Answer:
in seires connection?
Explanation:
I mean if the circuit is in seires the bulb must bd connected in seires and it must have the same voltage
Enzyme reaction rates Consider the illustration below. What variable might be on the horizontal axis? (Click on all that apply) Temperature pH
Activation energy Competitive inhibitor concentration Rate of reaction Noncompetitive inhibitor concentration Salt concentration
In general, a reaction is sped up by increasing temperature and slowed down by decreasing temperature. But extremely high temperatures can denature an enzyme, causing it to lose its form and cease functioning.
How is the rate of reaction affected by variations in pH or temperature?As enzymes have a maximum temperature and pH at which their rate is maximal, temperature and pH can both raise or reduce the enzyme reaction rate. The pace of reaction for the enzyme will be slowed down by changes in temperature and pH that are not optimal.
Which of the following factors will speed up an enzyme reaction?An enzyme's concentration increases along with the speed of an enzyme-catalyzed process. An enzyme-catalyzed process accelerates with rising temperatures at low temperatures. The protein is denatured at higher temperatures, which also causes a sharp drop in reaction rate.
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A response is typically sped up by rising temperature and slowed down by falling temperature. However, exceedingly hot temperatures can denature an enzyme, causing it to lose its shape and stop working.
Temperature and pH have the ability to increase and decrease the rate of an enzyme reaction since enzymes have a maximum temperature and pH at which they function at their highest rate. Unfavorable variations in temperature and pH will cause the enzyme's reaction to proceed more slowly. The rate of an enzyme-catalyzed process increases as the concentration of the enzyme rises. When temperatures are low, an enzyme-catalyzed reaction speeds up as they rise. At higher temperatures, the protein is denatured, which also results in a dramatic decrease in response rate.
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Need help!
List 5 interesting facts from the the states of matter.
Hint: sin2θ + cos2θ = 1 .
Consider the 692 N weight held by two
cables shown below. The left-hand cable had
tension 570 N and makes an angle of θ2 with
the ceiling. The right-hand cable had tension
530 N and makes an angle of θ1 with the
ceiling. a) What is the angle θ1 which the righthand cable makes with respect to the ceiling?
Answer in units of ◦.
b) What is the angle θ2 which the left-hand
cable makes with respect to the ceiling?
Answer in units of ◦.
a) The angle θ1 which the righthand cable makes with respect to the ceiling is sin^(-1)(692 N / 530 N).
b) The angle θ2 which the left-hand cable makes with respect to the ceiling is sin^(-1)(692 N / 570 N).
We may utilise the tension of the right-hand cable as well as its vertical and horizontal components to determine the angle 1. θ2 = sin^(-1)(692 N / 570 N).
We may apply the ideas of trigonometry and vector addition to address this issue.
a) The tension of the right-hand wire as well as its vertical and horizontal components can be used to determine the angle 1.
T1sin(1) calculates the vertical component of the right-hand cable's tension, which is equal to the object's weight (692 N).
T1sin(θ1) = 692 N
We may rearrange the equation to find 1:
θ1 = sin^(-1)(692 N / T1)
We can find 1 by substituting the given tension value, T1 = 530 N:
θ1 = sin^(-1)(692 N / 530 N)
b) Similarly, we can use the formula to determine the angle 2 the left-hand cable's tension and its vertical and horizontal components.
The vertical component of the left-hand cable's tension is given by T2sin(θ2), and it should also be equal to the weight of the object (692 N).
T2sin(θ2) = 692 N
To find θ2, we can rearrange the equation:
θ2 = sin^(-1)(692 N / T2)
Substituting the given tension value T2 = 570 N, we can solve for θ2:
θ2 = sin^(-1)(692 N / 570 N)
Calculating these angles using the given tension values will provide the answers in degrees.
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23.15. Can an object carry a charge of 2.0 10-19 C?
Answer:
Ok, the minimal quantity of charge that we can find is on the electron or in the proton (the magnitude is the same, but the sign is different)
Where the charge of a single proton is:
C = 1.6x10^-19 C
Now, you need to remember that when we are working with charges, we are working with discrete math:
What means that?
If the minimum positive is the charge of one proton, then the consecutive charge will be the charge of two protons (there is no somethin in between)
So the consecutive charge will be:
C = 2*1.6x10^-19 C = 3.2x10^-19 C.
So, because we are working in discrete math, we can not have any object that has charge between 1.6x10^-19 C and 3.2x10^-19 C.
