Answer:
∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)
Step-by-step explanation:
Start with the Maclaurin series for cos x.
cos x = ∑ₙ₌₀°° (-1)ⁿ x²ⁿ / (2n)!
Substitute ⅓ x².
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓ x²)²ⁿ / (2n)!
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ (⅓)²ⁿ x⁴ⁿ / (2n)!
cos (⅓ x²) = ∑ₙ₌₀°° (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)
Multiply by 8x.
8x cos (⅓ x²) = ∑ₙ₌₀°° 8x (-1)ⁿ x⁴ⁿ / (9ⁿ (2n)!)
8x cos (⅓ x²) = ∑ₙ₌₀°° 8 (-1)ⁿ x⁴ⁿ⁺¹ / (9ⁿ (2n)!)
Answer:
4 1/6 cups of almonds left
Step-by-step explanation:
Granola recipe = 2 1/3 cups of almonds
2 1/2 batches of granola = 2 1/3 cups of almonds × 2 1/2
= 2 1/3 × 2 1/2
= 7/3 × 5/2
= (7*5)/(3*2)
= 35/6
= 5 5/6 cups of almonds
A bag of almonds = 2 cups
5 bags of almonds = 10 cups
Cups of almonds left = 10 cups - 35/6 cups
= 60-35/6
= 25/6
= 4 1/6 cups
Answer:
1:1
Step-by-step explanation:
Answer:
The coordinates of the point are (-3,-5)
Step-by-step explanation:
Here, we want to find the coordinates of the point that divides the segment in the ratio 3:2
We shall use the internal division formula;
(x,y) = (mx2 + nx1)/(m + n) , (my2 + ny1)/(m+ n)
Where in this case;
(x1,y1) = (6,-2)
(x2,y2) = (-9,-7)
(m, n) = 3,2
Substituting these values;
(x,y) = (3(-9) + 2(6))/(3+2) , (3(-7) + 2(-2))/(3+2)
(x,y) = (-27 + 12)/5 , (-21 -4)/5
(x ,y) = (-15/5, -25/5)
(x , y) = (-3,-5)
Answer:
G(t)=12-2t
Step-by-step explanation:
Okay, first we need to find out how many gallons he lost, so we multiply 2 by 3 and get 6 gallons used.
Next, now knowing 6 gallons are left and 6 have been used we now add to get 12 gallons originally.
Then, now that we have the rate of change and the starting number we put together the equation to the way that best suits the question
Last, to check our work plug six into t next to the two and solve to get six gallons used,
I hope this helps you
If i am right a thanks would be appreciated if i am wrong please leave a comment
