If ϕ = 90° − θ, what is the value of sin2 ϕ + sin2 θ?

Q: Obtain expressions in component form for the following polar coordinates. A) 13.0 m, 140 degrees…

A: The projections of vector R on the axis: Rx=RcosθRy=Rsinθ   The vector in the component notation:…

Q: The curved portion of the v-t curve shown in the figure are second degree parabolas with horizontal…

A: Given slope at t=0 and t=12 sec. We have to  Determine the displacement at t=18 sec. 30 Ans: 282

Q: Let: A = 423 units @ 50.6 degrees %3D B = 211 units @ 10.2 degrees If C= A + B

A: VVEV Vector addition…

Q: Part A A =-2.00 + 6.00j and B=5.00i – 3.003. %3D Express your answer in degrees. Vη ΑΣφ Submit…

A: Dot product of A.B = AB cos(theta)

Q: Given the dimensions of the box, what is the best value of its volume? Length = 4.21 ± 0.30 cm Width…

A:

Q: You have been given the operations below. Do them and display your answers using the correct number…

A: Question 1 solution

Q: 6. A projectile starting from ground hits a target on the ground located at a distance of 1500…

A:

Q: iven the vectors: A = 14 cm ∡ 139°, B = 9.8 cm ∡ 26°, C = 0.17 m ∡ 97° and D = 154 mm ∡ 317°. Find…

A: Given- A = 14 cm ∡ 139°=0.14 m B = 9.8 cm ∡ 26°=0.098 m C = 0.17 m ∡ 97° D = 154 mm ∡ 317°=0.154 m

Q: A person is standing at the edge of the water and looking out at the ocean (see figure). The height…

A: Given, Height of person,h=1.5 m Radius of Earth,R=6.38×106m

Q: The line from a point 150 feet from the base of a redwood tree to the top of the tree is 211 feet.…

A:

Q: If matrix A = 6 = then value of A100 is 100 10 100 100 100

A: Matrix A=[2   0;  0   1], Matrix A2 =A×A=[2   0;  0   1]×[2   0;  0   1]=[2×2+0×0     2×0+1×0;…

Q: Show that the force vector D = 2i – 4j +k is orthogonal to the force vector G = 3i + 43 + 10k. %3D

A: D→=2i^-4j^+k^ G→=3i^+4j^+10k^

Q: Given the resultant R = -3i + 4j , what is the direction in terms of angle θ from the +x axis?

A:

Q: The polar coordinates of a certain point are (r = 3.15 cm, 0 = %3D 262°). (a) Find its Cartesian…

A: The transformation equation for polar to cartesian coordinate is :          x=rcosθandy=rsinθ The…

Q: two points are given in polar coordinates by  (r, ?) = (2.20 m, 50.0°)  and  (r, ?) = (3.00 m,…

A:

Q: In Figure P1.49, find (a) the side opposite θ, (b) the side adjacentto ϕ, (c) cos θ, (d) sin ϕ, and…

A: Given:

Q: A high fountain of water is located at the center of a circularpool as shown in Figure P1.47. Not…

A: Given:Circumference of the pool = 15 mAngle of elevation =  55.0°

Q: • Name the components labelled in Fig. Q1(c) 3. 0959 0960 2

A:

Q: Rewrite the following measurements in the units suggested 40 km = m = Cm %3D ml ..... 450000000 gm…

A:

Q: -Use Excel to plot the relationship between (E, u), using E in the most left column in Excel. E^2…

A:

Q: For the plane shown in Figure 1, with respect to X and Y axes determine the location of the centroid

A:

Q: Given the following graph, calculate the slope and uncertainty in the slope. Period vs length T (s)…

A: From the graph, x1,y1=16.05cm,22.60cmx2,y2=6.60cm,3.70cm ∆y=0.6 cm Determine the slope as below.…

Q: In the figure given below, with F1 = 60j + 80k and F2= 50i -100j + 100k, what is the %3D value of B?…

A:

Q: 38N 86N 6cm P. Q In the figure length of the right part of the dotted vertical line equals O 3.52 cm…

A:

Q: Given the two displacement D = (6.00î + 3.00ĵ-1.00k̂)m E = (4.00î - 5.00ĵ+8.00k̂) Find the…

A: Vector 2D-E

Q: If Å = 2î + 2j – 3k, B = -4i -2j +3k, and C = Ã+ B. Then the angle between the vector C nd the %3D…

