given A=4i-10j and B= 7i+5j find b such that A+bB is a vector pointing along the x-axis (i.e has no y component)​

Answers

Answer 1

Answer:

-4/7

Explanation:

Given the following

A=4i-10j and B= 7i+5j

A+ bB = 4i-10j + (7i+5j)b

A+ bB =  4i-10j + 7ib+5jb

A+ bB =

The vector along the x-axis is expressed as i + 0j

If the vector A+ bB is pointing in the direction of the x-axis then;

[tex]A+ bB * \frac{i+0j}{|i+0j|} = 0 \\ (4+7b)i-(10-5b)j* \frac{i+0j}{\sqrt{1^2+0^2} } = 0\\(4+7b)i-(10-5b)j *(i+0j) = 0\\4+7b-0 =0\\7b=-4\\b = -4/7[/tex]

Hence the value of b is -4/7

Answer 2

The value of [tex]\beta[/tex] such that [tex]\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}[/tex] is 2.

According to the statement, we have following system of vectorial equations:

[tex]\vec A = 4\,\hat {i} - 10\,\hat{j}[/tex] (1)

[tex]\vec {B} = 7\,\hat{i} + 5\,\hat{j}[/tex] (2)

[tex]\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}[/tex] (3)

By applying (1) and (2) in (3):

[tex](4\,\hat{i}-10\,\hat{j}) + \beta\cdot (7\,\hat{i}+5\,\hat{j}) = c\,\hat{i}[/tex]

[tex](4+7\cdot \beta)\,\hat{i} +(-10+5\cdot \beta)\,\hat{j} = c\,\hat{i}[/tex]

And we get two scalar equations after analyzing each component:

[tex]4+7\cdot \beta = c[/tex] (4)

[tex]-10+5\cdot \beta = 0[/tex] (5)

We solve for [tex]\beta[/tex] in (5):

[tex]\beta = 2[/tex]

And for [tex]c[/tex] in (4):

[tex]c = 4+7\cdot (2)[/tex]

[tex]c = 18[/tex]

The value of [tex]\beta[/tex] such that [tex]\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}[/tex] is 2.

Please see this question related to Sum of Vectors for further details: https://brainly.com/question/11881720


Related Questions

If car A passes car B, then car A must be
A. accelerating at a greater rate than car B.
B. moving faster than car B, but not necessarily accelerating
C. accelerating
D. moving faster than car B and accelerating more than car B

Answers

Answer:

B. moving faster than car B, but not necessarily accelerating

Explanation:

Velocity is the speed of something. So car A's velocity is greater than car B but does not mean car A is accelerating.

A cataract is a clouding or opacity that develops in the eye's lens, often in older people. In extreme cases, the lens of the eye may need to be removed. What effect would this have on someone?

a. He would become nearsighted.
b. He would become farsighted.
c. He would become neither nearsighted nor farsighted.

Answers

Answer:

b. He would become farsighted.

Explanation:

A  cataract is defined as a medical condition where a person eyes becomes partially opaque and the person is not bale to see properly.

This is mainly caused due to aging or any injury in the eyes tissue which make up the lens of the eye.

It is the clouding of the lens of the eyes or opacity of the eyes. When treating cataract, in some cases the lens of the eyes are needed to be  removed. This may lead to person becoming far sighted.

Therefore, the correct option is (b).

A proton moves perpendicular to a uniform magnetic field at a speed of 1.75 107 m/s and experiences an acceleration of 2.25 1013 m/s2 in the positive x-direction when its velocity is in the positive z-direction. Determine the magnitude and direction of the field.

Answers

Answer:

B = 0.013(-j) T

Explanation:

Given that,

The speed of a proton, [tex]v=1.75\times 10^7\ m/s[/tex]

Acceleration experienced by the proton,[tex]a=2.25\times 10^3\ m/s[/tex]

We need to find the magnitude and the direction of the magnetic field. At equilibrium,

[tex]ma=qvB\\\\B=\dfrac{ma}{qv}\\\\B=\dfrac{1.67\times 10^{-27}\times 2.25\times 10^{13}}{1.6\times 10^{-19}\times 1.75\times 10^{7}}\\\\B=0.013\ T[/tex]

The velocity is in +z direction, force in +x direction, then the field must be in -y direction.

