$ is called a sum of cubes

Let's verify each case to determine the solution

case A) $-64x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-64=-4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case A) is not a sum of cubes

case B) $-32x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-32=-2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case B) is not a sum of cubes

case C) $32x^{6} y^{12} +125x^{9} y^{3}$

we know that

$32=2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

therefore

the case C) is not a sum of cubes

case A) $64x^{6} y^{12} +125x^{9} y^{3}$

we know that

$64=4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

Substitute

$4^{3}(x^{2})^{3}(y^{4})^{3} +5^{3}(x^{3})^{3}(y)^{3}$

$(4x^{2}y^{4})^{3} +(5x^{3}y)^{3}$

therefore

the answer is

$64x^{6} y^{12} +125x^{9} y^{3}$ is a sum of cubes

6 0

3 years ago

Read 2 more answers

In a recent survey 75 of the community favored building a police substation in their neighborlhood. If 20 citizens are chosen. W

Anton [14]

Answer:

Mean = 15

Standard deviation = 1.94

Step-by-step explanation:

We are given the following information:

We treat favoring of building a police substation as a success.

P(Success) = 75% = 0.75

Then the number of citizens follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 20

We have to find the mean and the standard deviation.

$\mu = np = 20(0.75 ) = 15\\\sigma = \sqrt{np(1-p)} = \sqrt{20(0.75)(1-0.75)} = 1.94$

Thus, the mean of favoring the substation is 15 and the standard deviation of favoring substation is 1.94

7 0

3 years ago

- Find the total tax deductions for each of the following weekly paychecks. weekly pay $198.00 $340.00 $250.00 FICA (7.65%)

Reptile [31]

Answer:

Total tax deduction per paycheck:

= Weekly pay * FICA tax rate.

Weekly pay $198.00:

= 198 * 7.65%

= 15.147

= $15.15

Weekly pay $340.00:

= 340 * 7.65%

= $26.01

Weekly pay $250.00:

= 250 * 7.65%

= 19.125

= $19.13

3 0

3 years ago

Solve the simultaneous equations 5x+4y = 1 and 3x - 6 y = 2.

hjlf

x=31,y=−61

Put the equations in standard form and then use matrices to solve the system of equations.

5x+4y=1,3x−6y=2

Write the equations in matrix form.

(534−6)(xy)=(12)

Left multiply the equation by the inverse matrix of (534−6).

inverse((534−6))(534−6)(xy)=inverse((534−6))(12)

The product of a matrix and its inverse is the identity matrix.

(1001)(xy)=inverse((534−6))(12)

Multiply the matrices on the left hand side of the equal sign.

(xy)=inverse((534−6))(12)

For the 2×2 matrix (acbd), the inverse matrix is (ad−bcdad−bc−cad−bc−bad−bca), so the matrix equation can be rewritten as a matrix multiplication problem.

(xy)=(5(−6)−4×3−6−5(−6)−4×33−5(−6)−4×345(−6)−4×35)(12)

Do the arithmetic.

(xy)=(71141212−425)(12)

Multiply the matrices.

(xy)=(71+212×2141−425×2)

Do the arithmetic.

(xy)=(31−61)

Extract the matrix elements x and y.

x=31,y=−61

5 0

4 years ago

Read 2 more answers

People at the state fair were surveyed about which type of

Ronch [10]

Answer:

Step-by-step explanation:

You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.

Pink Lemonade Yellow Lemonade TOTAL

Male 156 104 260

Female 72 48 120

TOTAL 228 152 380

P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6

P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6

Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6

6 0

4 years ago