Particularly, 2.0x10^-19 C is in that range, so we can conclude that:
No, an object can not carry a charge of 2.0x10^-19 C.
what is a everyday activities examples of newtons 1 law of motion
Answer:
bouncing a baskletball
Explanation:
Answer:someone kicking a soccer ball.
Explanation:
Because the ball isn’t in motion until acted on by another object (the foot)
the acceleration due to gravity on the moon is about 5.4ft/s2. if your weight is 150lbf on earth
... then your weight is 25.2 lbf on the moon.
A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0.800 m and a mass of 6.00 g . What is the frequency f1 of the string's fundamental mode of vibration
Answer:
the frequency of the fundamental mode of vibration is 199.6 Hz
Explanation:
Given;
tension of the piano wire, T = 765 N
length of the steel wire, L = 0.8 m
mass of the steel wire, m = 6.00 g = 6 x 10⁻³ kg
The frequency of the fundamental mode of vibration is calculated as;
\(f_o = \frac{1}{2l} \sqrt{\frac{T}{\mu} }\)
where;
μ is the mass per unit length \(= \frac{6.0 \times 10^{-3}}{0.8} = 7.5 \times 10^{-3} \ kg/m\)
\(f_o = \frac{1}{2l} \sqrt{\frac{T}{\mu} } \\\\f_o = \frac{1}{2\times 0.8} \sqrt{\frac{765}{7.5 \times 10^{-3}} } \\\\f_o = 199.6 \ Hz\)
Therefore, the frequency of the fundamental mode of vibration is 199.6 Hz
Which type of force enables all the matter made up of atoms to exist?
A. Electromagnetic
B. Normal
C. Strong nuclear
D. Gravitational
Answer:
D
Explanation:
Answer:
The answer is C. Strong Nuclear
Explanation:
I took this test and it was correct!
A rectangular container measuring 19 cm x 51 cm x 62 cm is filled with water. What is the mass of this volume of water in kilograms
A rectangular container measuring 19 cm x 51 cm x 62 cm is filled with water. The mass of this volume of water in kilograms is 60.4 kilograms (kg).
To calculate the mass of water in the rectangular container, we need to multiply the volume of water by the density of water.
1. Volume of water:
The volume of the rectangular container is given as:
Length (L) = 19 cm
Width (W) = 51 cm
Height (H) = 62 cm
The volume of water (V) is calculated as:
V = L × W × H
Converting the dimensions to meters:
L = 19 cm = 0.19 m
W = 51 cm = 0.51 m
H = 62 cm = 0.62 m
V = 0.19 m × 0.51 m × 0.62 m
V ≈ 0.0604 cubic meters (\(m^3\))
2. Density of water:
The density of water (ρ) is approximately 1000 kilograms per cubic meter (kg/\(m^3\)).
3. Mass of water:
Mass (m) = Volume × Density
m = 0.0604 m^3 × 1000 kg/\(m^3\)
m = 60.4 kilograms (kg)
Therefore, the mass of the volume of water in the rectangular container is approximately 60.4 kilograms (kg).
It's important to note that the density of water can vary slightly depending on temperature and impurities, but for most practical purposes, a density of 1000 kg/\(m^3\)is commonly used.
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The graph shows the velocity
of a T-Rex as a function
of time. The velocity
of the T-Rex between 2 and 4
seconds shown is
about...
The correct option is C, the velocity between 2s and 4s is 7 meters per second.
What is the velocity of the T-Rex between 2 and 4 seconds?Here we have the graph of the velocity of a T-Rex as function of time in seconds.
Here we need to find the average value between 2 seconds and 4 seconds.
At 2 seconds, the graph says that the velocity is 7m/s
And we can see an horizontal line that ends at 4s, so the veloicty at 4 seconds is 7m/s
Then the average velocity in that interval is that one (because it is constant)
Then the correct option is C.
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Why are undergraments usually made of cotton
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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A 15 kg box is pushed with a force of 35 N in the +x direction, and the box accelerates to the right. It does not accelerate up or down
The box accelerates to the right due to the applied force of 35 N in the +x direction.
Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the net force acting on the box is 35 N in the +x direction, and its mass is 15 kg. Therefore, we can calculate the acceleration using the formula:
acceleration = net force / mass
acceleration = 35 N / 15 kg = 2.33 m/s² (rounded to two decimal places)
Since the box is not accelerating up or down, we can conclude that the force applied is only causing the box to accelerate in the horizontal direction.
Other forces such as gravity and friction are not considered in this scenario. Thus, the 15 kg box will experience an acceleration of approximately 2.33 m/s² in the +x direction due to the applied force of 35 N.
