For this case we must complete squares:
We add the square of half the coefficient of the term "x",
on both sides of the equation:
According to the perfect square trinomial we have:
Rewriting the expression we have:
ANswer:
A cube has edge length s units. Use an exponent to write an expression for its volume
1 answer:
Answer:
s
Step-by-step explanation:
A cube's volume is its length * width * height. Its length, width, and height are all equal to s.
A cube's edge length is another word for its side length, which is the same for every edge in the cube.
To write the equation for the volume with s substituted for length, width, and height, we get that volume = s.
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A suitable vector calculator can perform this arithmetic directly, as can many graphing or scientific calculators that are capable of handling complex numbers. Mine says
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.