Answer:
Step-by-step explanation:
1) Solve the equation: [4ax - (a + b)](a + b) = 0, where a and b are constants.
- if a + b = 0, then x has infinitely many solutions
or
- 4ax = a + b
- x = (a + b)/4a, a≠0
2) Solve the equation m²x + 1 = m(x + 1), where m is a parameter.
- m²x + 1 - mx - m = 0
- (m²- m)x = m - 1
- m(m - 1)x = m - 1
- mx = 1
- x = 1/m, m≠0
3) Given that the equation a(2x - 1) = 3x - 3 has no solution, find the value of the parameter a.
- a(2x - 1) = 3x - 3
- 2ax - a = 3x - 3
- 2ax - 3x = a - 3
- (2a - 3)x = a - 3
- x = (a - 3)/(2a - 3)
<u>The equation has no solution if:</u>
2cos theta = 1 -> cos theta = 1/2
Then theta = pi/3 + 2npi or -pi/3 + 2npi, where n is random interger
And the domain is restricted in [0,2pi]
So answer will be pi/3 or 5pi/3
Answer:
0.375
Step-by-step explanation:
Just divide 3 over 8.
Answer:
Step-by-step explanation:
3x - 4y = 13 (1)
2x + y = 5 (2)
——————
3x - 4y = 13
4(2x + y = 5) (2) times 4
——————-
3x - 4y = 13
8x + 4y = 20
——————-
11x = 33
x = 33/11
x = 3
Plug x = 3 in (2):
2(3) + y = 5
6 + y = 5
y = 5-6
y = -1
Thus, x = 3 and y = -1
Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
