Answer: we can get the sequence of reasons with help of below explanation.
Step-by-step explanation:
Here It is given that, line segment BD is the perpendicular bisector of line segment AC. ( shown in below diagram)
By joining points B with A and B with C ( Construction)
We get two triangles ABD and CBD.
We have to prove that : Δ ABD ≅ Δ CBD
Statement Reason
1. AD ≅ DC 1. By the property of segment bisector
2. ∠BDA ≅ ∠ BDC 2. Right angles
3. BD ≅ BD 3. Reflexive
4. Δ ABD ≅ Δ CBD 4. By SAS postulate of congruence
Area yellow =11 x 6
= 66
red area = 7 x 2
=14
area of yellow
66 - 14 = 52
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
Answer:
120 cm^3
Step-by-step explanation:
the edges are 4 cm 5 cm 6 cm
volume of cuboid=l×b×h
=4cm×5cm×6cm
=120cm^3
First, divide -5 on both sides:
(x + 7) < -2
Then subtract 7 on both sides:
x < -9
x < -9 is your final answer.
