cooIcooIcooI17

avatar
BenutzernamecooIcooIcooI17
Punkte180
Membership
Stats
Fragen 39
Antworten 17

 #1
avatar+180 
0

We're converting the power of a microwave from Watts (W) to a new unit, Zaps (z). We know the conversion rates for both Watts and Zaps to SI units (kg, m, s, min).

 

Watts to SI:

 

1 W = 1 kg * m^2 / s^3

 

Zaps to SI:

 

1 z = 1 kg * m^2 / min^3

 

We want to find the power of a 900 W microwave in Zaps. To do this, we can write an equality where the power is the same but expressed in different units:

 

900 W = P z

 

Now we can manipulate the equation to solve for P (power in Zaps). We can do this by introducing a conversion factor that equates Watts and Zaps.

 

This factor will cancel out the desired units (kg and m^2) and leave us with a factor that relates Watts and Zaps through time units (seconds and minutes).

a. We know from the definitions of Watts and Zaps that:

 

- 1 W / (1 kg * m^2 / s^3) = 1 z / (1 kg * m^2 / min^3)

 

b. This simplifies to:

 

- 1 W * (min^3 / s^3) = 1 z

 

c. This conversion factor is equal to 1 because we're converting between equivalent units that express the same fundamental quantities (mass, length, time) but in different time scales (seconds vs minutes).

 

Apply the conversion factor to the original equation:

 

900 W * (min^3 / s^3) = P z

 

Since the conversion factor is 1 (as derived previously), we have:

 

900 W = P z

 

Therefore, the power of the 900 W microwave in Zaps is also 900 Zaps. However, to express the answer in scientific notation, we should recognize that 900 can be written as 9.00 x 10^2.

 

Answer: The power of the 900 W microwave in Zaps is 9.00 x 10^2 Zaps.

24.07.2024, 15:01
 #1
avatar+180 
0

We're converting the power of a microwave from Watts (W) to a new unit, Zaps (z). We know the conversion rates for both Watts and Zaps to SI units (kg, m, s, min).

 

Watts to SI:

 

1 W = 1 kg * m^2 / s^3

 

Zaps to SI:

 

1 z = 1 kg * m^2 / min^3

 

We want to find the power of a 900 W microwave in Zaps. To do this, we can write an equality where the power is the same but expressed in different units:

 

900 W = P z

 

Now we can manipulate the equation to solve for P (power in Zaps). We can do this by introducing a conversion factor that equates Watts and Zaps.

 

This factor will cancel out the desired units (kg and m^2) and leave us with a factor that relates Watts and Zaps through time units (seconds and minutes).

a. We know from the definitions of Watts and Zaps that:

 

- 1 W / (1 kg * m^2 / s^3) = 1 z / (1 kg * m^2 / min^3)

 

b. This simplifies to:

 

- 1 W * (min^3 / s^3) = 1 z

 

c. This conversion factor is equal to 1 because we're converting between equivalent units that express the same fundamental quantities (mass, length, time) but in different time scales (seconds vs minutes).

 

Apply the conversion factor to the original equation:

 

900 W * (min^3 / s^3) = P z

 

Since the conversion factor is 1 (as derived previously), we have:

 

900 W = P z

 

Therefore, the power of the 900 W microwave in Zaps is also 900 Zaps. However, to express the answer in scientific notation, we should recognize that 900 can be written as 9.00 x 10^2.

 

Answer: The power of the 900 W microwave in Zaps is 9.00 x 10^2 Zaps.

24.07.2024, 14:58
 #1
avatar+180 
0

We can find the values of b and c using the relationship between the quadratic formula and the roots of the equation.

 

Roots and Quadratic Formula:

 

The quadratic formula relates the coefficients (a, b, and c) of the quadratic equation to its roots (r1 and r2):

 

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

 

In this case, we know the roots (5 + 3i and 5 - 3i) and want to find b + c.

 

Properties of Complex Roots:

 

Complex numbers as roots of quadratic equations always come in conjugate pairs. This means that if one root is a + bi (where i is the imaginary unit), the other root will be a - bi.

 

In this case, our roots are 5 + 3i and 5 - 3i, which confirms they are complex conjugates.

 

Sum of Roots and Coefficients:

 

There's a useful relationship between the roots (r1 and r2) of a quadratic equation and its coefficients (a, b, and c):

 

Sum of roots (r1 + r2) = -b / a

 

Product of roots (r1 * r2) = c / a

 

Since we're looking for b + c, and the quadratic has a leading coefficient of 1 (a = 1), we can use these relationships directly.

 

Finding b + c:

 

Sum of Roots:

 

The sum of the roots (5 + 3i) and (5 - 3i) is:

 

(5 + 5) + (3i - 3i) = 10

 

Since the sum of roots is also -b / a (and a = 1), we have:

 

-b = 10

 

Therefore, b = -10

 

Product of Roots:

 

The product of the roots (5 + 3i) and (5 - 3i) is:

 

(5 + 3i) * (5 - 3i) = 25 + 25 = 50

 

Since the product of roots is also c / a (and a = 1), we have:

 

c = 50

 

b + c:

 

Finally, add b and c to find the desired value:

 

b + c = -10 + 50 = 40

 

Therefore, b + c = 40.

09.05.2024