Explanation:
a clinical thermometer is a thermometer used to measure human body temperature. mostade in the 20th century are mercury-in-glass thermometer. they ate accurate and sensitive having a narrow place where the mercury level rises very fast. a kink in the tube stops the mercury level from falling on its own.
hope it helps you
For each of the following statements about deep-water waves, determine if the statement is true or false, then explain why: The longer the wave, the deeper the wave base. The greater the wave height, the deeper the wave base. The longer the wave, the faster the wave travels. The greater the wave height, the faster the wave travels. The faster the wave, the greater the wave height.
Answer:
The longer the wave, the deeper the wave base - True
The greater the wave height, the deeper the wave base - false
The longer the wave, the faster the wave travels- true
The greater the wave height, the faster the wave travels- false
The faster the wave, the greater the wave height - False
Explanation:
When a wave has a high length it means that the wave base will be deeper.
The longer the wave, the deeper the wave base - True
When the weight height is big , the wave base will be deeper.
The greater the wave height, the deeper the wave base - false
The longer the wave, the faster the wave travels- true
The greater the wave height, the faster the wave travels- false
The faster the wave, the greater the wave height - False
uestloh 1
Which is taller, a 20ft giraffe or a 240 inch pole?
(Show your conversion factor in fraction form!)
Answer:
Height of pole = Height of giraffe
Explanation:
Given:
Height of giraffe = 20 ft
Height of pole = 240 inch
Find:
Which is taller
Computation:
Height of giraffe = 20 ft
We know that 1 ft = 12 inch
So,
Height of giraffe = 20 × 12 inch
Height of giraffe = 240 inch
and
Height of pole = 240 inch
Height of pole = Height of giraffe
A student measures the depth of a water well with an adjustable frequency audio oscillator. 2 successive resonant frequencies are heard at 40Hz and 50Hz. What is the depth of the well?
Answer:
17.15 m
Explanation:
Assuming the well is empty (full of air instead of water), the speed of sound is v = 343 m/s.
The water well acts as a pipe closed at one end. Therefore, the depth of the water well must be an odd multiple of a quarter of the resonant wavelength.
L = (2n − 1) λ/4, n = 1, 2, 3, etc.
v = λf, so λ = v/f. Substituting:
L = (2n − 1) v/(4f)
Solving for frequency:
f = (2n − 1) v/(4L)
The difference between two successive resonant frequencies is therefore:
Δf = (2(n+1) − 1) v/(4L) − (2n − 1) v/(4L)
Δf = (2n + 1) v/(4L) − (2n − 1) v/(4L)
Δf = 2 v/(4L)
Δf = v/(2L)
Plugging in values:
50 Hz − 40 Hz = 343 m/s / (2L)
2L = 34.3 m
L = 17.15 m
Describe the following as a (a) distance (b) speed (c) acceleration (d) force
6. Force
7 speed
8 distance
9 acceleration
lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they:________.
Answer: React with the skin
Explanation:
lab safety test Safety goggles and an apron must be worn when handling chemicals labeled corrosive because they React with the skin
In no more than five simple statements, use the kinetic theory to explain why an iron bar expands when it is heated.
Answer:
Iron expands because heating increases the space between the molecules
Explanation:
According to the kinetic molecular theory, all matter is composed of atoms and molecules which are in constant motion.
When a substance is heated, molecules of the substance begin to vibrate faster. This faster vibration leads to increased space between the molecules (expansion) . The kind of motion motion and degree of spacing of the molecules determine the state of matter in which the substance is found.
Hence, when an iron bar is heated, it expands due to increased motion of its molecules leading to spaces between them.
The pH scale is used to tell if a substance
is an acid or base. Substances with a pH
of 7 are neutral. An acid is anything
below 7 and a base is anything above 7.
Bleach has a pH of about 12. What type of
substance is bleach?
A. base
B. acid
C. neutral
Answer: Bleach is a base
Explanation: If bleach had a pH level of 12, a number above 7, than it is a base. Hope this helps!
You and your family are going on a trip in Europe. Calculate the speed in the following scenario. State how you calculated your answer and include correct units. A car travels 240 kilometers in 3 hours; What is the speed of the car during that time?
Answer:
22.2 m/s or 80 km/h
Explanation:
Given that
Distance travelled by the car, d = 240 km
Time taken by the car, t = 3 hours.
Speed of the car, v = ? m/s
for easy calculations, we will be converting the units to meters and seconds respectively.
240 km to meters would be
240 * 1000 m = 240000 m
3 hrs to seconds would be
3 * 60 mins * 60 seconds = 10800 s
now, we have our distance and time to be
d = 240000 m
t = 10800 s
speed is defined as the ratio of distance with respect to time taken, effectively,
Speed = distance/time
speed, v= 240000 / 10800
v = 22.2 m/s
therefore, the speed of the car during the time is 22.2 m/s, or if the speed is needed in km/h, we can convert it
22.2 * 3600/1000 =
80 km/h
State 1 difference between 1 way rotary motion and reversible rotary motion
Answer:
The difference between One-way as well as reversible rotary motion is described below.
Explanation:
Unless rotary motions occur restricted to single direction exclusively (i.e. whether clockwise as well as anti-clockwise only), it is defined as another rotary 'one-way' motion.This motor establishes that continuously variable movement at 360 ° chemically guided is conceivable. The rotating is regulated, and for a particular direction, the biochemical occurrences guiding rotation become incredibly selective.Comic-strip hero Superman meets an asteroid in outer space and hurls it at 800 m/s, as fast as a bullet. The asteroid is a thousand times more massive than Superman. In the strip, Superman is seen at rest after the throw. Taking physics into account, what would be his recoil speed (in km/s)?
Answer:
800km/s
Explanation:
Initial momentum = final momentum
the total momentum is zero, Before the release of the asteroid , but Superman and the asteroid are not moving.
So, according to the Conservation of momentum the total momentum when the astronaut is been thrown will equals to zero . Then we can say
Initial momentum = final momentum
Because the momentum of the Superman immediately the asteroid is been thrown is equal to the momentum of the asteroid
Momentum =(mass ×velocity)
the mass of the asteroid i= 1000M
Given velocity = 800 m/s,
momentum =(1000M)(800 m/s)
= 800,000M m/s.
to get the answer, we need to divide by Superman's mass, M, which gives his recoil velocity of 800,000 m/s.
But we're told to convert to km/ s
We know that 1m/s=0.001km/s
=(800,000M m/s)× (0.001km/s)
=800km/s
Therefore, his recoil speed (in km/s) is 800km/s
1
A force 2ON acts at a distance of 2n from a pivot.
what is the moment
force about the pivot
Answer:
[tex]\large \boxed{\mathrm{40 \ Nm}}[/tex]
Explanation:
[tex]\sf Moment \ (Nm) = Force \ (N) \times Distance \ from \ pivot \ (m)[/tex]
[tex]M=20 \times 2[/tex]
[tex]M=40[/tex]
*If someone says v-u=0 ,what does it mean. *What is the relation among mometum,mass and velocity. *A moving bus a little distance forward even when breaks are applied on it which Newton's laws work here? *Under what conditions acceleration of a moving object will be zero?
Answer:
1) It means that the acceleration is 0
2) Momentum, p = Mass, m × Velocity, v
3) Newton's second law of motion
4) The conditions where there are no resultant forces acting on the object
Explanation:
1) The value v - u = 0 means that the acceleration is 0
The relation between v and u is v = u + a·t
v - u = a·t
When v - u = 0 we have;
a·t = 0
a = 0 or t = 0
Acceleration, a = 0
2) The relation between momentum, mass and velocity is
Momentum, p = Mass, m × Velocity, v
p = m × v
3) The bus moving a little distance forward even when the breaks are applied is due to the following relation;
Force = Rate of change of momentum produced
Which is Newton's second law of motion
Therefore, where the the force is low, the rate of change of the momentum and therefore, the velocity will be low, and the bus will still move further after applying the breaks
4) According to Newton's first law of motion, the conditions under which the acceleration of a moving object will be zero includes conditions where there are no resultant forces acting on the object.
Marco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the frequency as 3 hertz, which statement about the wave is accurate?
This question is incomplete; here is the complete question:
Marco is conducting an experiment. He knows the wave that he is working with has a wavelength of 32.4 cm. If he measures the frequency as 3 hertz, which statement about the wave is accurate?
A. The wave has traveled 32.4 cm in 3 seconds.
B. The wave has traveled 32.4 cm in 9 seconds.
C. The wave has traveled 97.2 cm in 3 seconds.
D. The wave has traveled 97.2 cm in 1 second.
The answer to this question is D. The wave has traveled 97.2 cm in 1 second.
Explanation:
The frequency of a wave, which is in this case 3 hertz, represents the number of waves that go through a point during 1 second. According to this, if the frequency of the wave is 3 hertz this means in 1 second there were 3 waves. Moreover, if you multiply the wavelength (32.4cm) by the frequency (3) you will know the distance the wave traveled in 1 second: 32.4 x 3 = 97.2 cm. This makes option D the correct one as the distance in 1 second was 97.2 cm.
Answer:Is D!
Explanation:TEAT(Sorry) -_-*
hooke's law is described mathematically using the formula fsp=-kx. which statement is correct about spring force, fsp? A. It is always a positive force B. It is larger than the applied force C. It is the force doing the push or pull D. It is a vector quantity
Answer:
A. It is always a positive force
Explanation:
Hooke's law describes the relation between an applied force and extension ability of an elastic material. The law states that provided the elastic limit, e, of a material is not exceeded, the force, F, applied is proportional to the extension, x, provided temperature is constant.
i.e F = - kx
where k is the constant of proportionality, and the minus sign implies that the force is a restoring force.
The applied force can either be compressing or stretching force.
Millimeters, centimeters, meters,
kilometers, inches, feet, and
miles are all examples of
plz help
Millimeters, centimeters, meters, kilometers, inches, feet, and miles are all examples of unit of length like: distance between two points and displacement of any object.
What is unit?The quantity with a constant magnitude that is used to measure the magnitudes of other quantities of the same type is referred to as a unit in physics.The formula: physical quantity = numerical value × unit. can be used to determine a physical quantity's magnitude.A unit shouldn't alter as time or environmental factors like pressure and temperature change.It ought to be precisely defined.It need to be readily available and repeatable.Meter is a Si unit of length whereas centimeter is CGS unit of length and Feet is FPS unit of lengths. Another units are also useful in measuring lengths.
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How can you define a solution to an equation?
How to find average acceleration only using displacement and time?
Answer:
Average acceleration = Displacement / (time)^2
Explanation:
The unit for acceleration is
[tex]m {s}^{ - 2} [/tex]
Displacement = m
Time = s
Hence the units of displacement and time should be manipulated to get the unit of acceleration.
You can't. You can only find average velocity.
But if you also know that initial velocity is zero ... the object started from rest ... then
Avg acceleration =
2 x displacement / time-squared
(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is 120 m2 and their inside surface is at 18.0 oC, while their outside surface is at 5.0 oC. (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction
Answer:
a. 960 W b. One 1 kW room heater
Explanation:
a. The rate of heat conduction P = kA(T₂ - T₁)/d where k = 2 × 0.040 W/m-K = 0.080 W/m-K since the thermal conductivity of glass wool is 0.040 W/m-K and that of the material is twice the thermal conductivity of glass wool, A = area of walls = 120 m², T₁ = outside surface temperature = 5.0 °C, T₂ = inside surface temperature = 18.0 °C and d = thickness of wall = 13.0 cm = 0.13 m
P = kA(T₂ - T₁)/d
= 0.080 W/m-K × 120 m²(18.0 °C - 5.0 °C)/0.13 m
= 9.6 Wm/K × 13 K/0.13 m
= 124.8 Wm/0.13 m
= 960 W
b. The number of 1 kW room heater required will be
n = rate of heat conduction/power of one room heater = 960 W/ 1 kW = 960 W/1000 W = 0.96 ≅ 1
So we need only one 1 kW room heater.
An aircraft travelling at 600km/h accelerates steadily at 10km/h per second. Taking the speed of sound as 1100km/h at the aircraft's altitude how long will it take to reach the sound barrier?
speed of sound is the final velocity [tex] v=1100[/tex]
and initial velocity $u=600$ , $a=10$
$v=u+at$
$t=\dfrac{v-u}{a}= \dfrac{500}{10}$
$\implies t=50 h$
Find the odd one out a)Planets moving on it's axis,Strings of guitar (being played),Motion of a ferry wheel,The vehicles moving on a straight road. b)Motion of the moon around the earth,Motion of the earth around the sun,Motion of a merry-go-round,Heart-beat in a healthy person. c)Motion of a bullet fired from gun,Motion of a football player in the ground,Motion of a vehicle on a straight road,Motion of an apple falling from a tree
Answer:
a) Strings of guitar (being played)
b) Heart-beat in a healthy person
c) Motion of an apple falling from a tree
Explanation:
a) The motion of the string of a guitar being played is the only motion involving simple harmonic motion.
b) All the other motions are circular motion except the heart beat in a healthy person, which is periodic.
c) The motion of an apply falling from a tree is the only motion under the complete influence of gravity from the onset till the end.
Which statement best describes semi-conductors? Lack free electrons that can move to other atoms Electrons within their atoms are strongly held by the nuclei Most electrons within their atoms are paired Electricity can flow through it under special conditions
Answer:
Option D (Electricity can flow through it under special conditions ) seems to be the correct choice.
Explanation:
A semiconductor has become a crystal substance with improved electrochemical properties although the temperature is increased. That would be to say, it often functions as an insulating material rather than as a conductor or a circuit. Chemical solvents could perhaps greatly enhance its conducting capacity.Other options that are provided are not related to the given theory. So that the above would be the correct choice.
Statement "Lack free electrons that can move to other atoms " describe semi-conductor.
Properties of Semiconductor:A semiconductor is a type of crystalline solid that is halfway between a conductor and an insulator in terms of electrical conductivity. A semiconductor is conducting in nature because it has free electrons and holes.So that, Lack free electrons that can move to other atoms.Learn more about the Semiconductor here:
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Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quasar. Express your answer using two significant figures.2.) A 6 MSun black hole that formed in the supernova of a massive star. Express your answer using two significant figures.3.) A mini-black hole with the mass of the Moon. Express your answer using two significant figures.4.) Estimate the Schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that your weight is 50 kg.) Express your answer using one significant figure.
Answer:
(I). The Schwarzschild radius is [tex]2.94\times10^{8}\ km[/tex]
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is [tex]1.1\times10^{-7}\ km[/tex]
(IV). The Schwarzschild radius is [tex]7.4\times10^{-29}\ km[/tex]
Explanation:
Given that,
Mass of black hole [tex]m= 1\times10^{8} M_{sun}[/tex]
(I). We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Where, G = gravitational constant
M = mass
c = speed of light
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times1\times10^{8}\times1.989\times10^{30}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=2.94\times10^{8}\ km[/tex]
(II). Mass of block hole [tex]m= 6 M_{sun}[/tex]
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times6\times1.989\times10^{30}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=17.7\ km[/tex]
(III). Mass of block hole m= mass of moon
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times7.35\times10^{22}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=1.1\times10^{-7}\ km[/tex]
(IV). Mass = 50 kg
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times50}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=7.4\times10^{-29}\ km[/tex]
Hence, (I). The Schwarzschild radius is [tex]2.94\times10^{8}\ km[/tex]
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is [tex]1.1\times10^{-7}\ km[/tex]
(IV). The Schwarzschild radius is [tex]7.4\times10^{-29}\ km[/tex]
The energy conservation allows to find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
The schwarschild radius is defined as the distance from a black hole center at radius which the escape velocity is equal to the light speed, in some cases it is also called the event horizon.
Let's use Newton's second law where force is the universal law of attraction and acceleration is centripetal.
F = ma
F = [tex]G \frac{Mm}{r^2}[/tex]
Where F is the force, M the mass of the black hole, m the handle of the body, r the radius and v the speed of the body.
The energy of the gravitational field is
F = [tex]- \frac{dU}{dr }[/tex]
U = [tex]-G \frac{Mm}{r}[/tex]
Let's use conservation of energy
Em₀ = K + U = ½ m v² - [tex]G \frac{Mm}{r}[/tex]
In infinity the energy
Em_f = 0
energy is conserved
Em₀ = Em_f
½ m v² - [tex]G \frac{Mm }{r}[/tex] = 0
r = [tex]\frac{2GM}{v^2}[/tex]
From the definition of the Schwarschild radius this speed is equal to the light speed
v = c
r = [tex]\frac{2GM}{c^2 }[/tex]
They ask to calculate the radius for several cases of different mass, claculate the constant value
V = [tex]\frac{2 \ 6.67 \ 10^{-11} }{(3 \ 10^8) ^2 }[/tex]
V = 1.482 10⁻²⁷
1) A black hole of mass M = 1 10⁸ [tex]M_{sum}[/tex]
The tabulated mass of the sun is [tex]M_{sum}[/tex] = 1.989 10³⁰ kg
Let's substitute
r = 1.482 10⁻²⁷ 1 10⁸ 1.989 10³⁰
r = 2.94 10⁸ km
With two significant figures
r = 2.9 10⁸ km
2) A black hole of mass M = 6 [tex]M_{sum}[/tex]
r = 1.482 10⁻²⁷ 6 1.989 10-30
r = 17.7 km
3) a mini black hole with the mass of the moon
Tabulated mass of the moon M = 7.35 10²² kg
r = 1.482 10⁻²⁷ 7.35 10²²
r = 1.1 10⁻⁷ km
4) A person of M = 50 kg
r = 1.482 10⁻²⁷ 50
r= 7 10-29 km
In conclusion using the conservation of energy we can find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
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select the correct relationship of the densities of the given substances: !●water < iron < aluminium < mercury ● Iron < water < mercury < aluminium ● water < aluminium < iron < mercury ● none of the above. asap plz!!!
Answer:
option a is correct
Explanation:
water ∠iron∠aluminium∠mercury
water density =1.0000
iron =7.487
aluminium=2.07
mercury=13.59
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 4 : 45 4:45 p.m. At this time, he started pumping gas into the tank. At exactly 4 : 50 4:50, the tank was full and he noticed that he had pumped 12.5 12.5 gallons. What is the average rate of flow of the gasoline into the gas tank
Answer:
Explanation:
Average rate = gallons / minutes
If 12.5gallons in 5mins
Xgallons in 1mins
12.5/5 = 2.5gallons per minute
Identify the wood turning equipment and what it does.
А
is used to turn wood. It rotates and carves wood to produce a
form.
Answer:
lathe
perfectly symmetrical
Answer: A lathe is used to turn wood . It rotates and carves wood to produce a perfectly symmetrical form .
First one is lathe .
Second one is perfectly symmetrical .
Explanation: I just took the test on Plato and had 100%
Will mark as BRAINLIEST.......
The position vector is given by vector r= 5t² I cap + 2 t³ j cap + 2 k cap. Find it's velocity and acceleration at t=2s.
Answer:
We have the position vector given in terms of time t. r(t) = t^3*i + t^2*j
To find the velocity vector we have to differentiate r(t) with respect to time.
r'(t) = 3t^2*i + 2t*j
The vector representing acceleration is the derivative of the position vector
r''(t) = 6t*i + 2*j
When time t = 2.
The velocity vector is 3*2^2*i + 2*2*j
=> 12*i + 4*j
The speed is the absolute value of the velocity vector or sqrt(12^2 + 4^2) = sqrt (144 + 16) = sqrt 160
The acceleration vector is 6*2*i + 2*j
=> 12*i + 2*j
The required acceleration at t=2 is 12*i + 2*j and the speed is sqrt 160.
Explanation:
Can I have thx and brainliest?
A car travels from point A to B in 3 hours and returns back to point A in 5 hours. Points A and B are 150 miles apart along a straight highway. Which of the following statements most accurately describes the motion of the car? Choose 1 answer:(Choice A) A The average velocity is 40 miles per hour. (Choice B) B The total displacement of the trip is 300 miles. (Choice C) C The average speed is 37.5 miles per hour. (Choice D) D The car travels at 50 mph for the first half and 30 mph for the second half.
Answer: D
Explanation:
Given that a car travels from point A to B in 3 hours and returns back to point A in 5 hours. Points A and B are 150 miles apart along a straight highway.
From point A to B
The speed = distance / time
Where
Distance = 150 mile
Time = 3 hours
Substitute the values into the formula
Speed = 150/3 = 50 mile/ hours
From Point B to Point A
Distance = 150 miles
Time = 5 hours
Where speed = distance/ time
substitute all the parameters into the formula
Speed = 150/5 = 30 mph
Therefore, The car travels at 50 mph for the first half and 30 mph for the second half.
The correct answer is option D
Water floats on a liquid called "carbon tetrachloride." The two liquids do not mix. A light ray passing from water into carbon tetrachloride has an incident angle of 45.0° and an angle of refraction of 40.1°. If the index of refraction of water is 1.33, what is the index of refraction of carbon tetrachloride?
Answer:
1.26
Explanation:
[tex]index \: of \: refraction \: = \: \ \frac{ \sin(angle \: of \: incidence) }{ \sin(angle \: of \: refraction) } [/tex]
[tex] \frac{ \sin(45.0) }{ \sin(40.1) } [/tex]
= 1.26
Refractive index is defined as the ratio of speed of light in the vacuume and in the medium.The index of refraction of carbon tetrachloride is 1.26.
Refractive index:
It is defined as the ratio of speed of light in the vacuume and in the medium.
[tex]\bold { n={\dfrac {c}{v}}}[/tex]
where
c -speed of light in vacuum
v - phase velocity of light in the medium.
It can also be calculated by the angle of refration,
[tex]\bold { n={\dfrac {sin\ i}{sin\ r}}}[/tex]
Where,
Sin i - angle of incidence = 45.0
sin r - angle of refraction = 40.1
Put the values in the formula,
[tex]\bold { n= {\dfrac {45.0}{40.1 }}}\\\\\bold { n= 1.26}[/tex]
Thereforew, the index of refraction of carbon tetrachloride is 1.26.
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Express the time spent to daily life activities during holidays as a fraction of whole day 1. Represent the fractions in pictorial form. 2. Write the fractions in simplest form. 3. Arrange them in ascending order.
Answer:
(II). The fractions in simplest form
[tex]\dfrac{31}{35}[/tex], [tex]\dfrac{91}{165}[/tex] and [tex]\dfrac{13}{5}[/tex]
(III). The fractions in ascending order
[tex]\dfrac{91}{165}<\dfrac{31}{35}<\dfrac{13}{5}[/tex]
Explanation:
Given that,
(I). Represent the fractions in pictorial form
(II). Write the fractions in simplest form.
(III). Arrange them in ascending order.
Suppose, The fractions in pictorial form
(a). [tex]\dfrac{3}{5}+\dfrac{2}{7}[/tex]
(b). [tex]\dfrac{9}{11}-\dfrac{4}{15}[/tex]
(c). [tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}[/tex]
We need to write in simplest form
Using given fraction
(a). [tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{3\times7}{5\times7}+\dfrac{2\times5}{7\times5}[/tex]
[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{21}{35}+\dfrac{10}{35}[/tex]
[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{21+10}{35}[/tex]
[tex]\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{31}{35}[/tex]
(b). [tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{9\times15}{11\times15}-\dfrac{4\times11}{15\times11}[/tex]
[tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{135-44}{165}[/tex]
[tex]\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{91}{165}[/tex]
(c). [tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7}{10}+\dfrac{2\times2}{5\times2}+\dfrac{3\times5}{5\times2}[/tex]
[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7}{10}+\dfrac{4+15}{10}[/tex]
[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{7+4+15}{10}[/tex]
[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{26}{10}[/tex]
[tex]\dfrac{7}{10}+\dfrac{2}{5}+\dfrac{3}{2}=\dfrac{13}{5}[/tex]
We need to arrange them in ascending order
Using simplest form
The simplest fraction in ascending order
[tex]\dfrac{91}{165}<\dfrac{31}{35}<\dfrac{13}{5}[/tex]
Hence, This is required solution.
Calculate the volume of this regular solid. A cylinder labeled B at the top, 13 centimeters high with a radius of 4 centimeters. What is the volume of the cylinder? Round your answer to the nearest hundredth.
Answer:
The volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Explanation:
Given that,
The height of the cylinder is 13 cm
Radius of the cylinder is 4 cm
We need to find the volume of the cylinder. The formula that is used to find the volume of a cylinder is given by :
[tex]V=\pi r^2 h\\\\V=\dfrac{22}{7} \times (4)^2 \times 13\\\\V=653.71\ \text{cm}^3[/tex]
So, the volume of the cylinder is [tex]653.71\ \text{cm}^3[/tex]
Answer:
653.45 is the answer
Explanation:
