3.2.2.
vertical pylons bound huge
sagging chain. The cables that
canvas
bridge, are called shrouds.
dinat: axis OU direct vertically
Oh for example
the equation
Where X and at change
located 50 meters from the pylon.
Give your answer in meters.
3.2.3. The most beautiful bridges are cable-stayed.
vertical pylons bound huge
sagging chain. The cables that
hang from the chain and support canvas
bridge, are called shrouds.
The figure shows a diagram of one
cable-stayed bridge. Let us introduce a coordinate system
dinat: axis OU direct vertically
along one of the pylons, and the axis Oh for example
wim along the bridge deck, as shown in
figure. In this coordinate system, the chain
the equation
Where X and at change
rush in meters. Find the length of the guy
located 100 meters from the pylon.
Give your answer in meters.
4. Quadratic equations
4.1.1. (prototype 27959) In the side wall
you
is changing
tap opening,
M - initial
height of the water column
- attitude
cross-sectional areas of the crane and
tank, and g- acceleration of gravity
(consider
). After how much
seconds after opening the tap in the tank remain
a quarter of the original volume is missing
4.1.2.(28081) In the side wall of the high
honeycomb of the column of water in it, expressed in
is changing
time in seconds elapsed since
tap opening,
M - initial
height of the water column
- relatively
and tank, and g- free fall acceleration
Koryanov A.G., Nadezhkina N.V.
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nia (consider
). After some
water weight?
4.1.3.(41369) In the side wall of the high
cylindrical tank at the very bottom
crane attached. After opening the water
starts to flow out of the tank, while you
honeycomb of the column of water in it, expressed in
is changing
time in seconds elapsed since
tap opening,
M - initial
height of the water column
- relatively
Crane Cross-Section Areas
and tank, and g- free fall acceleration
nia (consider
). After some
seconds after opening the valve in the tank
a quarter of the original
water weight?
4.2.1. (prototype 27960) In the side wall
high cylindrical tank at the very
the bottom is fixed crane. After its opening
water begins to flow out of the tank, while
is changing
elementary
M/min - constant
yannye, t
Give your answer in minutes.
4.2.2.(28097) In the side wall of the high
cylindrical tank at the very bottom
crane attached. After opening the water
starts to flow out of the tank, while you
honeycomb of the column of water in it, expressed in
is changing
elementary
M/min - by-
standing, t– time in minutes elapsed
neck from the moment the tap is opened. During
how long will the water flow out of
tank? Give your answer in minutes.
4.2.3.(41421) In the side wall of the high
cylindrical tank at the very bottom
crane attached. After opening the water
starts to flow out of the tank, while you
honeycomb of the column of water in it, expressed in
is changing
elementary
M/min - constant
yannye, t– time in minutes elapsed since
the moment the valve is opened. During some
how long will water flow out of the tank?
Give your answer in minutes.
4.3.1. (prototype
Automobile,
moving at the initial moment of time
not with speed
Started tor-
permanent
acceleration
Behind t seconds after start
braking he went the way
(m). Determine the time elapsed from
moment of the start of braking, if
it is known that during this time the car
rode 30 meters. Express your answer in seconds
4.3.2.(28147) Car moving in
Started braking from a constant
acceleration
t
passed the way
(m). Define-
time the car traveled 90 meters.
Express your answer in seconds.
4.3.3.(41635) Car moving in
initial moment of time with speed
Started braking from a constant
acceleration
t seconds after the start of braking
Koryanov A.G., Nadezhkina N.V. Tasks B12. Application Content Tasks
www.alexlarin.net
passed the way
(m). Define-
the time elapsed since the start
braking, if you know what it is
time the car traveled 112 meters.
Express your answer in seconds.
5. Quadratic inequalities
5.1.1. (prototype 27956) Volume dependence
demand volume q(units per month) for products
monopoly enterprise from the price p
(thousand roubles.)
given
formula
The company's revenue for
month r
Determine
highest price p, at which the month
revenue
Will be at least
240 thousand rubles Give the answer in thousand rubles.
5.1.2.(28049) The dependence of the volume of demand
q
acceptance-monopolist
(thousand roubles.)
given
formula
The company's revenue for
month r(in thousand rubles) is calculated according to
Determine
highest price p, at which the month
revenue
will be at least
700 thousand rubles Give the answer in thousand rubles.