How much energy is stored in a spring that is compressed 0.650m if the spring constant is 725N/m?

Answers

Answer:

53.8Joule

Explanation:

hope it is helpful

please mark it as brainliest

Answer:

approximate 153.1J

Explanation:

W= 1/2k(x^2) = 1/2x725x(0.650)^2 = 153.15625 (J)

A car starting at rest accelerates at 3m/s² How far has the car travelled after 4s?​

Answers

Answer:

24m

Explanation:

you can use the formula

s=ut+1/2at²

s=0+1/2(3)(4)²

=1/2(3)(8)

=24m

I hope this helps

What type of potential energy is a 9 volt battery an example of?
Gravitational potential energy
Elastic potential energy
Electrical potential energy
chemical potential energy​

Answers

Answer:

chemical potential energy​

Explanation:

A 9v battery comes in different formats, such that the most common one is the carbon-zinc and alkaline chemistry, so these are alkaline batteries (there are also rechargeable or lithium batteries, these also depend on chemical interactions).

These batteries "draw" the energy from chemical interactions of the materials inside of it, so the type of potential energy that is stored in a battery is actually chemical (regardless of the fact that the energy can be transformed into electrical energy later) the "potential" refers to how the energy is stored.

Then the correct option is chemical potential energy​

Answer:

Chemical Potential Energy

Explanation:

Hope this helps!!

Have a blessed day/night!! <33

which watch is more preferable for the measurement of time among pendulum, quartz and atomic watch

Answers

Answer:

pendulum, quartz

Explanation:

how does laser works ?

Answers

Explanation:

Lasers produce a narrow beam of light in which all of the light waves have very similar wavelengths. The laser's light waves travel together with their peaks all lined up, or in phase. This is why laser beams are very narrow, very bright, and can be focused into a very tiny spot.

herical piece of candy is suspended in flowing water. The candy has a density of 1950 kg/m3 and has a 1.0 cm diameter. The water velocity is 1.0 m/s, the water density is assumed to be 1000.0 kg/m3, and the water viscosity is 1.010-3 kg/m/s. The diffusion coefficient of the candy solute in water is 2.010-9 m2/s, and the solubility of the candy solute in water is 2.0 kg/m3. Calculate the mass tran

Answers

Answer: Below is the complete question

A spherical piece of candy is suspended in flowing water. The candy has a density of 1950 kg/m3 and has a 1.0 cm diameter. The water velocity is 1.0 m/s, the water density is assumed to be 1000.0 kg/m3, and the water viscosity is 1.0x10-3 kg/m/s. The diffusion coefficient of the candy solute in water is 2.0x10-9 m2/s, and the solubility of the candy solute in water is 2.0 kg/m3. Calculate the mass transfer coefficient (m/s)

answer:

mass transfer coefficient = 9.56 * 10^-5 m/s

Explanation:

Candy density = 1950 kg/m^3

Candy diameter = 1 cm

Velocity of water = 1 m/s

water density = 1000 kg/m^3

Viscosity of water = 1 * 10^-3 kg/m/s

diffusion coefficient of candy in water = 2 * 10^-9 m^2/s

solubility of candy = 2 kg/m^3

Determine the mass transfer coefficient ( m/s )

( Sh) mass transfer coefficient ( flow across sphere ) = 2 + 0.6Re^1/2 * SC^1/3

where : Re = vdp / μ ,   Sh = KLd / Deff

attached below is the remaining solution .

mass transfer coefficient =  9.56 * 10^-5 m/s

Which of the following is not true about Triton, the large moon of Neptune? It is more reflective than Earth's Moon. It is larger than Earth's Moon. It is in a retrograde orbit. It has a thin atmosphere. It has nitrogen geysers.

