Answer:
1 C
2 G
Step-by-step explanation:
Answer: 4 times
Solution: 60 minutes * 7 = 420
280/420 = ans
ans * 6 = 4
Answer: (1/3,2)
Step-by-step explanation:
Let O(x,y) be the circumference of the triangle PQR,
Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.
Thus, PO = QO
By the distance formula,
![(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-5%29%5E2%20%3D%20%28x-4%29%5E2%2B%28y-1%29%5E2)
![\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y](https://tex.z-dn.net/?f=%5Cimpliesx%5E2%2B%204x%20%2B%204%20%2B%20y%5E2%2B%2025%20-%2010%20y%20%3D%20x%5E2%2B16%20-%208%20x%20%2B%20y%5E2%2B1%20-%202y)
![\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y](https://tex.z-dn.net/?f=%5Cimplies%204x%20%2B%204%20%2B%2025%20-%2010%20y%20%3D%2016%20-%208%20x%20%2B%201%20-%202y)
![\implies 4x +8x-10y+2y = 16 + 1 -25-4](https://tex.z-dn.net/?f=%5Cimplies%204x%20%2B8x-10y%2B2y%20%3D%2016%20%2B%201%20-25-4)
![\implies 12x - 8y = 17 - 29](https://tex.z-dn.net/?f=%5Cimplies%2012x%20-%208y%20%3D%2017%20-%2029)
---------(1)
Similarly, QO = RO
![\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2](https://tex.z-dn.net/?f=%5Cimplies%20%28x-4%29%5E2%20%2B%20%28y-1%29%5E2%20%3D%20%28x%2B2%29%5E2%2B%28y%2B3%29%5E2)
![\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2%20%2B%2016%20-%208x%20%2B%20y%5E2%2B%201%20-%202y%20%3D%20x%5E2%2B%204%20%2B%204%20x%20%2By%5E2%2B%209%20%2B%206%20y)
![\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y](https://tex.z-dn.net/?f=%5Cimplies%2016%20-%208x%20%2B%201%20-%202y%20%3D%204%20%2B%204%20x%20%2B%209%20%2B%206%20y)
![\implies - 8x -4x-2y-6y=4+9-16-1](https://tex.z-dn.net/?f=%5Cimplies%20-%208x%20-4x-2y-6y%3D4%2B9-16-1)
![\implies -12 x - 8 y = 13 - 17](https://tex.z-dn.net/?f=%5Cimplies%20-12%20x%20-%208%20y%20%3D%2013%20-%2017)
------------(2)
By adding equation (1) and (2),
24 x = - 8
x = 1/3
By putting this value in equation (1),
We get,
Thus, 4 - 8 y = -12
8 y = 16
y = 2
Answer:
The correct answer is 75 cubic feet.
Step-by-step explanation:
Volume of each block of cube is 1 cubic foot. Since the block is of the shape of a cube, the side length is 1 foot.
Number of blocks needed to fill the bottom of the the chest is 25.
Height of the chest is 3 feet.
Therefore there are three layers to be filled by blocks. Each layer needs 25 blocks each. Thus number of blocks needed to fill the whole chest is 25 × 3 = 75.
Volume of 75 blocks = Volume of the chest = 75 × 1 = 75 cubic feet.
Therefor the volume of the chest is given by 75 cubic feet.
First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.