SSS similarity requires the three sides of both triangles to be in the same ratio. In contrast, SSS congruence requires the sides to be equivalent. SSS congruence is effectively SSS similarity with ratio one, and both determine that the triangle's angles are equivalent.
The number of combinations of 2 health care providers of different types possible are 47.
<u>Explanation:</u>
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Doctors = 4
Dentists = 3
Nurses = 5
combinations of two different health care providers = ?
Combination would be = ⁴C₁ X ³C₁ + ³C₁ X ⁵C₁ + ⁴C₁ X ⁵C₁
ⁿCₐ = n! / ( n - a )! X a!
So on calculating the combination we get,
= 4 X 3 + 3 X 5 + 4 X 5
= 12 + 15 + 20
= 47
Therefore, the number of combinations of 2 health care providers of different types possible are 47.
Answer:
-3
Step-by-step explanation:
p(x) = x^2-6x+5
Let x= 4
p(4) = 4^2-6(4)+5
Exponents first
= 16 -6(4) +5
Multiply
= 16 -24 +5
Add and subtract
= -8+5
= -3
Explanation:
Let 
and 
. The differential volume dV of the cylindrical shells is given by
![dV = 2\pi x[f(x) - g(x)]dx](https://tex.z-dn.net/?f=dV%20%3D%202%5Cpi%20x%5Bf%28x%29%20-%20g%28x%29%5Ddx)
Integrating this expression, we get
![\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%20%3D%202%5Cpi%5Cint%7Bx%5Bf%28x%29%20-%20g%28x%29%5D%7Ddx)
To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:
We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:
or
Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is
