The weight of a container completely filled with water is 2.25 kg. The container weighs 0.77 kg when it's 0.2 part is filled with water. Find the weight(in kg) of the container when0.4 part of it is filled with water?
ABCD is cyclic quadrilateral, AB is the diameter of the circle. If angle ACD =50 degree, find the measure of angle BAD
PLS HELP ME!
For the 2nd problem, I believe you are missing an image. Remember, opposite angles of a cyclic quadrilateral is 180°
Suppose ∠ACB = 90°and ∠ACD = 50° which is given.
Then, ∠DCB = 90° + 50° = 140°.
Hence, ∠BAD = 180° - 140° = 40°.
Sure, I can help you with that!
For the first question:
Let's denote the weight of the container by C and the weight of water by W.
Given information:
Weight of container completely filled with water = 2.25 kg
Weight of container when 0.2 part is filled with water = 0.77 kg
To find the weight of the container when 0.4 part is filled with water, we can use the concept of ratios.
Since the weight of the container is a combination of the weight of water and the weight of the container itself, we can set up a ratio between the weights of the container and water.
When the container is completely filled with water, the ratio of the weight of water to the weight of the container is W/C = 2.25/1.
When 0.2 part is filled with water, the ratio becomes W/C = 0.77/0.2.
Now, we can set up an equation to find the value of the weight of the container when 0.4 part is filled with water:
(0.77/0.2) = (W/(C+0.4))
Now, we can solve this equation to find the weight of the container when 0.4 part is filled with water:
0.77/0.2 = W/(C+0.4)
Cross-multiplying:
0.77(C + 0.4) = 0.2W
Expanding the brackets:
0.77C + 0.308 = 0.2W
Simplifying:
0.77C = 0.2W - 0.308
Dividing both sides by 0.77:
C = (0.2W - 0.308)/0.77
Now, you can substitute the given weight of water (W) into this equation to find the weight of the container (C) when 0.4 part is filled with water.
For the second question:
Given: ABCD is a cyclic quadrilateral with AB as the diameter of the circle, and angle ACD = 50 degrees.
In a cyclic quadrilateral, opposite angles are supplementary, which means they add up to 180 degrees.
So, angle ABD is supplementary to angle ACD.
Therefore, angle ABD = 180 degrees - angle ACD
Plugging in the value of angle ACD:
angle ABD = 180 degrees - 50 degrees
Simplifying:
angle ABD = 130 degrees
Hence, the measure of angle BAD is 130 degrees.
I hope this helps! Let me know if you have any further questions.