A: Given : A = 2i + 2j - 3k B = - 4i - 2j + 3k C = A + B

Q: Given o1 =20 degrees find 02 in degrees

A: According to snell lawsinisinr=n2n1Herei=incident angle r=refracted anglen2=refractive index of…

Q: What is the slope the graph A versus B? For a given set of values A (2cm, 4cm, 6cm, 8cm, 10cm) B…

A: A (in cm) B (in cm) 2 0.8 4 1.6 6 2.4 8 3.2 10 4

Q: Let A = (2i + 6j)m and B= (-i+ 2j)m . Find the magnitude of 2A – 3B O 8.22 O 6.22

A: A=(2i+6j) m B=(-i+2j) m

Q: For an angle, u measured from the positive x - axis, the valuesof sin u and cos u are always (choose…

A: Maximum value of sin and cos functions are +1 and the minimum value for both is -1.Thus, option (d)…

Q: polar angle of point

A:

Q: Solve the following operation(s) and express final answers to the correct number of significant…

A: We have to solve the following operations and express final answers to the correct number of…

Q: How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful…

A: Given data:  Distance traveled (d) = 1.00 ft = 0.3048 m

Q: For numbers 23 and 24, complete the table by completing the unknown data L2 AXIS COG Wi P1 WBEAM…

A: Draw the free-body diagram of the system.

Q: Two vectors A= 11-2j and B = 21 +3j.Find the approximate angle between the vectors (-3A) and (2B)?…

A: Solution: Given that A =i-5j B = 2i+3j to find the angle between -3A and 2B

Q: If ū = (7, –6, 0) and i = (1, 1,0), find the length and direction of ủ x ủ and i xu. %3D Length of u…

A:

Q: Using trigonometrical functions, find out missing part (? or x) in the following figures. B 14 115 А…

A:

Q: Convert the following quantities into standard units {SI unit} 1: 100 cm2 = m2 2: 100 Miles %3D 3:…

A:

Q: 2 points you have the matrix 30 1 A = |-1 2 0 3 1 2 Very specific inverted? 0.2 0.8 0.4 0.6

A: The matrix which is specifically invert is called inversion of matrix.

Q: Find the resultant R using component method Magnitude Angle (*) y a 18.5 30 16.0215 9.25 b 20.5 260…

A: Given Data : The x and y components of all the four vectors a, b, c, and d are given in the table.

Q: What is the magnitude of (12i+8.0j-6.0k) cm/s? O 12 cm/s O 8.0 cm/s O 24 cm/s O 15 cm/s O 16 cm/s

A:

Q: 13. Using trigonometric functions, find the missing part (? or x) in the following figures. B 14 115…

A:

Q: To estimate the size of the moon, a person holds a round pencil of diameter 0.70 cm. When the pencil…

A: Calculate the angle subtended by the moon. θ= Diameter of pencil/distance of moon from eye    =…

Q: You obtained the following data performing a lab experiment: t (s) y(m) 1 5 2…

A: t (s) t2 (s2) y (m) 1 1 5 2 4 20 3 9 45 4 16 80

Q: A woman measures the angle of elevation of a mountaintop as 12.0∘ . After walking 1.00 km closer to…

A: The most significant definitions that are used when dealing with heights and distances are given as:…

Q: A surveyor measures the distance across a straight river by the following method: Starting directly…

A: We need to calculate the width of the river given the information collected by the surveyor.

Q: Q.6 Give the reading of the micrometers below: 10 30 40 50 60 45 61 7. 40 d=? mm

A: Solution: To  give the reading of the micrometers

Refraction of Light

Refraction is a change in the direction of light rays when they travel from one medium to another. It is the bending of light when it goes through different media.

Angle of Refraction

Light is considered by many scientists to have dual nature, both particle nature and wave nature. First, Particle nature is one in which we consider a stream of packets of energy called photons. Second, Wave nature is considering light as electromagnetic radiation whereas part of it is perceived by humans. Visible spectrum defined by humans lies in a range of 400 to 700 nm wavelengths.

Index of Refraction of Diamond

Diamond, the world’s hardest naturally occurring material and mineral known, is a solid form of the element carbon. The atoms are arranged in a crystal structure called diamond cubic. They exist in a huge variety of colours. Also, they are one of the best conductors of heat and have a very high melting point.