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2 years ago

Help me I'm stuck perhaps a little while

Mathematics

2 answers:

Finger [1]2 years ago

4 0

The answer is 6 1/3 u have to simplify

lys-0071 [83]2 years ago

3 0

Shouldn't it be 5 4/3?

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What are the domain and range of the function f(x) = 3X + 5?

Yakvenalex [24]

Answer:

Domain: x ER

Range: f(x) ER

4 0

3 years ago

Please, I need help in this ??

nignag [31]

Answer:

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

Step-by-step explanation:

$\int\frac{x^{4}}{x^{4} -1}dx$

Adding and Subtracting 1 to the Numerator

$\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx$

Dividing Numerator seperately by $x^{4} - 1$

$\int 1 + \frac{1}{x^{4}-1 }\, dx$

Here integral of 1 is x +c1 (where c1 is constant of integration

$x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx$ ----------------------------------(1)

We apply method of partial fractions to perform the integral

$\frac{1}{(x-1)(x+1)(x^{2}+1)}$ = $\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}$ ------------------------------------------(2)

$\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}$

1 = $A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)$ -------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = $\frac{1}{4}$

1 = B(-1-1)(1+1)

B = $-\frac{1}{4}$

1 = C(i-1)(i+1)

C = $-\frac{1}{2}$

Substituting A, B, C in equation (2)

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }$

On integration

Here $\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx$

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\frac{1}{4} ln(x-1)$ - $\frac{1}{4} ln(x+1)$ - $\frac{1}{2} arctanx$ + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

$x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2$

Here c1 + c2 can be added to another and written as c

Therefore,

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

4 0

3 years ago

Granola costs $6.50 per pound. Assorted nuts cost $9 per pound. How many pounds of granola and nuts are needed to make 9 pounds

bezimeni [28]

Answer:

3.6 pounds of granola and 5.4 pounds of nuts

Step-by-step explanation:

Let the required granola be x pounds, then amount of nuts is 9 - x.

<u>The price of the mixture is as below equation:</u>

6.5x + 9(9 - x) = 8*9
6.5x + 81 - 9x = 72
81 - 2.5x = 72
2.5x = 81 - 72
2.5x = 9
x = 9/2.5
x = 3.6

<u>Find the amount of nuts:</u>

9 - 3.6 = 5.4

7 0

1 year ago

How to solve 3(×-5)-5=23

USPshnik [31]

Step 1: Simplify both sides of the equation.

3(x−5)−5=23

(3)(x)+(3)(−5)+−5=23(Distribute)

3x+−15+−5=23

(3x)+(−15+−5)=23(Combine Like Terms)

3x+−20=23

3x−20=23

Step 2: Add 20 to both sides.

3x−20+20=23+20

3x=43

Step 3: Divide both sides by 3.

3x /3 = 43 /3

x= 43 /3

4 0

2 years ago

Read 2 more answers

These four numbers are plotted on a number line: -2/3 5/8 -3/5 -1/2 Which is the correct ordering on the number line, from left

Yuki888 [10]

Answer:

-2/3 -3/5 -1/2 3/8

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3 0

2 years ago