The gravitational force between Pluto and Charon is 3.61 × 1018 N. Pluto has a mass of 1.3 × 1022 kg, which is only slightly gre

(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:

4321 = 1234 * 3 + 619

1234 = 619 * 1 + 615

619 = 615 * 1 + 4

615 = 4 * 153 + 3

4 = 3 * 1 + 1

Now we will express 1 as a linear combination of 4321 and 1234:

1 = 4 - 3

1 = 4 - (615 - 4 * 153) = 4 * 154 - 615

1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234

1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234

This reduces to

1 ≡ -1082 * 1234 (mod 4321)

Thus, the inverse is

-1082 ≡ 3239 (mod 4321)

(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.

<span>Which formula can be applied to find the side length of the rhombus?

 The correct answer is the first choice: 10/Cos(30°)

 Explanation:

 1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:

 Cos(</span>α)=Adjacent side/Hypotenuse
<span>
 </span>α=30°
<span> Adjacent side=(20 in)/2=10 in
 Hypotenuse=x

 2. Inputting these numbers into the equation yields:
</span>
 Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x

 3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:

 x=10/Cos(30°)
</span>

Density can be defined as:

Where:

m is mass

V stands for volume

To isolate the mass, we derive:

Volume can be expressed as:

We then use the following conversion:

After applying the conversion, we arrive at:

Additionally, we have these conversions:

When we apply these conversions for density, we conclude:

Finally, the mass of the water required is:

Answer:

A total of 1190 kilograms of water is needed to fill the waterbed.

Answer:

d) Both blocks experienced equivalent energy loss due to friction

Explanation:

As stated in the question, two tractors are pulling two identical stone blocks the same distance across similar surfacesAdditionally, block A moves at double the speed of block B when completing the race

This implies both blocks suffer from comparable friction loss

Moreover, we understand that

Energy loss from friction is

Thus, the friction loss should be identical for both blocks

therefore, option d is the accurate choice

21 minutes. Step-by-step explanation: Considering the following: Using CITY STREET: The duration to drive to the nearest bowling alley is 45 minutes, which is 0.75 hours. The travel speed is 30 miles per hour. Switching to FREEWAY: the travel speed here is 65 miles per hour. Assuming both routes cover the same distance, the time required on the FREEWAY will be as follows: The distance calculated using the city route results in 30 mph = distance / 0.75 hour, giving a distance of 22.5 miles. As the distance remains consistent: Time taken on the FREEWAY = distance / speed, which results in 22.5 / 65 = 0.3461538 hours. Converting to minutes = 0.3461538 × 60, which rounds to approximately 21 minutes.