Answer:
1080
___ rode a plane for 5^2 miles on a flight to ___. She then took a flight to ___ which was 5^4 miles. How much further did she fly on the second flight?
you can decide where she went and what her name was.
Step-by-step explanation:
6^3 = 213
6^4 = 1296
1296 - 216 = 1080
Answer:
C. 2(k +2)(k +5)(k +1)
Step-by-step explanation:
The LCM will be the product of unique factors.
The unique factors are 2, (k+1), (k+2), (k+5), so the LCM is their product:
2(k+1)(k+2)(k+5) . . . . matches choice C
Answer:
144pi
Step-by-step explanation:
The formula for the volume of a cylinder is base*height
The base of a cylinder is a circle, so it's pi*r^2
r = 6, so pi*r^2 is 36pi
height is 4 so 36pi*4 is 144pi
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
Answers:
1) 3/8 + 3/6 = 7/8
3/8 + 3/6
Simplify
3/4 + 1/2
Transform the expression
3 + 4/8
Calculate
=7/8
_____________
2) 5/9 + 1/3 = 8/9
5/9 + 1/3
Transform the expression
5 + 3/9
Calculate
= 8/9
_____________
3) 5/12 + 7/8 = 31/24
5/12 + 7/8
Transform the expression
10 + 21/24
Calculate
= 31/24
_____________
4) 7/9 - 1/6 = 11/18
7/9 - 1/6
Transform the expression
14 - 3/18
Calculate
= 11/18
_____________
5) 4 2/5 + 2 1/5 = 33/5
4 2/5 + 2 1/5
Convert the number
22/5 + 11/5
Calculate
22 + 11/5
Calculate
= 33/5
_____________
6) 5 3/8 + 2 7/8 = 33/4
5 3/8 + 2 7/8
Convert the number
43/8 + 23/8
Calculate
43 + 23/8
Calculate
= 66/8
