9514 1404 393
Answer:
2√30 ∠-120°
Step-by-step explanation:
The modulus is ...
√((-√30)² +(-3√10)²) = √(30 +90) = √120 = 2√30
The argument is ...
arctan(-3√10/-√30) = arctan(√3) = -120° . . . . a 3rd-quadrant angle
The polar form of the number can be written as ...
(2√30)∠-120°
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<em>Additional comments</em>
Any of a number of other formats can be used, including ...
(2√30)cis(-120°)
(2√30; -120°)
(2√30; -2π/3)
2√30·e^(i4π/3)
Of course, the angle -120° (-2π/3 radians) is the same as 240° (4π/3 radians).
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At least one app I use differentiates between (x, y) and (r; θ) by the use of a semicolon to separate the modulus and argument of polar form coordinates. I find that useful, as a pair of numbers (10.95, 4.19) by itself does not convey the fact that it represents polar coordinates. As you may have guessed, my personal preference is for the notation 10.95∠4.19. (The lack of a ° symbol indicates the angle is in radians.)
I wonder if you mean to write ![\sqrt[3]{256}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256%7D)
in place of 
...
If you meant what you wrote, then we have
If you meant to write (the cube root of 256), then we could go on to have
![\sqrt[3]{256}=\sqrt[3]{16^2}=\sqrt[3]{(4^2)^2}=\sqrt[3]{4^4}=\sqrt[3]{4^3\cdot4}=4\sqrt[3]4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B256%7D%3D%5Csqrt%5B3%5D%7B16%5E2%7D%3D%5Csqrt%5B3%5D%7B%284%5E2%29%5E2%7D%3D%5Csqrt%5B3%5D%7B4%5E4%7D%3D%5Csqrt%5B3%5D%7B4%5E3%5Ccdot4%7D%3D4%5Csqrt%5B3%5D4)
Answer:
The diameter is twice that, or approx. 7.90 units.
Step-by-step explanation:
the equation for the volume of a cylinder of radius r and height h is
V = πr²h. Here we need to calculate the diameter after having found the radius. Solving V = πr²h for r², we get:
V
r² = -----------
πh
Substituting the given values, we obtain for r² the following:
145 units³
r² = ------------------------ = 15.6 units²
3.14159(5 units)
Taking the square root of both sides, we get:
r = √15.60, or approx. 3.95 units.
The diameter is twice that, or approx. 7.90 units.
Answer:
pencils= .75 erasers= .29¢
Step-by-step explanation:
