OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
1 answer:
Find m∠BOC, if m∠MOP = 110°.
Answer:
m∠BOC= 40 degrees
Step-by-step explanation:
A diagram has been drawn and attached below.
- OM bisects AOB into angles x and x respectively
- ON bisects ∠BOC into angles y and y respectively
- OP bisects ∠COD into angles z and z respectively.
Since ∠AOD is a straight line
x+x+y+y+z+z=180 degrees
We are given that:
m∠MOP = 110°.
From the diagram
∠MOP=x+2y+z
Therefore:
x+2y+z=110°.
Solving simultaneously by subtraction
x+2y+z=110°.
We obtain:
x+z=70°
Since we are required to find ∠BOC
∠BOC=2y
Therefore from x+2y+z=110° (since x+z=70°)
70+2y=110
2y=110-70
2y=40
Therefore:
m∠BOC= 40 degrees
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Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
For, A to be greatest ,
⇒
⇒
⇒
Therefore, from equation (3), k = 5 - h²
⇒
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Width = 2h =√10 and
Height =
Answer:
(a) If f and t are both even functions, product ft is even.
(b) If f and t are both odd functions, product ft is even.
(c) If f is even and t is odd, product ft is odd.
Step-by-step explanation:
Even function: A function g(x) is called an even function if
Odd function: A function g(x) is called an odd function if
(a)
Let f and t are both even functions, then
The product of both functions is
The function ft is even function.
(b)
Let f and t are both odd functions, then
The product of both functions is
The function ft is even function.
(c)
Let f is even and t odd function, then
The product of both functions is
The function ft is odd function.