Answers

Answer:

Triton is the largest of Neptune's 13 moons. It is unusual because it is the only large moon in our solar system that orbits in the opposite direction of its planet's rotation―a retrograde orbit. ... Like our own moon, Triton is locked in synchronous rotation with Neptune―one side faces the planet at all times.

If at a particular instant and at a certain point in space the electric field is in the x-direction and has a magnitude of 3.10 V/mV/m , what is the magnitude of the magnetic field of the wave at this same point in space and instant in time

Answers

Answer:

B = 1.03 10⁻⁸ T

Explanation:

For an electromagnetic wave, the electric and magnetic fields must oscillate in phase so that they remain between them at all times, otherwise the wave will extinguish

       

This relational is expressed by the relation

           E /B = c

           B = E / c

let's calculate

            B = 3.10 / 3 10⁸

            B = 1.03 10⁻⁸ T

Q.3. The equivalent resistance across AB is:
(a)1
(c)2
(b)3
(d)4

Answers

Answer:

1 ohm

Explanation:

First of all, the equivalent resistance for two resistors (r₁ and r₂) in parallel is given by:

1 / Eq = (1 / r₁) + (1 / r₂)

The equivalent resistance for resistance for two resistors (r₁ and r₂) in series is given by:

Eq = r₁ + r₂

Hence as we can see from the circuit diagram, 2Ω // 2Ω, and 2Ω // 2Ω, hence:

1/E₁ = 1/2 + 1/2

1/E₁ = 1

E₁ = 1Ω

1/E₂ = 1/2 + 1/2

1/E₂ = 1

E₂ = 1Ω

This then leads to E₁ being in series with E₂, hence the equivalent resistance (E₃) of E₁ and E₂ is:

E₃ = E₁ + E₂ = 1 + 1 = 2Ω

The equivalent resistance (Eq) across AB is the parallel combination of E₃ and the 2Ω resistor, therefore:

1/Eq = 1/E₃ + 1/2

1/Eq = 1/2 + 1/2

1/Eq = 1

Eq = 1Ω

19 point please please answer right need help

Block on an incline
A block of mass m1 = 3.9 kg on a smooth inclined plane of angle 38is connected by a cord over a small frictionless
pulley to a second block of mass m2 = 2.6 kg hanging vertically. Take the positive direction up the incline and use 9.81
m/s2 for g.
What is the tension in the cord to the nearest whole number?

Answers

Explanation:

We can write Newton's 2nd law as applied to the sliding mass [tex]m_1[/tex] as

[tex]T - m_1g\sin38 = m_1a\:\:\:\:\:\:\:(1)[/tex]

For the hanging mass [tex]m_2,[/tex] we can write NSL as

[tex]T - m_2g = -m_2a\:\:\:\:\:\:\:(2)[/tex]

We need to solve for a first before we can solve the tension T. So combining Eqns(1) & (2), we get

[tex](m_1 + m_2)a = m_2g - m_1g\sin38[/tex]

or

[tex]a = \left(\dfrac{m_2 - m_1\sin38}{m_1 + m_2}\right)g[/tex]

[tex]\:\:\:\:= 0.30\:\text{m/s}^2[/tex]

Using this value for the acceleration on Eqn(2), we find that the tension T is

[tex]T = m_2(g - a) = (2.6\:\text{kg})(9.51\:\text{m/s}^2)[/tex]

[tex]\:\:\:\:=24.7\:\text{N}[/tex]

Observe: Air pressure is equal to the weight of a column of air on a particular location. Air pressure is measured in hectopascals (hPa). Note how the air pressure changes as you move Station B towards the center of the high-pressure system.

a. What do you notice?
b. Why do you think this is called a high-pressure system?

Answers

Answer:

A. When moving towards a high pressure center the pressure values ​​increase in the equipment

B. This area is called high prison since the weight of the atmosphere on top is maximum

Explanation:

A) A high atmospheric pressure system is an area where the pressure is increasing the maximum value is close to 107 Kpa, the other side as low pressure can have small values ​​85.5 kPa.

