Find the lengths a, b, c, and d in the following figure:

Question

2021-05-02

First find PQ and QR. For PQ, use the right-triangle:

\(\displaystyle{\tan{{\left({24}^{\circ}\right)}}}={\frac{{{1}}}{{{P}{Q}}}}\), so \(\displaystyle{P}{Q}={\frac{{{1}}}{{{\tan{{\left({24}^{\circ}\right\rbrace}}}}}}\)

For QR, first find its opposite angle to be \(\displaystyle{180}^{\circ}-{24}^{\circ}-{48}^{\circ}={108}^{\circ}\)

Now using the law of sines:

\(\displaystyle{\frac{{{\sin{{\left({108}^{\circ}\right)}}}}}{{{Q}{R}}}}={\frac{{{\sin{{\left({24}^{\circ}\right)}}}}}{{{2}}}}\), thus \(\displaystyle{Q}{R}={\frac{{{2}{\sin{{\left({108}^{\circ}\right)}}}}}{{{\sin{{\left({24}^{\circ}\right)}}}}}}\)

Therefore:

\(\displaystyle{P}{R}={P}{Q}+{Q}{R}={\frac{{{1}}}{{{\tan{{\left({24}^{\circ}\right)}}}}}}+{\frac{{{2}{\sin{{\left({108}^{\circ}\right)}}}}}{{{\sin{{\left({24}^{\circ}\right)}}}}}}\approx{6.92}\)

\(\displaystyle{\tan{{\left({24}^{\circ}\right)}}}={\frac{{{1}}}{{{P}{Q}}}}\), so \(\displaystyle{P}{Q}={\frac{{{1}}}{{{\tan{{\left({24}^{\circ}\right\rbrace}}}}}}\)

For QR, first find its opposite angle to be \(\displaystyle{180}^{\circ}-{24}^{\circ}-{48}^{\circ}={108}^{\circ}\)

Now using the law of sines:

\(\displaystyle{\frac{{{\sin{{\left({108}^{\circ}\right)}}}}}{{{Q}{R}}}}={\frac{{{\sin{{\left({24}^{\circ}\right)}}}}}{{{2}}}}\), thus \(\displaystyle{Q}{R}={\frac{{{2}{\sin{{\left({108}^{\circ}\right)}}}}}{{{\sin{{\left({24}^{\circ}\right)}}}}}}\)

Therefore:

\(\displaystyle{P}{R}={P}{Q}+{Q}{R}={\frac{{{1}}}{{{\tan{{\left({24}^{\circ}\right)}}}}}}+{\frac{{{2}{\sin{{\left({108}^{\circ}\right)}}}}}{{{\sin{{\left({24}^{\circ}\right)}}}}}}\approx{6.92}\)

asked 2021-04-19

In the figure, a cube of edge length L = 0.599 m and mass 970 kg is suspended by a rope in an open tank of liquid of density 1.05E+3 kg/m3. Find (a) the magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) the magnitude of the total upward force on the bottom of the cube, and (c) the tension in the rope. (d) Calculate the magnitude of the buoyant force on the cube using Archimede's principle.

asked 2021-03-20

Find the tension in each cord in Figure if the weight ofthe suspended object is w.

a)

b)

a)

b)

asked 2021-04-24

A wind farm generator uses a two-bladed propellermounted on a pylon at a height of 20 m. The length of eachpropeller blade is 12 m. A tip of the propeller breaks offwhen the propeller is vertical. The fragment flies offhorizontally, falls, and strikes the ground at P. Just beforethe fragment broke off, the propeller was turning uniformly, taking1.2 s for each rotation. In the above figure, the distancefrom the base of the pylon to the point where the fragment strikesthe ground is closest to:

a) 130 m

b) 160 m

c) 120 m

d) 140 m

e) 150 m

asked 2021-05-04

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)

I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)

Part A

What is Q for path abc?

Express your answer to two significant figures and include the appropriate units.

Part B

f Pc=1/2Pb, what is W for path cda?

Express your answer to two significant figures and include the appropriate units.

Part C

What is Q for path cda?

Express your answer to two significant figures and include the appropriate units.

Part D

What is Ua?Uc?

Express your answer to two significant figures and include the appropriate units.

Part E

If Ud?Uc=42J, what is Q for path da?

Express your answer to two significant figures and include the appropriate units.

asked 2021-02-23

A block of mass m=3.6 kg, moving on africtionless surface with a speed \(\displaystyle{v}_{{1}}={9.3}\) m/s makes a perfectly elastic collision with a block of mass Mat rest. After the collision, the 3.6 kg block recoils with a speed of \(\displaystyle{v}_{{1}}={2.7}\) m/s in figure, the speed of the vlock of mass M after the collision is closest to:

a. 9.3 m/s

b. 6.6 m/s

c. 8.0 m/s

d. 10.7 m/s

e. 12.0 m/s

asked 2021-03-26

A pair of forces with equal magnitudes, opposite directions,and different lines of action is called a "couple". When acouple acts on a rigid object, the couple produces a torque thatdoes not depend on the location of the axis. The drawing shows acouple acting on a tire wrench, each force being perpendicular tothe wrench. Determine an expression for the torque produced by thecouple when the axis is perpendicular to the tired and passesthrough (a) point A, (b) point B, and (c) point C. Express youranswers in terms of the magnitude F of the force and the length Lof the wrench

asked 2021-05-08

In the figure a worker lifts a weight \(\displaystyle\omega\) by pulling down on a rope with a force \(\displaystyle\vec{{{F}}}\). The upper pulley is attached to the ceiling by a chain,and the lower pulley is attached to the weight by another chain.The weight is lifted at constant speed. Assume that the rope,pulleys, and chains all have negligible weights.

A) In terms of \(\displaystyle\omega\),find the tension in the lower chain.

B) In terms of \(\displaystyle\omega\),find the tension in upper chain.

C) In terms of \(\displaystyle\omega\),find the magnitude of the force \(\displaystyle\vec{{{F}}}\) if the weight is lifted at constant speed.

A) In terms of \(\displaystyle\omega\),find the tension in the lower chain.

B) In terms of \(\displaystyle\omega\),find the tension in upper chain.

C) In terms of \(\displaystyle\omega\),find the magnitude of the force \(\displaystyle\vec{{{F}}}\) if the weight is lifted at constant speed.

asked 2021-05-01

Find all zeros of p(x), real or imaginary. \(p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27\) List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of \(p(x) = (x-c)(x^{3}+Ax^{2}+Bx+D)\) State the exact answer and a decimal approximation of each zero to the tenths place

asked 2021-03-21

The lens and mirror in the figure below are separated by 1.00 m and have focal lengths of +79.6 cm and -50.2 cm, respectively

asked 2021-04-13

A slab of insulating material of uniform thickness d, lying between \(\displaystyle{\frac{{-{d}}}{{{2}}}}\) to \(\displaystyle{\frac{{{d}}}{{{2}}}}\) along the x axis, extends infinitely in the y and z directions, as shown in the figure. The slab has a uniform charge density \(\displaystyle\rho\). The electric field is zero in the middle of the slab, at x=0. Which of the following statements is true of the electric field \(\displaystyle{E}_{{{\vec}}}\) at the surface of one side of the slab?