Domain: all real numbers
Range: y<0
Original price:
6(3.5)
21
New Price:
1.15(21)
24.15
24.15-21
$3.15 more
Step-by-step explanation:
Explanation:
The trick is to know about the basic idea of sequences and series and also knowing how i cycles.
The powers of i will result in either: i, −1, −i, or 1.
We can regroup i+i2+i3+⋯+i258+i259 into these categories.
We know that i=i5=i9 and so on. The same goes for the other powers of i.
So:
i+i2+i3+⋯+i258+i259
=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)
We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.
=65(i)+65(i2)+65(i3)+64(i4)
From here on out, it's pretty simple. You just evaluate the expression:
=65(i)+65(−1)+65(−i)+64(1)
=65i−65−65i+64
=−65+64
=−1
So,
i+i2+i3+⋯+i258+i259=-1
Answer:
![\sqrt[3]{x^{10} }[\tex]Step-by-step explanation:Exponential Rules:[tex]x^{a} + x^{b} = x^{a + b}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%20%7D%5B%5Ctex%5D%3C%2Fp%3E%3Cp%3E%3Cstrong%3EStep-by-step%20explanation%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EExponential%20Rules%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%5Btex%5Dx%5E%7Ba%7D%20%2B%20x%5E%7Bb%7D%20%3D%20x%5E%7Ba%20%2B%20b%7D)
![\sqrt[b]{x^{a} } =x^{\frac{a}{b} } Original Equation:[tex]\sqrt[3]{x^{10} } = x^{\frac{10}{3} } Answer:[tex]\sqrt[3]{x^{10} }[\tex]Convert the cubed root to a power. Cubed root = [tex]\frac{1}{3}](https://tex.z-dn.net/?f=%5Csqrt%5Bb%5D%7Bx%5E%7Ba%7D%20%7D%20%3Dx%5E%7B%5Cfrac%7Ba%7D%7Bb%7D%20%7D%20%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EOriginal%20Equation%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%20%7D%20%20%3D%20x%5E%7B%5Cfrac%7B10%7D%7B3%7D%20%7D%20%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EAnswer%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%20%7D%5B%5Ctex%5D%3C%2Fp%3E%3Cp%3EConvert%20the%20cubed%20root%20to%20a%20power.%20Cubed%20root%20%3D%20%5Btex%5D%5Cfrac%7B1%7D%7B3%7D)

Convert them, so they have a common denominator - 


[tex]\sqrt[3]{x^{10} }[\tex] = [tex]x^{\frac{10}{3} } [\tex]