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aev [14]
2 years ago
13

If you subtract 16 from my number and multiply the difference by -7, the result is -154 What is my number

Mathematics
1 answer:
adell [148]2 years ago
7 0

Answer:

16-x*(-7)=-154

7x =-154-16

7x/7=-170/7

X=-24.29

Step-by-step explanation:

Let x represent "my number"

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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
Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t
Marat540 [252]

Answer:

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0 (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B, C - Circunference constants.

Given the number of variable, we need the location of three distinct points:

(x_{1},y_{1}) = (6,0)

36 +6\cdot A + C = 0

(x_{2},y_{2}) = (8,4)

80 + 8\cdot A + 4\cdot B + C = 0

(x_{3},y_{3}) = (3,9)

90 + 3\cdot A + 9\cdot B + C = 0

Then, we have the following system of linear equations:

6\cdot A + C = -36 (2)

8\cdot A +4\cdot B + C = -80 (3)

3\cdot A + 9\cdot B + C = -90 (4)

The solution of this system is:

A = -6, B = -8, C = 0

By comparing the general form with the standard form of the equation of the circunference is:

A = -2\cdot h (5)

B = -2\cdot k (6)

C = h^{2}+k^{2}-r^{2} (7)

Where:

h, k - Coordinates of the center of the circle.

r - Radius of the circle.

If we know that A = -6, B = -8 and C = 0, then coordinates of the center of the circle and its radius are, respectively:

h = -\frac{A}{2}

k = -\frac{B}{2}

r = \sqrt{h^{2}+k^{2}-C}

h = 3, k = 4, r = 5

The location of the new cell phone tower is (h,k) = (3,4), and the equation of the circle is x^{2}+y^{2} -6\cdot x - 8\cdot y = 0.

3 0
2 years ago
What is the slope and y-intercept of the line 2x + 3y = 12
sdas [7]

Answer:

2/3 is the slope and 4 is the 4 intersept

Step-by-step explanation:

7 0
3 years ago
What is the least even number you can make with the digits 5 2 7 3 6 4 0?
coldgirl [10]
0234576 You just need to put the numbers in order form least to greatest and leave an even number at the end. 
5 0
3 years ago
Darlene was asked to identify which of the following numbers is prime. Witch number should she choose
nordsb [41]
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191 those are some prime numbers :)
5 0
3 years ago
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