5.1.3.(41311) The dependence of the volume of demand
q(units per month) for pre-
acceptance-monopolist
(thousand roubles.)
given
formula
The company's revenue for me-
a month r(in thousand rubles) is calculated according to the form-
Determine the largest
price p, at which the monthly revenue
will be at least 360 thousand rubles. From-
Vet bring in thousand rubles.
5.2.1. (prototype 27957) Height above ground
the lei of the ball tossed up changes
according to law
Where h- you-
honeycomb in meters t– time in seconds, pro-
gone from the moment of the throw. How much se-
kund the ball will be at a height not
less than three meters?
5.2.2.(28065) Height above the ground
Where h– height in met-
rah, t
children to be at a height of at least 5 meters
5.2.3.(41341) Height above the ground
the ball thrown up changes according to the law
Where h– height in met-
rah, t– time in seconds elapsed since
moment of throw. How many seconds the ball boo-
children to be at a height of at least 8 met-
5.3.1. (prototype 27958) If enough
quickly rotate a bucket of water on the wind
rope in a vertical plane, then the water
will not spill out. When rotating
derka the force of water pressure on the bottom does not remain
is constant: it is maximum at
bottom point and minimum at the top.
Water will not pour out if its strength
pressure on the bottom will be positive during
all points of the trajectory except the top one,
where it can be equal to zero. To the top-
her point the pressure force, expressed in
newtons, is equal to
Where m –
mass of water in kilograms
- speed
bucket movements in m/s, L- rope length
ki in meters, g- acceleration of free
falls (consider
). From what
at the lowest speed it is necessary to rotate the
boldly so that the water does not spill out if
the length of the rope is 40 cm? The answer is
One of the most famous bridges in the world is the Golden Gate Bridge in San Francisco. You yourself have probably seen him in American films. It is designed as follows: between two huge pylons installed on the shore, the main load-bearing chains are stretched, to which, perpendicular to the ground, beams are suspended vertically. To these beams, in turn, the bridge deck is attached. If the bridge is long, additional supports are used. In this case, the suspension bridge consists of "segments".
The figure shows a diagram of one of the segments of the bridge. Let us designate the origin of coordinates at the point of installation of the pylon, direct the Ox axis along the bridge deck, and Oy - vertically along the pylon. The distance from the pylon to the beams and between the beams is 100 meters.
Determine the length of the beam closest to the pylon if the shape of the bridge chain is given by the equation:
y=0.0061\cdot x^2-0.854\cdot x+33
in which x and y are quantities that are measured in meters. Express your answer as a number in meters.
Show SolutionDecision
The beam length is the y coordinate. According to the condition of the problem, the beam closest to the pylon is located at a distance of 100 m from it. Thus, we need to calculate the value of y at the point x = 100 . Substituting the value into the chain shape equation, we get:
y=0.0061\cdot 100^2-0.854\cdot 100+33
y=61-85.4+33
y=8.6
This means that the length of the beam closest to the pylon is 8.6 meters.
Online USE test in mathematics 2016 Option No. 13. The test complies with the Federal State Educational Standards 2016. JavaScript must be enabled in your browser to take the test. The answer is entered in a special field. The answer is an integer or a decimal, for example: 4,25 (discharge division only separated by commas). Units of measure are not written. After entering the estimated answer, click the "Check" button. In the course of the decision, you can observe the number of points scored. All scores for tasks are distributed in accordance with KIM.
PART B ACTIVITIES
The diagram shows the average monthly air temperature in Minsk for each month in 2003. Months are indicated horizontally, temperatures are indicated vertically in degrees Celsius. Determine from the diagram how many months in 2003 the average temperature was negative.Does not work? View answer An automobile magazine determines car ratings based on safety ratings S, comfort C, functionality F, quality Q, and design D. Each indicator is evaluated by the readers of the journal on a 5-point scale. Rating R is calculated using the formula R = (3S + C + F + 2Q + D)/40. The table gives estimates of each indicator for three car models. Determine which car has the highest rating. In response, write down the value of this rating.
Does not work? View answer In triangle ABC, angle C is 90°, AC = 5, cosA = 4/5. Find the height CH.
Does not work? View answer The figure shows a graph of the antiderivative y \u003d F (x) of some function y \u003d f (x), defined on the interval (2; 13). Using the figure, determine the number of solutions to the equation f(x) = 0 on the interval .
Does not work? View answer
Oy Ox
x and y measured in meters. Find the length of the cable located 10 meters from the pylon. Give your answer in meters.
Decision.
Answer: 22.2.
Note 1.
Note that we calculated the length of the cable located at a distance of 10 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 10 m from the right pylon.
Note 2.