When moving towards a high pressure center the pressure values ​​increase in the equipment

B) This area is called high prison since the weight of the atmosphere on top is maximum

in general they are areas of good weather

What is the largest known star?

Answers

Answer:

UY Scuti is slightly larger than VY Canis Majoris

Explanation:

These stars are millions of miles away and cannot be seen by the naked eye.

Beetlejuice is another large star that can be seen by the eye.

A toy car of mass 600g moves through 6m in 2 seconds.The average kinetic energy og the toy car is?

Answers

Explanation:

kE =1/2mv²

1/2(0.6×(3m/s)²

1/2(0.6×9m/s)

2.7J I think this is the answer

The average kinetic energy of the toy car is 2.7 J.

What is kinetic energy?

The energy of the body by the virtue of its motion is known as the kinetic energy of the body. It is defined as the product of half of mass and square of the velocity.

Given data;

Mass of car is,m= 600 g = 0.6 kg

d is the distance travelled = 6 m

T is the time travelled = 2 sec

The velocity of the car is found as;

v  = d /t

V = 6m / 2 sec

V = 3 m/sec

KE =1/2mv²

KE = 1/2 × 0.6 kg ×( 3 m/sec )²

KE = 2.7 J

Hence, the average kinetic energy of the toy car is 2.7 J.

To learn more about kinetic energy refer to the link;

https://brainly.com/question/999862

#SPJ2

1. Una pelota rueda hacia la derecha siguiendo una trayectoria en línea recta de modo que recorre una distancia de 10m en 5 s , después cambia su trayectoria cuando es lanzada hacia arriba 25m durante 7 s. Calcular la velocidad y la rapidez al punto final (altura maxima) al que llegó la pelota.

2. Una mariposa vuela en línea recta hacia el sur recorriendo una distancia de 15 m durante 28 s, después cambia de dirección hacia el Oeste recorriendo una distancia de 50 m en un tempo de 80 s ¿cuál es la velocidad y rapidez de la mariposa?

3.- Una persona camina durante 21 minutos hacia el este de su casa una distancia de 1500 m y después cambia su dirección hacia el Norte recorriendo una distancia de 3350 m en un tiempo 32 minutos llegando al supermercado. ¿Calcula la velocidad y rapidez de la persona?

4.- Un automóvil se mueve al Oeste recorriendo una distancia de 80 km en 1.2 horas, posteriormente cambia su trayectoria hacia el Sur, recorriendo una distancia de 120 km en un tiempo 1.6 hora. ¿Calcula la velocidad y rapidez del automóvil?

Answers

Answer:

https://youtu.be/ymHHdoCGJOU

1. A 2.7-kg copper block is given an initial speed of 4.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest. (a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in temperature.

Answers

Answer:

ΔT = 0.017 °C

Explanation:

According to the given condition, the change in internal energy of the block must be equal to 85% of its kinetic energy:

Change in Internal Energy = (0.85)(Kinetic Energy)

[tex]mC\Delta T = (0.85)\frac{1}{2}mv^2\\\\C\Delta T = (0.425)v^2\\\\\Delta T = \frac{0.425v^2}{C}[/tex]

where,

ΔT = increase in temperature = ?

v = speed of block = 4 m/s

C = specific heat capacity of copper = 389 J/kg.°C

Therefore,

[tex]\Delta T = \frac{(0.425)(4\ m/s)^2}{389}\\\\[/tex]

ΔT = 0.017 °C

Which of the following groups is the largest ?

population
community
ecosystem
biome

Answers

Answer:

B. Community

Took science classes for 6 years now

Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 21.0 cm and carries a clockwise current of 16.0 A , as viewed from above, and the outer wire has a diameter of 32.0 cm.

Required:
a. What must be the direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?
b. What must be the magnitude of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

Answers

Solution :

a). B at the center :

     [tex]$=\frac{u\times I}{2R}$[/tex]

Here, one of the current is in the clockwise direction and therefore, the other current must be in the clockwise direction in order to cancel out the effect of the magnetic field that is produced by the other.

Therefore, the answer is ANTICLOCKWISE or COUNTERCLOCKWISE

b). Also, the sum of the fields must be zero.

Therefore,

[tex]$\left(\frac{u\times I_1}{2R_1}\right) + \left(\frac{u\times I_2}{2R_2}\right) = 0$[/tex]

So,

[tex]$\frac{I_1}{d_1}= \frac{I_2}{d_2}$[/tex]

[tex]$=\frac{16}{21}=\frac{I_2}{32}$[/tex]

[tex]$I_2=24.38 $[/tex] A

Therefore, the current in the outer wire is 24.38 ampere.

Answer:

(a) counter clockwise

(b) 24.38 A

Explanation:

inner diameter, d = 21 cm

inner radius, r = 10.5 cm

Current in inner loop, I = 16 A clock wise

Outer diameter, D = 32 cm

Outer radius, R = 16 cm

(a) The magnetic filed due to the inner wire is inwards to the plane of paper. According to the Maxwell's right hand thumb rule, the direction of magnetic field in outer wire should be outwards so that the net magnetic field is zero at the center.

So, the direction of current in outer wire is counter clock wise in direction.

(b) Let the current in outer wire is I'.

The magnetic field due to the inner wire is balanced by the magnetic field due to the outer wire.

[tex]\frac{ \mu 0}{4\pi}\times \frac{2 I}{r}=\frac{\mu 0}{4\pi}\times \frac{2 I'}{R}\\\frac{16}{10.5}=\frac{I'}{16}\\\\I' = 24.38 A[/tex]

What is cubical expansivity of liquid while freezing

Answers

Answer:

"the ratio of increase in the volume of a solid per degree rise of temperature to its initial volume" -web

Explanation:

tbh up above ✅

Answer:

cubic meter

Explanation:

Increase in volume of a body on heating is referred to as volumetric expansion or cubical expansion

State the law of conservation of momentum

Answers

Explanation:

Conservation of momentum, general law of physics according to which the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant

A bus starts from rest and accelerates at 1.5m/s squared until it reaches a velocity of 9m/s .the bus continues at this velocity and then deccelerate at -2m/s squared until it comes to stop 400m from it's starting point. how much time did the bus takes to cover the 400m?​

Answers

Answer:

23s

Explanation:

s=ut+1/2at^2

the distance (s) is 400, initial velocity (u) is 0, acceleration (a) is 1.5 therefore

400=0t+1/2(1.5)t^2

400/0.75=0.75t^2/0.75

t^2=√533.33

t=23s

I hope this helps and sorry if it's wrong

which characteristic of nuclear fission makes it hazardous?

Answers

Answer:The radioactive waste

Explanation:Fission is the splitting of a heavy unstable nucleus into two Lighter nuclei

A scientist who studies insects, spiders, snails, and other bugs of an environment .

Botanist
Chemist
Ecologist
Entomologist

Answers

Question:- A scientist who studies insects, spiders, snails, and other bugs of an environment

Answer:- Entomologist

Explanation:-

Entomologist word comes from two words Entomon and biologist

Entomon which means insectbiologist which means the person who study living forms

Yea, gonna need some help. Thanks

Answers

Answer:

t = 3.48 s

Explanation:

The time for the maximum height can be calculated by taking the derivative of height function with respect to time and making it equal to zero:

[tex]h(t) = -16t^2+v_ot+h_o\\\\\frac{dh(t)}{dt}=0=-32t+v_o\\\\v_o = 32t[/tex]

where,

v₀ = initial speed = 110 ft/s

Therefore,

[tex]110 = 32t\\\\t = \frac{110}{32}\\\\[/tex]

t = 3.48 s

.
A mass of 8.72 kg gains 446 J of gravitational potential energy. To what height was it lifted?

Answers

Answer:

[tex]\boxed {\boxed {\sf 5.22 \ m}}[/tex]

Explanation:

Gravitational potential energy is the energy an object possesses due to its position. It is calculated using the following formula:

[tex]E_P=mgh[/tex]

Where m is the mass, g is the acceleration due to gravity, and h is the height.

The object has a mass of 8.72 kilograms. Assuming this occurs on Earth, the acceleration due to gravity is 9.8 meters per second squared. The object gains 446 Joules of potential energy.

Let's convert the units of Joules. This makes the process of canceling units simpler later on. 1 Joule is equal to 1 kilogram meter squared per second squared. The object gains 446 J, which is equal to 446 kg *m²/s².

EP= 446 kg*m²/s²m= 8.72 kg g= 9.8 m/s²

Substitute the values into the formula.

[tex]446 \ kg*m^2/s^2 = 8.72 \ kg * 9.8 \ m/s^2 *h[/tex]

Multiply on the right side of the equation.

[tex]446 \ kg*m^2/s^2 = 85.456 kg*m/s^2 *h[/tex]

We are solving for the height, so we must isolate the variable h. It is being multiplied by 85.456 kg*m/s². The inverse operation of multiplication is division, so we divide both sides by this value.

[tex]\frac{ 446 \ kg*m^2/s^2}{85.456 kg*m/s^2} = \frac{85.456 kg*m/s^2 *h}{85.456 kg*m/s^2}[/tex]

[tex]\frac{ 446 \ kg*m^2/s^2}{85.456 kg*m/s^2} =h[/tex]

The units of kg*m/s² cancel, leaving meters as our unit.

[tex]\frac{ 446 }{85.456 } \ m =h[/tex]

[tex]5.2190601011 \ m =h[/tex]

The original measurements of mass and potential energy have 3 significant figures, so our answer must have the same.

For the number we calculated, that is the hundredths place. The 9 in the thousandths place to the right tells us to round the 1 up to a 2.

[tex]5.22 \ m \approx h[/tex]

The object was lifted to a height of approximately 5.22 meters.

Find the intensity of the electromagnetic wave described in each case. (a) an electromagnetic wave with a wavelength of 655 nm and a peak electric field magnitude of 1.5 V/m. 0.002984 W/m2 (b) an electromagnetic wave with an angular frequency of 6.5 ✕ 1018 rad/s and a peak magnetic field magnitude of 10−10 T. 1.19366E-6 W/m2

Answers

The intensity of the electromagnetic wave in terms of the electric field is 0.00298 W/m² and the intensity of the electromagnetic wave in terms of the magnetic field is 1.193x10⁻⁶  W/m².

The intensity of the electromagnetic wave is related to the electric field as well as to the magnetic field.    

a) Intensity of the electromagnetic wave for the electromagnetic field.

The intensity of the electromagnetic wave (I) in terms of the electromagnetic field is given by:

[tex] I = \frac{E^{2}*c*\epsilon_{0}}{2} [/tex]   (1)

Where:

c: is the speed of light = 3.00*10⁸ m/s  

E: is the magnitude of the electric field = 1.5 V/m

ε₀: is the permittivity of free space = 8.85*10⁻¹² C²/Nm²

Hence, the intensity of the electromagnetic wave (eq 1) is:

[tex] I = \frac{(1.5 V/m)^{2}*3.00 \cdot 10^{8} m/s*8.85 \cdot 10^{-12} C^{2}/(N*m^{2})}{2} = 0.00298 W/m^{2} [/tex]                                                                                          

b) Intensity of the electromagnetic wave for the magnetic field

We can calculate the intensity of the electromagnetic wave (I) in terms of the magnetic field with the following equation:

[tex] I = \frac{cB^{2}}{2\mu_{0}} [/tex]   (2)

Where:

B: is the magnitude of the magnetic field = 10⁻¹⁰ T

μ₀: is the vacuum permeability = 4π*10⁻⁷ m*T/A

Therefore, the intensity of the electromagnetic wave (eq 2) is:

[tex] I = \frac{3.00 \cdot 10^{8} m/s*(1\cdot 10^{-10} m*T/A)^{2}}{2*4\pi \cdot 10^{-7} T/A} = 1.193 \cdot 10^{-6} W/m^{2} [/tex]

Learn more about electromagnetic waves and magnetic and electric fields here: https://brainly.com/question/11647801?referrer=searchResults                                          

                                   

I hope it helps you!

A simple model of the human eye ignores its lens entirely. Most of what the eye does to light happens at the outer surface of the transparent cornea. Assume that this surface has a radius of curvature of 6.50 mm and that the eyeball contains just one fluid, with a refractive index of 1.41. Determine the distance from the cornea where a very distant object will be imaged.

Answers

Answer:

the distance from the cornea where a very distant object will be imaged is 23.35 mm

Explanation:

Given the data in the question;

For a spherical refracting surface;

[tex]n_i[/tex]/[tex]d_0[/tex] + [tex]n_t[/tex]/[tex]d_i[/tex] = ( [tex]n_t[/tex] - [tex]n_i[/tex] )/R

where [tex]n_i[/tex] is the index of refraction of the light of ray in the incident medium

[tex]d_0[/tex] is the object distance

[tex]n_t[/tex] is the index of refraction of light ray in the refracted medium

[tex]d_i[/tex] is the image distance

R is the radius of curvature

Now, let [tex]d_0[/tex] = ∞, such that;

[tex]n_i[/tex]/∞ + [tex]n_t[/tex]/[tex]d_i[/tex] = ( [tex]n_t[/tex] - [tex]n_i[/tex] )/R

0 + [tex]n_t[/tex]/[tex]d_i[/tex] = ( [tex]n_t[/tex] - [tex]n_i[/tex] )/R

we make [tex]d_i[/tex] subject of the formula

[tex]n_t[/tex]R = [tex]d_i[/tex]( [tex]n_t[/tex] - [tex]n_i[/tex] )

[tex]d_i[/tex] = ( [tex]n_t[/tex] × R ) / ( [tex]n_t[/tex] - [tex]n_i[/tex] )

given that; R = 6.50 mm, [tex]n_t[/tex] = 1.41, we know that [tex]n_i[/tex] = 1.00

so we substitute

[tex]d_i[/tex] = (1.41 × 6.50 mm ) / ( 1.41 - 1.00 )

[tex]d_i[/tex] = 9.165 / 0.41

[tex]d_i[/tex] = 23.35 mm

Therefore, the distance from the cornea where a very distant object will be imaged is 23.35 mm

A man is pulling a 20 kg box with a rope that makes an angle of 60 with the horizontal.If he applies a force of 150 N and a frictional force of 15 N is present, calculate the acceleration of the box.​

Answers

F (horizontal) = (150 N) cos(60°) - 15 N = (20 kg) a

==>   a = ((150 N) cos(60°) - 15 N)/(20 kg) = 3 m/s²

To calculate the acceleration of the box, we need to consider the net force acting on it. So, the acceleration of the box is 3 m/s².

The net force is the vector sum of the applied force and the force of friction. First, let's find the horizontal and vertical components of the applied force:

Horizontal component of the applied force (F[tex]_{horizontal}[/tex]) = F[tex]_{applied}[/tex] × cos(θ)

F[tex]_{horizontal}[/tex] = 150 N × cos(60°)

F[tex]_{horizontal}[/tex] = 150 N × 0.5

F[tex]_{horizontal}[/tex] = 75 N

Vertical component of the applied force (F[tex]_{vertical}[/tex]) = F[tex]_{applied}[/tex] × sin(θ)

F[tex]_{vertical}[/tex] = 150 N × sin(60°)

F[tex]_{vertical}[/tex] = 150 N × (√3 / 2)

F[tex]_{vertical}[/tex] ≈ 129.9 N

Now, let's calculate the net force in the horizontal direction:

Net Force in the horizontal direction (F[tex]_{net horizontal}[/tex]) = F[tex]_{horizontal}[/tex] - F[tex]_{friction}[/tex]

F[tex]_{net horizontal}[/tex] = 75 N - 15 N

F[tex]_{net horizontal}[/tex] = 60 N

Now, we can calculate the acceleration (a) using Newton's second law of motion, F = ma:

F[tex]_{net horizontal}[/tex] = m × a

60 N = 20 kg × a

Now, solve for acceleration (a):

a = 60 N / 20 kg

a = 3 m/s²

So, the acceleration of the box is 3 m/s².

