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If the shortest leg in the following 30°-60°-90° triangle has length 9 meters, what are the lengths of the other leg and the hypotenuse? Enter the exact, fully simplified answers. 30° 2x √3x The

Answer:

6

Explanation:

because the numbers before the decimal point are whole numbers so that would mean the 4 & 0 before the points the ones and tens place. and anything behind a decimal goes in order as usual ones,tens,hundredths, thousandths, ten thousandths, and so on. so that what makes the 6 be in the hundredths place.

Answer:

In the centre of a star, the temperature and pressure are so high that four protons can fuse to form helium, in a series of steps.  

Explanation:

Explanation:

In scientific notation the Sun's mass is: =1.989 x 10 ^30 kg

Answer:

I think in scientific notation the Sun's mass becomes: M Sun = 1.989 x 10 30 kg. The number above the ten, called the power of ten or exponent, stands for the number of decimal places. If it is positive, as in the mass of the Sun, the decimal places are in front of the decimal point.

I hope this help you!:)

Answer:

5 years

Explanation:

\(\frac{1}{8}(40)\\\\= 5\)

Answer:

ΔL = L * 1.9E-5 * ΔT

ΔA = A * 2 * 1.9E-5 * ΔT

ΔA = .6 * 3.8E-5 * 1.5E4 mm = .34 mm

New area = 600.34 mm

Note: (L + ΔL)^2 = L + 2 L ΔL + ΔL^2       where ΔL is a small quantity

(L + ΔL)^2 - L^2 = 2 L ΔL = L ΔA

where the coefficient of area expansivity is twice that of linear expansivity

Answer:

Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases.

Answer:

25kJ

Explanation:

K = 1/2 mv^2 = 1/2 x 2000kg x (5.0m/s)^2

= 25 x 10^3 J = 25kJ

Answer:

This level of needs is known as safety needs. Safety needs are the need for security, stability, and protection from physical and emotional harm. These needs include physical safety, financial security, health and well-being, and protection from discrimination and harassment.

Explanation:

Hope this helps!!!!!!!!!!!!!

Answer:

2.61

Explanation:

91.44/35=2.61257142857  or 2.61

The power factor when the generator frequency is 1.73 kHz is 0.243.

We can start by using the formula for the resonant frequency of an RLC circuit:

f0 = 1 / (2π√(LC))

where f0 is the resonant frequency, L is the inductance, and C is the capacitance.

Substituting the given values, we get:

\(1.25 kHz = 1 / (2π√(L(6.35×10^-6)))\)

Solving for L, we get:

L = 1 / (4π^2(1.25×10^3)^2(6.35×10^-6)) = 20.2 mH

Next, we can use the formula for the power dissipated in an RLC circuit:

P = V^2 / R

where P is the power dissipated, V is the voltage across the circuit, and R is the resistance.

Substituting the given values, we get:

29.5 W = (15.6 V)^2 / R

Solving for R, we get:

R = (15.6 V)^2 / 29.5 W = 8.24 Ω

Therefore, the values of the inductance and resistance are 20.2 mH and 8.24 Ω, respectively.

To calculate the power factor when the generator frequency is 1.73 kHz, we need to find the impedance of the circuit at this frequency. The impedance of an RLC circuit is given by:

Z = √(R^2 + (ωL - 1/ωC)^2)

where ω is the angular frequency.

Substituting the given values, we get:

Z = √(8.24^2 + (2π×1.73×20.2×10^-3 - 1/(2π×1.73×6.35×10^-6))^2) = 33.9 Ω

The power factor can be calculated as:

cos(φ) = R / Z

cos(φ) = 8.24 Ω / 33.9 Ω = 0.243

Therefore, the power factor when the generator frequency is 1.73 kHz is 0.243.

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Explanation:

The answer is (B). The speed of light is the same for all observers regardless of their motion relative to the light source.

The speed would an observer on Earth measures for the light from the spotlight will be 3×10⁸ m/sec.

Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.

The given data in the problem is;

The speed of light is, \(\rm C =3 \times 10^8\ m/sec\)

All frames of reference have the same speed of light in a vacuum. Therefore the speed would an observer on Earth measures for the light from the spotlight will be 3×10⁸ m/sec.

Hence option B is correct.

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The maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.

