Graph the linear inequality x<3
1 answer:
Dot or draw a small uncolored circle at 3 and straight line to the left or to negative infinity as shown in the number line below.
or if you mean in coordinate plane then just draw the straight horizon line (ellipsis) at x=3 and color from x=2 to negative infinite or to the left side as shown in the second image.
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Answer:
The given power series is a solution of the differential equation (1+x^2)y' + 2xy = 0
Step-by-step explanation:
This is a very trivial exercise, follow the steps below for the solution:
Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.
.....................(1)
Step 2: Find the derivative of y, i.e. y'
Step 3: Substitute y and y' into equation (2) below:
(Verified)
Since the LHS = RHS = 0, the given power series is a solution of the differential equation (1+x^2)y' + 2xy = 0
Answer: The answer is (D) Reflection across the line y = -x.
Step-by-step explanation: In figure given in the question, we can see two triangles, ΔABC and ΔA'B'C' where the second triangle is the result of transformation from the first one.
(A) If we rotate ΔABC 180° counterclockwise about the origin, then the image will coincide with ΔA'B'C'. So, this transformation can take place here.
(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.
(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.
(D) Finally, if we reflect ΔABC across the line y = -x, the the image formed will be different from ΔA'B'C', in fact, it is ΔA'D'E', as shown in the attached figure. So, this transformation can not take place here.
Thus, the correct option is (D).
