Answer:
surface area = 245.04 cm² (nearest tenth)
Step-by-step explanation:
Surface area of a closed cylinder = 
Given:
- diameter = 6 cm ⇒ radius = 3 cm
- height = 10 cm
⇒ surface area = 2 × 
× 3² + 2 × × 3 × 10
= 78
= 245.04 cm² (nearest tenth)
Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
![*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)](https://tex.z-dn.net/?f=%2Az%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D%5B2%5E%7B5%7D%5D%5E%7B%5Cfrac%7B1%7D%7B5%7D%20%7D%20%28cos%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29%2Bisin%28%5Cfrac%7B1%7D%7B5%7D%29%28280%29)
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
Answer:
87.92 ft
Step-by-step explanation:
The circumference of a circle can be found using the formula: c = 2pi(r) OR c = pi(d).
r stands for the radius, d stands for the diameter. Because you're given the diameter of the circle, you can simply multiply 28 by pi (3.14), and you'll get the circumference!
Answer:
48
Step-by-step explanation:
The exterior of the crate is 10 inches long, meaning that the inside measurement is 8 inches. Next, the 8 inch width corresponds to 6 inches inside. Finally, the 3 inch height corresponds to 1 inch interior height.
Thus the inside floor of the box is 8 by 6 inches, or 48 square inches.
Since the inside height is only 1 inch, this means that 48 one-inch cubical blocks will fit inside the crate.