To calculate the maximum distance at which the eye can resolve two headlights at night, we can use the formula for the angular resolution of the human eye, which is based on the Rayleigh criterion:

θ = 1.22 * (λ / D)

Where:
θ = angular resolution in radians
λ = wavelength of light (average wavelength of visible light is approximately 550 nm, or 5.5 x 10^-7 meters)
D = diameter of the aperture (pupil diameter, given as 0.4 cm or 0.004 meters)

First, calculate the angular resolution:

θ = 1.22 * (5.5 x 10^-7 m / 0.004 m) = 1.678 x 10^-4 radians

Now, to find the maximum distance (d) at which the eye can resolve two headlights, we can use the formula

d = L / tan(θ)
Where:
L = distance between the headlights (assuming a standard separation of 2 meters)
Before calculating, we need to make sure that the angular resolution (θ) is in the same unit (radians) as the tangent function requires:
θ = 1.678 x 10^-4 radians
Now, calculate the maximum distance:
d = 2 m / tan(1.678 x 10^-4) ≈ 11937.3 meters
Therefore, the maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.

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Answer:

10 ohms

Explanation:

V = IR

2 v is the drop in the battery

2 = .2 R

R = 10 ohms

The relationship that gives the value of the unknown resistor R when R₃ is adjusted so that the voltmeter reading is zero is the parallel resistance formula.

When R₃ is adjusted to balance the circuit, the resistance of R₁ and R₂ combined in parallel will be equal to the resistance of the unknown resistor R. Thus, the formula for calculating the resistance of R is R = (R₁ x R₂) / (R₁ + R₂).
Hi! In the experimental setup you've described, the circuit utilizes known resistors R₁ and R₂, variable resistor R₃, a voltage source, and a voltmeter to determine the value of an unknown resistor R. When the voltmeter reading is adjusted to zero, it indicates that the circuit is in a balanced state.

In this case, the relationship that gives the value of the unknown resistor R can be determined using the Wheatstone Bridge principle. The Wheatstone Bridge formula is:

(R₁ / R₂) = (R / R₃)

To find the value of R, you can rearrange the formula:

R = R₃ * (R₁ / R₂)

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The equivalent resistance of the resistors connected in parallel is 8.57 ohms.

Resistance is the opposition to current flow in a circuit.

To calculate the equivalent of the resistances connected in parallel, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the equivalent resistance is 8.57 ohms.

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The plane travels a distance of 325 miles if the airplane travels for 2.5 hours at an average speed of 130 miles per hour. Using the distance formula (d = rt), we can calculate the distance.

To find the distance traveled by the airplane, we can use the distance formula, which is represented as d = rt. In this formula, "d" represents the distance, "r" represents the rate or speed at which the object is traveling, and "t" represents the time taken for the travel.

Given that the airplane travels for 2.5 hours at an average rate of 130 miles per hour, we can substitute these values into the formula. The rate of the airplane is 130 miles per hour, and the time taken is 2.5 hours.

Using the formula, we can calculate the distance traveled as follows:

d = rt

d = 130 mph × 2.5 hours

Multiplying the rate (130 mph) by the time (2.5 hours) gives us:

d = 325 miles

Therefore, the airplane travels a distance of 325 miles during the 2.5 hours of travel at an average rate of 130 miles per hour.

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Answer:

easy

speed = distance/time = 50 / 0.3 = 500/3 m/sec

Answer:jkknbfds

Explanation:jjbhfdrtb

The number of seconds in the 40 second interval starting at t = 0 during which the voltage is below 0.21m V is: 19.06 - 7.03 = 12.03 s = 12.97 (approx.) Thus, the correct option is (c) 12.97.

The voltage V, in an electric circuit is measured in millivolts (mV) and is given by the formula V=0.2

sin0.1π(t -0.5)+0.3, where t is the time in seconds from the start of an experiment. We have to use the graph of the function to estimate how many seconds in the 40 second interval starting at t = 0 during which the voltage is below 0.21mV.

Graph of the given function is shown below:

Graph of the given function

As per the graph, it is observed that the voltage is below 0.21 mV from 7.03 s to 19.06 s.

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Answer:

-0.08m/s²

Explanation:

Answer:

  the torque on the joint at the main stem is increased as the person moves toward the end of the branch, as is the stress within the branch.

Explanation:

In general, a branch will break when its load limits are exceeded, and/or when the stress is applied at a rate that exceeds its ability to accommodate.

Two things happen when a person moves toward the end of a tree branch:

So, if the branch doesn't break due to increased stress within the branch, the joint may fail due to its torque limit being exceeded as a person moves closer to the end.

__

From an engineering point of view, the stress limits constitute a threshold that will result in breakage with probability 1 when exceeded. When the limits are far above the applied stress, the probability of breakage is near 0. So, one could say the probability increases when the person approaches the end of the branch, since it goes from near 0 to 1.

The total momentum is always conserved in the following situations: when all the forces on the system are internal to the system, and when the net force on the system is zero.

In a system where all the forces are internal, the external forces do not act on the objects within the system. As a result, the internal forces between the objects can only transfer momentum within the system, but not change the total momentum of the system. This principle is known as the law of conservation of momentum.

When the net force on the system is zero, it means that the total force acting on the system is balanced and there is no external force causing an acceleration. According to Newton's second law of motion (F = ma), if the net force is zero, the acceleration of the system is zero. Therefore, the velocities of the objects in the system remain constant, and the total momentum of the system is conserved.

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The cart impacts the safety barrier with speed \(v_0\) = 3.30 m/s, the values of the constants are approximately  \(k_1\) is 45.513 N/m, and  \(k_2\) is 79.173 N/m.

The values for the constants  \(k_1\)  and  \(k_2\) can be calculated as:

Here, it is given that:

Initial speed, \(v_0\) = 3.00 m/s

Maximum spring deflection, \(x_{max\) = 415 mm = 415 × \(10^{(-3)\) m

Velocity at half-maximum deflection, \(v_{half\) = 2.64 m/s

At maximum deflection ( \(x_{max\)), the cart comes to a stop, so the final velocity (\(v_f\)) is 0 m/s.

Using the equation for deceleration:

a = - \(k_1\) x -  \(k_2\)\(x^3\)

When the cart is at maximum deflection, x =  \(x_{max\) and \(v_f\) = 0, so we have:

0 = - \(k_1\) ( \(x_{max\)) -  \(k_2\)( \(x_{max\))³

When the cart is at half-maximum deflection, x =  \(x_{max\) /2 and  \(v_f\) = \(v_{half\), so we have:

\(v_{half\)  = - \(k_1\) ( \(x_{max\)/2) -  \(k_2\)\((xmax/2)^3\)

We have a system of two equations to solve for  \(k_1\)  and  \(k_2\).

From the first equation, we can express  \(k_1\)  in terms of  \(k_2\):

 \(k_1\)  = -( \(k_2\)\((xmax)^3\)) /  \(x_{max\)

Substituting this expression for  \(k_1\)  into the second equation, we get:

\(v_{half\)  = ( \(k_2\)\((xmax)^2\)) / 2 -  \(k_2\)\((xmax)^3\) / 8

To solve for  \(k_2\), we rearrange the equation:

 \(k_2\)\((xmax)^3\) / 8 - ( \(k_2\)\((xmax)^2\)) / 2 +  \(v_{half\)  = 0

Substituting the given values:

(\(415^3\)/8) \(k_2\) - (\(415^2\)/2) \(k_2\) + 2.64 = 0

Simplifying and solving the equation, we find:

 \(k_2\) ≈ 79.173 \(N/m^3\)

Substituting this value of   \(k_2\)  back into the expression for  \(k_1\) :

 \(k_1\)  = -(  \(k_2\) \((xmax)^3\)) /  \(x_{max\)

 \(k_1\)  ≈ -79.173 × \((415 * 10^{(-3)} )^3 / (415 * 10^{(-3)} )\)

 \(k_1\)  ≈ 45.513 N/m

Thus, the values for the constants are approximately  \(k_1\)  = 45.513 N/m and  \(k_2\) = 79.173 N/m.

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Your question seems incomplete, the probable complete question is:

The cart impacts the safety barrier with speed v0 = 3.00 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = -k1x - k2x3, where x is the amount of spring deflection from the undeformed position and k1 and k2 are positive constants. If the maximum spring deflection is 415 mm and the velocity at half-maximum deflection is 2.64 m/s, determine the values for the constants k1 and k2.

Explanation: dfvjdsbv dvjdbv dvuhdv

Answer:

Option D

Explanation:

The options for the question are

a) How do galaxies rotate?

b) What is the weather on Neptune?

c) What is the core of Saturn made of?

d) What other solar systems have planets?

Solution

The Hubble space telescope was designed and integrated into the extraterrestrial system in order to capture information about the surrounding universe. If the  Keck Observatory has a better observation capacity than the Hubble space telescope then the scientist would be interested to know the surrounding planets in the solar system.

Hence, option D is correct