9514 1404 393
Answer:
64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729
Step-by-step explanation:
The row of Pascal's triangle we need for a 6th power expansion is ...
1, 6, 15, 20, 15, 6, 1
These are the coefficients of the products (a^(n-k))(b^k) in the expansion of (a+b)^n as k ranges from 0 to n.
Your expansion is ...
1(2k)^6(-1/3)^0 +6(2k)^5(-1/3)^1 +15(2k)^4(-1/3)^2 +20(2k)^3(-1/3)^3 +...
15(2k)^2(-1/3)^4 +6(2k)^1(-1/3)^5 +1(2k)^0(-1/3)^6
= 64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729
Answer: the width of the uniform path is 9 meters.
Step-by-step explanation:
Let x represent the width of the uniform path.
A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the uniform path is (18 + 2x) meters and the combined width of the pool and the uniform path is (22 + 2x) meters.
If the area of the pool and the path combined is 1440 square meters, it means that
(18 + 2x)(22 + 2x) = 1440
396 + 36x + 44x + 4x² = 1440
4x² + 80x + 396 - 1440 = 0
4x² + 80x - 1044 = 0
Dividing both sides of the equation by 4, it becomes
x² + 20x - 261 = 0
x² + 29x - 9x - 261 = 0
x(x + 29) - 9(x + 29) = 0
x - 9 = 0 or x + 29 = 0
x = 9 or x = 29
Since the width cannot be negative, then x = 9 meters
-7 replaces the t so it would be
w(-7) = -2(-7)+1
= 14+1
= 15
Answer:
(1.36 × 
) - (4 × 
) = 132000kg
1.32 × kg = 1320000
Answer: (3, -3)
Step-by-step explanation:
You substitute each point into the function and see if it fits:
(-2, -1) ⇒ -2(-2) + 3 = 4 + 3 = 7 ≠ -1
(3, -3) ⇒ -2(3) + 3 = -6 + 3 = -3
(3, 3) ⇒ -2(3) + 3 = -6 + 3 = -3 ≠ 3
(-3, -9) ⇒ -2(-3) + 3 = 6 + 3 = 9 ≠ -9