Answer: 22.2
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 20 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 20.04.
Note 1.
Note that we calculated the length of the cable located at a distance of 20 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 20 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
Answer: 20.04
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 30 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 17.67.
Note 1.
Note that we calculated the length of the cable located at a distance of 30 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 30 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
Answer: 17.67
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 40 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 15.2.
Note 1.
Note that we calculated the length of the cable located at a distance of 40 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 40 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
Answer: 15.2
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 50 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 12.75.
Note 1.
Note that we calculated the length of the cable located at a distance of 50 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 50 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
Answer: 12.75
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 60 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 10.44.
Note 1.
Note that we calculated the length of the cable located at a distance of 60 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 60 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
Answer: 10.44
The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds.
Let's introduce a coordinate system: axis Oy direct it vertically along one of the pylons, and the axis Ox direct along the bridge canvas, as shown in the figure.
In this coordinate system, the line along which the bridge chain sags has the equation where x and y measured in meters. Find the length of the cable located 70 meters from the pylon. Give your answer in meters.
Decision.
The task is reduced to calculating the value, let's find it:
Answer: 8.39.
Note 1.
Note that we calculated the length of the cable located at a distance of 70 m from the left pylon (see Fig.), due to symmetry, it is equal to the length of the cable located at a distance of 70 m from the right pylon.
Note 2.
In fact, the line that the chain sags in the field of gravity is a "chain line", which is similar to, but different from, a parabola. Catenary equation: where is a material dependent parameter.
1. The equation of the process in which the gas participated is written aspVa=const, where p(Pa) - gas pressure,V - volume of gas in cubic meters,ais a positive constant. For what is the smallest value of the constanta halving the volume of gas involved in this process leads to an increase in pressure of at least 4 times?
Answer: 2
2. The installation for demonstrating adiabatic compression is a vessel with a piston that sharply compresses the gas. In this case, the volume and pressure are related by the relationpV 1.4 = const,where p (atm.) is the pressure in the gas,V- volume of gas in liters. Initially, the volume of the gas is 1.6 liters, and its pressure is equal to one atmosphere. In accordance with the technical specifications, the pump piston can withstand a pressure of not more than 128 atmospheres. Determine the minimum volume the gas can be compressed to. Express your answer in liters.
Answer: 0.05
3. In an adiabatic process, for an ideal gas, the lawpVk=const, where p - gas pressure in pascals,V- volume of gas in cubic meters. In the course of an experiment with a monatomic ideal gas (for itk=5/3) from the initial state, in whichconst= 10 5 Pa∙m 5 , the gas begins to compress. What is the largest volumeVcan occupy gas at pressuresp not lower than 3.2∙10 6 Pa? Express your answer in cubic meters.
Answer: 0.125
4. At a temperature of 0°C, the rail has a length = 10 m. As the temperature rises, thermal expansion of the rail occurs, and its length, expressed in meters, changes according to the lawl(t°)=l 0 (1+a∙t°), where a=1.2∙10 -5 (°C) -1 - coefficient of thermal expansiont°- temperature (in degrees Celsius). At what temperature will the rail lengthen by 3 mm? Express your answer in degrees Celsius.
Answer: 25
5. After rain, the water level in the well may rise. The boy measures the time of falling small pebbles into the well and calculates the distance to the water using the formulah=5t2, where h - distance in meters,t- fall time in seconds. Before the rain, the fall time of the pebbles was 0.6 s. By how much should the water level rise after rain in order for the measured time to change by 0.2 s? Express your answer in meters..
Answer: 1
6. The height above the ground of a tossed ball changes according to the lawh(t)=1.6+8t-5t 2 , where h - height in meters,t - time in seconds elapsed since the throw. How many seconds will the ball be at a height of at least three meters?
Answer: 1.2
7. A crane is fixed in the side wall of a high cylindrical tank at the very bottom. After it is opened, water begins to flow out of the tank, while the height of the water column in it, expressed in meters, changes according to the lawH(t)=at 2 +bt+ H 0 , where H 0 \u003d 4 m - initial water level,a\u003d 1/100 m / min 2, and b= -2/5 m/min - constant,t - time in minutes elapsed since the valve was opened. How long will water flow out of the tank? Give your answer in minutes.
Answer: 20
8. A crane is fixed in the side wall of a high cylindrical tank at the very bottom. After it is opened, water begins to flow out of the tank, while the height of the water column in it, expressed in meters, changes according to the law
where t - time in seconds elapsed since the tap was opened, H 0 \u003d 20 m - the initial height of the water column,k =1/50 - the ratio of the cross-sectional areas of the valve and tank, andg g \u003d 10m / s 2 ). After how many seconds after opening the tap, a quarter of the original volume of water will remain in the tank?
