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3 years ago

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Let omega be a complex number such that omega^3 = 1. Find all possible values of {1}{1 + \omega} + {1}{1 + \omega^2}. Enter all

the possible values, separated by commas.

1 answer:

Norma-Jean [14]3 years ago

8 0

Answer:

1 is Answer.

Step-by-step explanation

$\frac{1}{1+omega^{2} } + \frac{1}{1+omega }\\$

= $\frac{(-1)*(omega + 1)}{omega^{2} }$

As we know that ω²+ω+1=0

Thus putting in above equation, we get

= $\frac{1}{(-1)*omega } + \frac{1}{(-1)*omega^{2} }$

Rearranging and simplifying:

= $\frac{-1}{omega } + \frac{-1}{omega^{2} }$

= $\frac{(-1)*(omega + 1)}{omega^{2} }$

= $\frac{(-1)*(- omega^{2} )}{omega^{2} }$

= 1 Answer

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Answer:

D. 1/15

Step-by-step explanation:

Actual tree = 10 ft = 12 × 10 = 120 in.

Model tree = 8 in.

Scale factor = model tree/actual tree

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A survey found that 12 out of every 15 people in the united States prefer eating at a restaurant over cooking at home. if 400 pe

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500 people took the survey.

12 out of 15 people is 80% of the population. 12/15 = 0.80
Thus, 80% of the population prefers eating in the restaurant.

If 400 represents the people who prefers eating in the restaurant; then, 400 is the 80% of the population. To get the total population or 100%, we must divide 400 by 0.80 or 80%

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3 years ago

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Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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