All categories

2 years ago

Find the values of z and y pls :)

Mathematics

1 answer:

stellarik [79]2 years ago

4 0

Measure of z is 116°.The measure of y is 48°.Hope this helps.

You might be interested in

True or false?

olga2289 [7]

Answer:

True

Step-by-step explanation:

An exterior angle must form a linear pair with an interior angle.

3 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

Need help please on Pre Calculus!!! Directions: verify each identity

Juliette [100K]

You first simplify

tan(x) = cos(x)/sin(x) and cot(x) = sin(x)/cos(x)

Then you plug that in and then you simplify even more

3 0

3 years ago

What is the slope of the line that passes through the points (12,-8) and (-9,-11)

Sauron [17]

Answer: 1/7

Explanation:

1. Use the formula, y2-y1/x2-x1
Plug in the points, (12, -8) and (-9, -11) into the formula.
Point (12, -8): 12 is the X1 and -8 is the y1.
Point (-9, -11): -9 is the X2 and -11 is the y2
So, -11--8/-9-12

2. -11--8/-9-12= -3/-21= 1/7

I hope this helps!!

3 0

2 years ago

Assume f(x) = g(x). Which of the following two functions may be used to represent the function 3x = x – 4?

mixer [17]

$\bf \stackrel{f(x)}{3x}~~=~~\stackrel{g(x)}{x-4}$

6 0

2 years ago