Answer: 50
9. A stone-throwing machine shoots stones at some sharp angle to the horizon. The flight path of the stone is described by the formulay=ax2+bx, where b= 1, a= -1/100 m -1 - constant parameters,x(m)- displacement of the stone horizontally,y(m)- the height of the stone above the ground. At what maximum distance (in meters) from a fortress wall 8 m high should a car be positioned so that the stones fly over the wall at a height of at least 1 meter?
Answer: 90
10. The dependence of temperature (in degrees Kelvin) on time for the heating element of a certain device was obtained experimentally and, in the temperature range under study, is determined by the expressionT(t)=T0+bt+at2, where t is the time in minutes,T0=1400 K, a\u003d -10 K / min 2, b=200 K/min. It is known that at a heater temperature above 1760 K, the device may deteriorate, so it must be turned off. Determine the maximum time after the start of work to turn off the device. Express your answer in minutes.
Answer: 2
11. To wind the cable at the factory, a winch is used, which winds the cable on a coil with uniform acceleration. The angle through which the coil turns changes with time according to the law , where t- time in minutes,ω \u003d 20 ° / min - the initial angular velocity of rotation of the coil, andβ =4°/min 2- angular acceleration with which the cable is wound. The worker must check the winding progress no later than the moment when the winding angle φ reaches 1200 °. Determine the time after the start of the work of the swans, no later than which the worker must check her work. Express your answer in minutes.
Answer: 20
12. A part of some device is a rotating coil. It consists of three homogeneous cylinders: a central massm=8 kg and radius R=10 cm, and two lateral with massesM=1 kg and with radii R+ h. In this case, the moment of inertia of the coil relative to the axis of rotation, expressed in kg∙cm 2 , is given by the formula
At what maximum valueh the moment of inertia of the coil does not exceed the limit value of 625 kg∙cm 2 ? Express your answer in centimeters.
Answer: 5
13. The figure shows a diagram of a cable-stayed bridge. The vertical pylons are connected by a sagging chain. The cables that hang from the chain and support the bridge deck are called shrouds. Let's introduce a coordinate system: axisOh ydirect it vertically along one of the pylons, and the axisO xwe will direct along the bridge bed. In this coordinate system, the line along which the bridge chain sags has the equationy=0.005x2 -0.74x+25, where x and ymeasured in meters. Find the length of the cable located 30 meters from the pylon. Give your answer in meters.
Answer: 7.3
14. To obtain an enlarged image of a light bulb on the screen in the laboratory, a converging lens with a main focal length is usedf=30 see distance d1from the lens to the light bulb can vary from 30 to 50 cm, and the distanced2from the lens to the screen - in the range from 150 to 180 cm. The image on the screen will be clear if the ratio
Specify the smallest distance from the lens that a light bulb can be placed so that the image on the screen is clear. Express your answer in centimeters.
Answer: 36
15. Before departure, the locomotive blew a beep with a frequencyf 0 =440 Hz. A little later, a locomotive blew a horn approaching the platform. Due to the Doppler effect, the frequency of the second beepfgreater than the first: it changes according to the law
where c is the speed of sound (in m/s). A person standing on the platform distinguishes signals by tone if they differ by at least 10 Hz. Determine the minimum speed at which the locomotive approached the platform if the person could distinguish the signals, andc=315 m/s. Express your answer in m / s.
Answer: 7
16. According to Ohm's law for a complete circuit, the current strength, measured in amperes, is equal to, where ε - source emf (in volts),r=1 Ohm is its internal resistance,R- circuit resistance (in ohms). At what least resistance of the circuit will the current strength be no more than 20% of the short circuit current strength? (Express your answer in ohms.)
Answer: 4
17. The amplitude of the pendulum oscillations depends on the frequency of the driving force, determined by the formula
where ω - driving force frequency (in s -1 ), A 0 - constant parameter,ω p=360 s -1 - resonant frequency. Find the maximum frequency ω, less than the resonant one, for which the oscillation amplitude exceeds the valueA0no more than 12.5%.
Answer: 120
18. The coefficient of performance (COP) of a certain engine is determined
where T1- heater temperature (in degrees Kelvin),T2- refrigerator temperature (in degrees Kelvin). At what minimum temperature of the heaterT1The efficiency of this engine will be at least 15% if the temperature of the refrigeratorT2\u003d 340 K? Express your answer in degrees Kelvin.
Answer: 400
19. The coefficient of performance (COP) of the feed steamer is equal to the ratio of the amount of heat spent on heating the water with a massm B(in kilograms) on temperaturet1 up to temperature t2(in degrees Celsius) to the amount of heat obtained from burning wood massm d R kg. It is defined by the formula
where with c \u003d 4.2 ∙ 10 3 J / (kg K) - heat capacity of water,q dr \u003d 8.3 ∙ 10 6 J / kg - specific heat of combustion of firewood. Determine the smallest amount of firewood that will need to be burned in the forage steamer to heatm=83 kg of water from 10°C to boiling, if it is known that the efficiency of the feed steamer is not more than 21%. Express your answer in kilograms.
Answer: 18
20. The locator of a bathyscaphe, evenly plunging vertically down, emits ultrasonic pulses with a frequency of 749 MHz. The speed of descent of the bathyscaphe, expressed in m/s, is determined by the formula
where c\u003d 1500 m / s - the speed of sound in water,f 0is the frequency of the emitted pulses (in MHz),fis the frequency of the signal reflected from the bottom, recorded by the receiver (in MHz). Determine the highest possible frequency of the reflected signalf, if the bathyscaphe's sinking speed should not exceed 2 m/s.
Answer: 751
21. When approaching the source and receiver of sound signals moving in a certain medium in a straight line towards each other, the frequency of the sound signal recorded by the receiver does not match the frequency of the original signalf 0=150 Hz and is determined by the following expression:
where withis the speed of signal propagation in the medium (in m/s), andu=10 m/s and v=15 m/s - velocities of the receiver and source relative to the medium, respectively. At what maximum speedwith(in m/s) propagation of the signal in the medium the frequency of the signal in the receiverf will be at least 160 Hz?
Answer: 390
22. If you rotate a bucket of water on a rope in a vertical plane fast enough, then the water will not pour out. When the bucket rotates, the force of water pressure on the bottom does not remain constant: it is maximum at the bottom and minimum at the top. Water will not pour out if the force of its pressure on the bottom is positive at all points of the trajectory except the top, where it can be equal to zero. At the top point, the pressure force (in newtons) is
where m is the mass of water in kilograms,v- wind speed in m/s,L- the length of the rope in meters, g- free fall acceleration (calculateg\u003d 10m / s 2). With what minimum speed should the bucket be rotated so that the water does not spill out if the length of the rope is 40 cm? Express your answer in m / s.
Answer: 2
23. When a rocket moves, its visible length for a stationary observer, measured in meters, is reduced according to the law
where l 0 \u003d 5 m - the length of the resting rocket,c=3∙10 5 km/s is the speed of light, andv - rocket speed (in km/s). What should be the minimum speed of the rocket so that its observed length becomes no more than 4 m? Express your answer in km/s.
Answer: 180000
24. To determine the effective temperature of a star, the Stefan-Boltzmann law is used, according to which the radiation power of a heated bodyP, measured in watts, is directly proportional to its surface area and the fourth power of temperature:P=σST4, where σ =5,7∙10 - 8 - constant, the area S is measured in square meters, and the temperatureT- in degrees Kelvin. It is known that some star has an area of m 2, and the power it radiatesP not less than 9.12∙10 25Tue Determine the lowest possible temperature of this star. Give your answer in degrees Kelvin.
Answer: 4000
25. Distance from an observer at a heighthabove the ground, to the horizon line he sees is calculated by the formula, where R=6400 km is the radius of the Earth. A person standing on the beach sees the horizon at a distance of 4.8 km. A staircase leads to the beach, each step of which has a height of 20 cm. What is the least number of steps that a person needs to climb so that he can see the horizon at a distance of at least 6.4 kilometers?
Answer: 7
26. During the decay of a radioactive isotope, its mass decreases according to the law, where m0 is the initial mass of the isotope,t(min) - elapsed time from the initial moment,T- half-life in minutes. In the laboratory, a substance was obtained containing at the initial moment of timem0=40 mg isotope Z, whose half-life isT=10 min. In how many minutes will the mass of the isotope be at least 5 mg?
Answer: 30
27. At the shipyard, engineers are designing a new apparatus for diving to shallow depths. The design has the shape of a sphere, which means that the buoyant (Archimedean) force acting on the apparatus, expressed in newtons, will be determined by the formula:F A =αρgr 3, where a= 4.2 - constant, r
