Answer:
Volume of water required to fill the pyramid is rd of the water required to fill the prism completely.
Step-by-step explanation:
Let Mr Jackson has an empty rectangular pyramid and rectangular prism.
Height and base of both are congruent.
So volume of rectangular pyramid
Volume of the rectangular prism = (Area of the base)(height)
[ Since ]
Therefore, amount of water required to fill the pyramid is rd of the water required to fill the prism completely.
Answer:
15.6 ft
Step-by-step explanation:
Since the sails are similar then the ratios of corresponding sides are equal.
Comparing the shortest sides, that is
10 : 6 = 5 : 3
let the longest side be x, then using proportion
= 
( cross- multiply )
5x = 78 ( divide both sides by 5 )
x = 15.6
The longest side is 15.6 ft
One way to solve this is to use Pythagorean theorem: the square of one leg of triangle plus square of other leg of the triangle equals c the hypotenuse (longest side of triangle). You might see this as the formula a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
In this case, the legs are 3√2 and the hypotenuse is h.
Using the formula:
(3√2)² + (3√2)² = h²
18 + 18 = h²
h = 6
The other way to do this is with trigonometric angles.
Remember cosine is adjacent over hypotenuse.
cos(45°) = (3√2) / h
h = (3√2) / cos(45°)
h = 6
Answer:
Toshi must begin his walk at 11:00 AM in order that he can return by 8:00 PM.
Step-by-step explanation:
Since the Gotemba walking trail up Mount Fuji is about 9km long, and walkers need to return from the 18km walk by 8pm, if Toshi estimates that he can walk up the mountain at 1.5km / h on average, and down at twice that speed , these speeds taking into account meal breaks and rest times, to determine what is the latest time he can begin his walk so that he can return by 8pm the following calculation must be performed:
Climb: 1.5 km / h
Descent: 2 x 1.5 km / h = 3 km / h
Climb: 9 km / 1.5 km / h = 6 hours
Descent: 9km / 3 km / h = 3 hours
Total: 9 hours
8 PM = 20:00
20:00 - 09:00 = 11:00
Thus, Toshi must begin his walk at 11:00 AM in order that he can return by 8:00 PM.
