Answer: by combining 1/4 and 1/3 and then you find the amount of left over dog food. Multiply the fractions so they have common denominators, then add. You will get 3/12 + 4/12 = 7/12. 12 - 7 = 5, so there is 5/12 of the bag left.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
Answers:
- prime number = {2,3,5}
- composite number = {4,6}
- number less than four = {1,2,3}
- number more than or equal to three = {3,4,5,6}
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Explanation:
The list of all possible outcomes on a single standard die is {1,2,3,4,5,6}. The curly braces indicate set notation.
A prime number is a number where its only factors are 1 and itself. The value 1 is not prime, and it's not composite either.
Something like 3 is prime because its only factors are 1 and 3. Something like 4 is composite because 4 = 2*2. A composite value has factors other than 1 and itself.
Parts (iii) and (iv) are fairly straight forward. You simply list items less than four for part (iii) and you list items that are three or greater for part (iv).
Answer:
Step-by-step explanation:
L = Length
W = Width
W = 2L
2W + 2L = 174
2(2L) + 2L = 174
6L = 174
L = 29 ft
W = 2(29) = 58 ft
