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Lostsunrise [7]
2 years ago
12

You can use a system of equations to graph and solve the polynomial equation 3 x cubed + x = 2 x squared + 1. Which statement is

true? The system has one solution, and the equation has three zeroes. The y-coordinates of the solutions to the system and the zeroes of the equation are not equal. The x-coordinates of the solutions to the system and the zeroes of the equation are not equal. The equation has one zero, and the system has three solutions.
Physics
1 answer:
GuDViN [60]2 years ago
5 0

The equation has one zero, and the system has three solutions ( 1 real and 2 complex solutions).

<h3>Solution of the polynomial equation</h3>

The solution of the polynomial equation is determined as follows;

3x³ + x = 2x² + 1

3x³ - 2x² + x - 1 = 0

3(x - \frac{2}{9} )^3+ \frac{5}{9} (x - \frac{2}{9} )- \frac{205}{243} = 0\\\\x = 0.78 \ (one  \ real \ solution)\\\\x = -0.058-0.65i\\\\x = -0.058+0.65i \ \ (2  \ complex \ solutions)

Thus, we can conclude that the equation has one zero (real solution), and the system has three solutions ( 1 real and 2 complex solutions).

Learn more about polynomial equations here: brainly.com/question/2833285

#SPJ1

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Which statement correctly identifies a difference between the function of most arteries and veins?
olasank [31]

Answer:a

Explanation:

8 0
3 years ago
b) The distance of the red supergiant Betelgeuse is approximately 427 light years. If it were to explode as a supernova, it woul
Nat2105 [25]

Answer:

b) Betelgeuse would be \approx 1.43 \cdot 10^{6} times brighter than Sirius

c) Since Betelgeuse brightness from Earth compared to the Sun is \approx 1.37 \cdot 10^{-5} } the statement saying that it would be like a second Sun is incorrect

Explanation:

The start brightness is related to it luminosity thought the following equation:

B = \displaystyle{\frac{L}{4\pi d^2}} (1)

where B is the brightness, L is the star luminosity and d, the distance from the star to the point where the brightness is calculated (measured). Thus:

b) B_{Betelgeuse} = \displaystyle{\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2}} and B_{Sirius} = \displaystyle{\frac{26L_{Sun}}{4\pi (26\ ly)^2}} where L_{Sun} is the Sun luminosity (3.9 x 10^{26} W) but we don't need to know this value for solving the problem. ly is light years.

Finding the ratio between the two brightness we get:

\displaystyle{\frac{B_{Betelgeuse}}{B_{Sirius}}=\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2} \times \frac{4\pi (26\ ly)^2}{26L_{Sun}} \approx 1.43 \cdot 10^{6} }

c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is 1.581 \cdot 10^{-5}\ ly. Then

\displaystyle{\frac{B_{Betelgeuse}}{B_{Sun}}=\frac{10^{10}L_{Sun}}{4\pi (427\ ly)^2} \times \frac{4\pi (1.581\cdot 10^{-5}\ ly)^2}{1\ L_{Sun}} \approx 1.37 \cdot 10^{-5} }

Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.

4 0
3 years ago
Why is gravitational forces equal for everyone?
Alik [6]

That equation is Newton's universal law of gravitation. ... Any two masses exert equal-and-opposite gravitational forces on each other. If we drop a ball, the Earth exerts a gravitational force on the ball, but the ball exerts a gravitational force of the same magnitude (and in the opposite direction) on the Earth.

7 0
3 years ago
Light emitting diode (LEDs) light bulbs have become required in recent years, but do they make financial sense? Suppose a typica
kogti [31]

Answer:

The break even cost is $0.0063825

Explanation:

Break-even cost is the amount of money, or change in value, which equates to the amount at which an asset must be sold to equal the cost of acquiring it. For easier understanding it can be thought the amount of money for which a product or service must be sold to cover the costs of manufacturing or providing it.

Wattage = W

Cost per kilo watt hour = C

Number of hours per year = H

Price per bulb/CFL = P

Discount rate = 11%

Life of bulb = 2 years

Price of bulb = $0.39

Wattage consumption of bulb per hours = 60

Life of CFL = 24 years

Price of CFL = $3.10

Wattage consumption of CFL per hour = 15

Calculate the Equated Annual Cost (EAC) of bulb

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2years)}/ (PVIFA 11%, 2years)

PVIFA 11%, 2years = Annuity PV Factor = [1 – {(1 + r)^(-n)}]/r, where r is the rate per period and n is the number per periods

PVIFA 11%, 2 years = [1 – {(1 + 0.11)^(-2)}]/0.11 = 1.712523 (for 2 years)

PVIFA 11%, 24 years = [1 – {(1 + 0.11)^(-24)}]/0.11 = 8.348136 (for 2 years)

<u>Calculate the EAC of bulb</u>

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2 years)}/ (PVIFA 11%, 2 years)

EAC = {- 0.39 - (60/1000 x H x C) x (1.712523)}/ (1.712523)

EAC = {-0.39 – (51.37570 x C)}/ 1.712523, <em>consider this equation 1</em>

<u>Calculate the EAC of CFL</u>

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 24 years)}/ (PVIFA 11%, 24 years)

EAC = {- 3.10 - (15/1000 x 500 x C) x (8.348136)}/ (8.348136)

EAC = {-3.10 – (62.61102 x C)}/8.348137, <em>consider this equation 2</em>

<u>Equate 1 and 2 to find the amount of C</u>

{-0.39 – (51.37570 x C)}/ 1.712523 = {-3.10 – (62.61102 x C)}/8.348137

{-0.39 – (51.37570 x C) x 8.348137} = {-3.10 – (62.61102 x C) x 1.712523}

C = $0.0063825

Thus, the break- even cost per kilo – watt is $0.0063825

3 0
3 years ago
Why does sound propagate faster in solid bodies than in liquids and faster in liquids than in air?
storchak [24]

Answer:

see below

Explanation:

this is because particles in solids are packed very closely together, thus , the particles collide with each other frequently and thus transfer of energy is faster. however, particles in liquid are closely packed but not as close as in solid so the particles do not collide as frequently. thus, transfer of energy slower than in solid. furthermore, the particles in gas are spaced far apart from each other, thus the particles don't collide with each other frequently, thus transfer of energy is very slow in gas.

hope you get it,

please mark

4 0
3 years ago
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