Answer:
The next time both will leave the bus station at the same time is 7:15 a.m.
Step-by-step explanation:
Since 15 and 75 are multiples to each other.
So, L.C.M. of 15 and 75 is 75.
So, after 75 minutes both buses will leave the station at the same time.
Also since buses begin their routes at 6 a.m.
So, next time they will meet at
6 hours 0 minutes + 75 minutes = 7 hours 15 minutes = 7:15 a.m.
Find the volume of a cone with a diameter of 20m and a slant height of 26m.
Volume Formula of a Cone: V = pi(radius^2)(h/3)
Diameter: 20m
Slant Height (Height): 26m
Plug it in:
V = 3.14(10^2)(26/3)
V = 314(26/3)
Solve:
V = 314(0.87)
V = 273.18
Volume = 273.18
Round:
Volume = 273m^3
The volume of the cone is 273m^3 to the nearest whole number.
Answer:
![g(x) = \sqrt[3]{x-1} - 2](https://tex.z-dn.net/?f=%20g%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx-1%7D%20-%202%20)
Step-by-step explanation:
We want to find h and k in:
![g(x) = \sqrt[3]{x-h} + k](https://tex.z-dn.net/?f=%20g%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx-h%7D%20%2B%20k%20)
At the inflection point, the second derivative is equal to zero, so:


Then x - h = 0.
Inflection point is located at (1, -2), replacing this x value we get:
1 - h = 0
h = 1
We know that the point (-2.5, -3.5) belongs to the function, so:
![-3.5 = \sqrt[3]{-2.5-1} + k](https://tex.z-dn.net/?f=%20-3.5%20%3D%20%5Csqrt%5B3%5D%7B-2.5-1%7D%20%2B%20k%20)
k ≈ -2
All data, used or not, are shown in the picture attached.
Answer:
x+4=20 is a solution to 5(x+4)=100.
Step-by-step explanation:
Following PEMDAS, divide 5 from both sides of the equation 5(x+4)=100, and you have x+4=20 remaining.
This means that both equations have the same solution.