-12c to the fourth power +18c to the third power! :)
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.
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
Solution:
Let the length of rectangle=x
Width of rectangle=x/10
Perimeter is 2(Length+Width)
= 2(x+x/10)
Area of Rectangle= Length* Width=x*x/10
As, Perimeter=2(Area)
So,2(x+x/10)=2(x*x/10)
Multiplying the equation with 10, we get,
2(10x+x)=2x²
Adding Like terms, 10x+x=11x
2(11x)=2x^2
22x=2x²
2x²-22x=0
2x(x-11)=0
By Zero Product property, either x=0
or, x-11=0
or, x=11
So, Width=x/10=11/10=1.1
Checking:
So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2
Area=Length*Width=11*1.1=12.1
Hence, Perimeter= 2 Area
As,24.2=2*12.1=24.2
So, Perimeter=2 Area
So, Answer:Length of Rectangle=11 units
Width of Rectangle=1.1 units
The definition of a rhombus is that it's a polygon with four congruent sides. If you split one into two pieces with a diagonal, then yes, it will be two isosceles triangles because two sides are congruent.
Answer:
Linear Pair
Step-by-step explanation:
The kind of angle formed by a and b when put together is a straight angle.
A straight angle means that a+b=180 degrees.
a and b are supplementary.
They are also a linear pair since they are already put together. Meaning, they share a common vertex and a common side while forming a straight angle together.
They aren't complementary because the angles exceed 90 degrees when added together. Complementary angles should add up to 90 degrees exactly.
They aren't vertical angles because they don't happen across from each other in two intersecting lines. (Note: Vertical angles are also congruent.)
They aren't alternate interior because they don't even happen at two different intersections. So we would definitely not go to to that, alternate exterior, same side interior, same exterior, or corresponding angles. Because all of these require the angles to happen at two different intersections.
