Answer:
Step-by-step explanation:
The directional derivative of a function in a particular direction u is given as the dot product of the unit vector in the direction of u and the gradient of the function
g(x,y) = sin(π(x−5y)
∇g = [(∂/∂x)î + (∂/∂y)j + (∂/∂z)ķ] [sin(π(x−5y))
(∂/∂x) g = (∂/∂x) sin (πx−5πy) = π [cos(π(x−5y))]
(∂/∂y) g = (∂/∂y) sin (πx−5πy) = - 5π [cos (π(x−5y))]
∇g = π [cos(π(x−5y))] î - 5π [cos (π(x−5y))] j
∇g = π [cos (π(x−5y))] [î - 5j]
So, the question requires a direction vector and a point to fully evaluate this directional derivative now.
Answer:
Thus, the two root of the given quadratic equation 
is 5.24 and 0.76 .
Step-by-step explanation:
Consider, the given Quadratic equation,
This can be written as , 
We have to solve using quadratic formula,
For a given quadratic equation 
we can find roots using,
...........(1)
Where, 
is the discriminant.
Here, a = 1 , b = -6 , c = 4
Substitute in (1) , we get,
and 
We know 
(approx)
Substitute, we get,
(approx) and 
(approx)
(approx) and 
(approx)
Thus, the two root of the given quadratic equation is 5.24 and 0.76 .
I am not certain of what you wrote for the function but will assume that is likely exponential function or quadratic function.
First, (quadratic function) To solve this, you must know the quadratic formula. The x-intercept is value(s) that has the output value(y) of 0.
If the vertex of the quadratic function of (0,0), there is only one x-intercept. The number and value of the x-intercept depends on the slope and vertical displacement.
Second, (exponential function) note that there is no x-intercept. For instance, if a is 2, is there such value y that 2^y is 0? The smallest exponential value that is an integer is 1. Even broadening the limit to rational numbers, no such exponential value can have the result of 0. Therefore, in the basic form of exponential function, there is no x-intercept.
S/4-6.8=-9.8
S/4= -9.8+6.8
S/4= -3
S=-3*4
S= -12
Let angle be x
4 times complement = 4(90 - x)
2/3 times its supplement = 2/3(180 - x)
4(90 - x) = 2/3 (180 - x)
360 - 4x = 120 - 2/3 x
240 = 3 1/3 x
x = 240 / 10/3 = 240 * 3/10 = 72 degrees Answer
