Answer:
![37^3 = 50653](https://tex.z-dn.net/?f=37%5E3%20%3D%2050653)
Step-by-step explanation:
Given
![(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3](https://tex.z-dn.net/?f=%28x%20-%20y%29%5E3%20%3D%20x%5E3%20-%203x%5E2y%20%2B%203xy%5E2%20-%20y%5E3)
Required
Find ![37^3](https://tex.z-dn.net/?f=37%5E3)
Express 37 as 40 - 3
So, we have:
![37^3 = (40 - 3)^3](https://tex.z-dn.net/?f=37%5E3%20%3D%20%2840%20-%203%29%5E3)
Compare to ![(x -y)^3](https://tex.z-dn.net/?f=%28x%20-y%29%5E3)
![x = 40\ and\ y = 3](https://tex.z-dn.net/?f=x%20%3D%2040%5C%20and%5C%20y%20%3D%203)
Substitute 40 for x and 3 for y in ![(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3](https://tex.z-dn.net/?f=%28x%20-%20y%29%5E3%20%3D%20x%5E3%20-%203x%5E2y%20%2B%203xy%5E2%20-%20y%5E3)
![(40 - 3)^3 = 40^3 - 3*40^2*3 + 3*40*3^2 - 3^3](https://tex.z-dn.net/?f=%2840%20-%203%29%5E3%20%3D%2040%5E3%20-%203%2A40%5E2%2A3%20%2B%203%2A40%2A3%5E2%20-%203%5E3)
Evaluate all exponents
![(40 - 3)^3 = 64000 - 3*1600*3 + 3*40*9 - 27](https://tex.z-dn.net/?f=%2840%20-%203%29%5E3%20%3D%2064000%20-%203%2A1600%2A3%20%2B%203%2A40%2A9%20-%2027)
Evaluate all products
![(40 - 3)^3 = 64000 - 14400 + 1080 - 27](https://tex.z-dn.net/?f=%2840%20-%203%29%5E3%20%3D%2064000%20-%2014400%20%2B%201080%20-%2027)
![(40 - 3)^3 = 50653](https://tex.z-dn.net/?f=%2840%20-%203%29%5E3%20%3D%2050653)
Hence:
![37^3 = 50653](https://tex.z-dn.net/?f=37%5E3%20%3D%2050653)
Using the three trigonometric functions can be used to calculate unknown side lengths and angle in a right-angle triangle only.
But, if ever you we're given to find a non right-angle triangle, you will have to use sine rule or cosine rule.
Answer: ![f(x)=5x^2-4x+5](https://tex.z-dn.net/?f=f%28x%29%3D5x%5E2-4x%2B5)
Step-by-step explanation:
A quadratic function is as following; ![ax^2+bx+c](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc)
Notice that it cannot be
because if you solve;
which eliminates the
.
Answer:
27 divided by 3 is =9
Step-by-step explanation:
Answer:Let's assume x be the smaller number.
Given that, The greater number is 4 more than the smaller number.
So, greater number= x+4.
It's also given that, The sum of two numbers is 52. Which means sum of x and x+4 must be equa to 52. Hence,
x + (x + 4) = 52
Step-by-step explanation: