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3 years ago

If f^-1(y) is the inverse of f(x) which statements must be true?

1 answer:

6 0

Let us assume f(x) = 2x - 5
f⁻¹(x) = (x + 5)/2
f(f⁻¹(x)) = 2((x + 5)/2) - 5 = x
f⁻¹(f(x)) = (2x - 5 + 5)/2 = x
The domain of a function is the range of its inverse and vice versa
The range of a function is the domain of its inverse and vice versa
Therefore, statements A, B, D and E are true

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In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling

kirza4 [7]

Answer:

v₁ = 3.5 m/s

v₂ = 6.4 m/s

Explanation:

We have the following data:

m₁ = mass of trailing car = 400 kg

m₂ = mass of leading car = 400 kg

u₁ = initial speed of trailing car = 6.4 m/s

u₂ = initial speed of leading car = 3.5 m/s

v₁ = final speed of trailing car = ?

v₂ = final speed of leading car = ?

The final speed of the leading car is given by the following formula:

$v_2=\frac{2m_1}{m_1+m_2}u_1-\frac{m_1-m_2}{m_1+m_2}u_2\\\\v_2=\frac{(2)(400\ kg)}{400\ kg+400\ kg}(6.4\ m/s)-\frac{400\ kg-400\ kg}{400\ kg + 400\ kg}(3.5\ m/s)$

The final speed of the leading car is given by the following formula:

$v_1=\frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2\\\\v_1=\frac{400\ kg-400\ kg}{400\ kg + 400\ kg}(6.4\ m/s)+\frac{(2)(400\ kg)}{400\ kg+400\ kg}(3.5\ m/s)$

4 0

3 years ago

A figure shows a vertically moving block on the end of a cord. The graph next to the figure gives the vertical velocity componen

Sergio [31]

It should be 2/9/10 in functional form

3 0

3 years ago

A force of 6600 N is exerted on a piston that has an area of 0.010 m2

sveticcg [70]

Answer:

Choice A: approximately $0.015\; \rm m^2$ , assuming that the two pistons are connected via some confined liquid to form a simple machine.

Explanation:

Assume that the two pistons are connected via some liquid that is confined. Pressure from the first piston:

$\displaystyle P_1 = \frac{F_1}{A_1} = \frac{6.600\times 10^3\; \rm N}{1.0\times 10^{-2}\; \rm m^{2}} = 6.6\times 10^{5}\; \rm N \cdot m^{-2}$ .

By Pascal's Principle, because the first piston exerted a pressure of $6.6\times 10^{5}\; \rm N \cdot m^{-2}$ on the liquid, the liquid will now exert the same amount of pressure on the walls of the container.

Assume that the second piston is part of that wall. The pressure on the second piston will also be $6.6\times 10^{5}\; \rm N \cdot m^{-2}$ . In other words:

$P_2 = P_1 = 6.6\times 10^{5}\; \rm N \cdot m^{-2}$ .

To achieve a force of $9.900 \times 10^3\; \rm N$ , the surface area of the second piston should be:

$\displaystyle A_2 = \frac{F_2}{P_2} = \frac{9.900\times 10^{3}\; \rm N}{6.6\times 10^5\; \rm N \cdot m^{-2}} \approx 0.015\; \rm m^{2}$ .

4 0

3 years ago

10. Explain the principle of electric motor. Write its uses.

konstantin123 [22]

Explanation:

The principle of an electric motor is based on the current carrying conductor which produces magnetic field around it. A current carrying conductor is placed perpendicular to the magnetic field so that it experiences a force.

The largest electric motors are used for ship propulsion, pipeline compression and pumped-storage applications with ratings reaching 100 megawatts. Electric motors are found in industrial fans, blowers and pumps, machine tools, household appliances, power tools and disk drives.

6 0

2 years ago

Calculate the mass of an object with a density of 102.5 g/mL and volume of 375 mL.

AveGali [126]

Answer:

38,437.5

Explanation:

Density(d)= 102.5g/ml

Volume (v)=375ml

Mass(m) = ?

D =m/v

102.5= m/375

102.5*375=m

38,437.5=m

therefore Mass = 38,437.5g/ml.

6 0

3 years ago