To know  more about acceleration

https://brainly.com/question/460763

#SPJ2

Other Questions
Which Venn Diagram is NOT correct? slope of (30, 600) (75, 1050) Buffer solutions that maintain certain levels of pH or acidity are widely used in biochemical experiments. One common buffer system uses sodium dihydrogenphosphate and sodium monohydrogenphosphate. What are the formulas of these two compounds How to write this essay Simplify. Write your answer in exponent form. Write a good research question for each of the following topics:1. Belief systems2. Biodiversity and ecosystem loss3. Changing communities4. Digital world5. Family6. Humans and other species7. Sustainable living8. Trade and aid Factor the expression completely 16x2 - 9y2 Using a simple aproxamation above,calculate the volume of the right circular cylinder with a radius of 2 meters and a height of 9 m 93Find the value of y. Nm bo co: - Tn cui nm: trong kho: 800 sp; gi bn: 1200sp - S lng sn xut: 10.000 sp - Gi bn: 100.000 ng/sp Nm k hoch: - D kin s lng sn xut tng 10% - Tn cui nm: tng 10% so vi nm bo co - Gi bn: 95.000 ng/sp - Gi vn 1 sp: 79.500 ng (tng 6% so vi nm bo co) Yu cu:1/ Tnh doanh thu nm k hoch 2/ Tnh gi vn hng bn nm k hoch (FIFO) what type of variation is this relationship Sickle cell anemia, a recessive deadly blood cell disease, is much more common in tropical climates because carriers (heterozygotes) are resistant to a deadly parasitic disease carried by mosquitoes (malaria). Given this information which of the following scenarios is a possibility?A. The widespread availability of any drug that protects a population from malaria will have the side effect of reducing deaths from sickle cell anemia over many generations.B. Having malaria will begin to give immunity to sickle cell anemia as well. C. Populations in areas where there are fewer mosquitoes will have more and more sickle cell anemia as time goes on. D. Genetie drift will always be so strong in these populations that none of this selection will be impactful, even for extremely large populations.E. Over many generations the mosquitses must develop sickle cell anemia too. The molecular ion is not visible in the mass spectrum of 2-chloro-2- methylpropane. At what m/z value would the molecular ion be if it were visible? What evidence is there in the mass spectrum that suggests that the peak at m/z= 77 contains a chlorine atom? The contribution margin format income statement: Multiple Choice is most frequently used for financial statement reporting purposes. uses a behavior pattern classification for costs rather than a functional cost classification approach. emphasizes that all costs change in proportion to any change in revenues. results in a larger amount of operating income than the traditional income statement format. We don't need society to survive. Statements. Health Hi, I need help. Im supposed to say why we dont need society to survive health in statements in act 2 the lord chamberlian is now no less concerned that laetres comduct in paris does not make him look too good Choose the correct way to complete the sentence about why it is important to critically analyze media.By critically analyzing media, a consumer can recognize the purpose of messages, , and recognize marketing strategies used to influence the public. Following the Thirty Years' War, rulers from across Europe agreed to:A. recognize Protestantism as a legitimate religion rulers couldpromote in their kingdoms.B. establish constitutions that would place restrictions on monarumpower and authority.C. strip the Catholic Church of all the land it controlled in non-Catholic countries.D. break apart the Holy Roman Empire into a number of sovereignCatholic kingdoms. Arvind is depressed and does not really like himself. At his new school, there are two people who seem interested in being friends with him. Amanda seems to enjoy his company and gives him compliments. Lucas seems to enjoy hanging out with Arvind but also is critical of him. Research suggests that Arvind will: PLEAZE HELPPPPPPPPPP