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Mathematics

2 answers:

kykrilka [37]3 years ago

4 0

She can choose any one of 3 sweaters. For each choice of sweater . . .

She can choose any one of 4 skirts.

The total number of different ways to choose an outfit = (3 x 4) = 12 .

laiz [17]3 years ago

3 0

12 possible outcomes.

Sweater A
Sweater B
Sweater C

Skirt 1
Skirt 2
Skirt 3
Skirt 4

Possible ways:

A1, A2, A3, A4
B1, B2, B3, B4
C1, C2, C3, C4

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Whats 1-2x+3y for x=-2 and y=-5 ?

lawyer [7]

Answer:

-10

Step-by-step explanation:

2*-2=-4

3*-5=-15

1-(-4)+(-15)=-10

5 0

3 years ago

Integrate 1 - x / x(x2 + 1) d x by partial fractions.

solniwko [45]

Answer:

$log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x$

Step-by-step explanation:

step 1:- by using partial fractions

$[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }$ ......(1)

step 2:-

solving on both sides

$1-x=A(x^{2} +1)+(Bx+C)x......(2)$

substitute x =0 value in equation (2)

1=A(1)+0

A=1

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

-1 = C

step 3:-

substitute A,B,C values in equation (1)

now

$\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 } d x -\int\limits \frac{1}{x^{2}+1 } d x$