Answer:
x = 35°
Step-by-step explanation:
These are corresponding angles. When a transversal crosses 2 parallel lines, 4 angles are created at each intersection, and each pair of corresponding angles between those are congruent.
These angles are congruent, so you can set them equal to each other:
Then, just solve for x:
You can check that by plugging it back into both:
Answer:
<em>work done is equal to 384279168 lb-ft</em>
<em></em>
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = = <em>30791.6 ft^3</em>
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = <em>1921395.84 lb</em>
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> <em>work done is equal to 384279168 lb-ft</em>
Answer:
Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279
Step-by-step explanation:
Let the number of red fish and blue fish in the large tank are x and y respectively.
Similarly ratio of red fish and blue fish in the small tank are x' and y' respectively.
Since in each tank ratio of the red fish to blue fish is 333 : 444
That means x : y = 333 : 444
Or
⇒
⇒ y = --------(1)
Similarly x' : y' = 333 : 444
⇒
⇒
⇒ x' = ------(2)
Ratio of the fish in large tank to the fish in small tank is 464646 : 555
So (x + y) : (x' + y') = 464646 : 555
Now we replace the values of x and y' from equation (1) and equation (2)
Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279