Answer:Y=25:3
Step-by-step explanation:
Answer:
See the explanation
Step-by-step explanation:
We know that
f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x
Lets calculate the derivatives:
f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)
f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x
Similarly:
f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x
f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x
Rearrange:
f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24
f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x
Rearrange:
f''''(x) = 720x² + (24/x⁵) - 16sin2x +72
Answer:
105
Step-by-step explanation:
The numbers that can be used to form triangles are collectively called "triangle numbers." The n-th triangle number is the sum of all numbers less than or equal to n. It is ...
n(n+1)/2
For n=14, the number is 14(15)/2 = 7·15 = 105.
The clerk used 105 oranges to make the arrangement.
Sin is equal to the same number, no matter how big or small you make the triangle because the sine of the angle is equal to the opposite side divided by the hypotenuse.