4/? Is equivelantnto ?/9

What is the solution to the rational equation x over 2x minus 1 plus 1 over 4 equals 2 over 2x minus 1

weeeeeb [17]

Answer:

the solution of given rational equation is x= 3/2

Step-by-step explanation:

$\frac{x}{2x-1}+\frac{1}{4} = \frac{2}{2x-1}$

We need to solve the above rational equation and find value of x

Finding LCM of 4 and (2x-1) we get 4(2x-1).

Multiplying 4(2x-1) on both sides of equation and solving

$\frac{x}{2x-1}*4(2x-1)+\frac{1}{4}*4(2x-1) = \frac{2}{2x-1}*4(2x-1)\\4x+2x-1=8\\6x-1=8\\6x=8+1\\6x=9\\x=9/6\\x=3/2$

So, the solution of given rational equation is x= 3/2

6 0

4 years ago

Help me with these please

olchik [2.2K]

Step-by-step explanation:

(1) y = x e^(x²)

Take derivative with respect to x:

dy/dx = x (e^(x²) 2x) + e^(x²)

dy/dx = 2x² e^(x²) + e^(x²)

dy/dx = (2x² + 1) e^(x²)

Take derivative with respect to x again:

d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)

d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)

d²y/dx² = (4x³ + 6x) e^(x²)

Substitute:

d²y/dx² − 2x dy/dx − 4y

= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)

= 4x³ + 6x − 2x (2x² + 1) − 4x

= 4x³ + 6x − 4x³ − 2x − 4x

= 0

(2) y = sin⁻¹(√x)

sin y = √x

sin²y = x

Take derivative with respect to x:

2 sin y cos y dy/dx = 1

sin(2y) dy/dx = 1

dy/dx = csc(2y)

Take derivative with respect to x again:

d²y/dx² = -csc(2y) cot(2y) 2 dy/dx

d²y/dx² = -2 csc²(2y) cot(2y)

Substitute:

2x (1 − x) d²y/dx² + (1 − 2x) dy/dx

= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)

Use power reduction formula:

= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)

= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)

= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)

= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)

= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)

= -sin²(2y) csc²(2y) cot(2y) + cot(2y)

= -cot(2y) + cot(2y)

= 0

8 0

3 years ago

A college student earned $7000 during summer vacation working as a waiter in a popular restaurant. The student invested part of

Lemur [1.5K]

<span>.09X+.08(7,000-X)=588
.09X+560-.08X=588
.01X=588-560
.01X=28
X=28/.01

X=2,800 AMOUNT INVESTED @ 9%.
7,000-2,800=4,200 AMOUNT INVESTED @ 8%
PROOF:
.09*2,800+.08*4,200=588
252+336=588
588=588</span>

5 0

4 years ago

Helppppppppppppppppppppppppppppppppppppppp

Klio2033 [76]

Answer:

B

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Marco has a piece of wood that measures 9 x 1/10 + 6 x 1/100 + 4 x 1/1000 how can this measurement be written as a decimal? you

spin [16.1K]

Answer:

The decimal number is 0.964

Step-by-step explanation:

we have

$9(\frac{1}{10})+ 6(\frac{1}{100})+4(\frac{1}{1,000})$

step 1

Multiply each fraction by the whole number

$(\frac{9}{10})+ (\frac{6}{100})+(\frac{4}{1,000})$

step 2

Convert each fraction in a decimal number

Remember

Move the decimal point to the left as many places as there are zeros in the factor.

Move the decimal point one step to the left (10 has one zero).

Move the decimal point two steps to the left (100 has two zeros)

Move the decimal point three steps to the left (1000 has three zeros)

$0.9+0.06+0.004$

step 3

Adds the number

$0.964$

5 0

3 years ago