Answer:
dy/dx = -5y - y/x
Step-by-step explanation:
In xy + 5x = 30
Differentiating xy implicitly
y + xdy/dx
Assuming u = xy
In xy = In u
Differentiating In u = 1/u = 1/xy
Differentiating 5x = 5 and differentiating a constant (30) = 0
1/xy(y + xdy/dx) + 5 = 0
(y + xdy/dx)/xy = -5
(y + xdy/dx) = -5xy
xdy/dx = -5xy - y
dy/dx = = (-5xy - y)/x
dy/dx = -5y - y/x
In decimal form it is 8000.00, in word form it is exactly as in the question ten times to the right
Heya !
In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.
Here , one complex root is given -6i hence , the other must be 6i.
Hope it helps you ! :)
Answer:
The number is -6
The second operation is -60
Step-by-step explanation:
Let the number be x.
Solving (a): The value of x
Operations 1:
Multiply by 3: 3x
Add 40: 3x + 40
Operations 2:
Add 17: x + 17
Multiply by 2: (x + 17) * 2
To find x, equate both operations.
Collect like terms
Solving (b):
Operations:
Subtract 9: 
Multiply by 4: 
This gives:
For the axis of symmetry it will be -b/2a but in this case the axis of symmetry is going to be y=4. the x intercept will be the roots (2,0) and (6,0) and for the y intercept it will be (0,3) since the parabola crosses the y axis at (0,3)