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The coefficient of static friction between a rubber tire and dry pavement is about 0.800. Assume that a car’s engine only turns the two rear wheels and that the weight of the car is uniformly distributed over all four wheels.
What limit does the coefficient of static friction place on the time min required for a car to accelerate from rest to 60.0 mph (26.8 m/s)?
The coefficient of static friction places a limit of approximately 3.42 seconds on the minimum time required for the car to accelerate from rest to 60.0 mph (26.8 m/s).
To find the limit that the coefficient of static friction places on the minimum time required for a car to accelerate from rest to 60.0 mph (26.8 m/s), we need to consider the maximum acceleration the car can achieve due to the friction between the rear tires and the pavement.
The maximum acceleration can be determined using the formula:
a_max = μs * g
where μs is the coefficient of static friction and g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, since the car's engine only turns the two rear wheels, the maximum acceleration is limited by the friction force between the rear tires and the pavement.
Now, to calculate the minimum time required to accelerate to 60.0 mph (26.8 m/s), we can use the following kinematic equation:
v = u + a * t
where v is the final velocity (26.8 m/s), u is the initial velocity (0 m/s), a is the acceleration, and t is the time.
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the values, we get:
t = (26.8 m/s - 0 m/s) / a_max
t = 26.8 m/s / (μs * g)
Substituting the given value for the coefficient of static friction (μs ≈ 0.800) and the acceleration due to gravity (g ≈ 9.8 m/s²), we can solve for the minimum time required:
t = 26.8 m/s / (0.800 * 9.8 m/s²)
t ≈ 3.42 seconds
Therefore, the coefficient of static friction places a limit of approximately 3.42 seconds on the minimum time required for the car to accelerate from rest to 60.0 mph (26.8 m/s).
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The number of hours
of daylight tat a location receives varies depending on how far north or south it is from the
Answer:
equator
Explanation:
in south & north pole you could have 20+ hours daylight or night, everyday!
The environment affects people, but people don't affect the environment.
TRUE OR FALSE
Answer: False
Explanation:
The statement that the environment affects people, but people don't affect the environment is incorrect. It should be noted that people also affect the environment.
Some of our impact on the environment include pollution, deforestation, overpopulation, burning of fossil fuels etc. Thus has resulted in changes such as erosion, climate change, etc.
Your heart pumps blood into your aorta (diameter 2.5 cm) with a maximum flow rate of about 500 cm^3/s. Assume that blood flow in the aorta is laminar (which is not a very accurate assumption) and that blood is a Newtonian fluid with a viscosity similar to that of water.
a. Find the pressure drop per unit length along the aorta. Compare the pressure drop along a 10 cm length of aorta to atmospheric pressure (105 Pa).
b. Estimate the power required for the heart to push blood along a 10 cm length of aorta, and compare to the basal metabolic rate of 100 W.
c. Determine and sketch the velocity profile across the aorta (assuming laminar flow). What is the velocity at the center
Answer:
a. i) The pressure drop per unit length is 52,151.89 Pa
ii) The atmospheric pressure ≈ 19.175 × The pressure drop along 10 cm length of aorta
b i) The power required for the heart to push blood along a 10 cm length of aorta, is 2.6075945 Watts
ii) The basal metabolic rate ≈ 38.35 × The power to push the blood along a 10 cm length of aorta
c. i) Please find attached the drawing for the velocity profile created with Microsoft Excel
ii) The velocity at the center is approximately 2.04 m/s
Explanation:
The given diameter of the aorta, D = 2.5 cm = 0.025 m
The maximum flow rate, Q = 500 cm³/s = 0.0005 m³/s
Assumptions;
The blood flow is laminar
The blood is a Newtonian fluid
The viscosity of water ≈ 0.01 poise = 1 cp
a. i) The pressure drop per unit length of pipe ΔP/L is given by the Hagen Poiseuille equation as follows;
\(Q = \dfrac{\pi \cdot R^4}{8 \cdot \mu} \cdot \left(\dfrac{\Delta p}{L} \right)\)
Where;
Q = The flow rate = A·v
A = The cross sectional area
R = The radius = D/2
Δp/L = The pressure drop per unit length of the pipe
Therefore, we have;
\(\dfrac{\Delta p}{L} = \dfrac{Q\cdot 8 \cdot \mu }{\pi \cdot R^4} = \dfrac{0.0005 \times 8 \times 1}{\pi \times 0.0125^4 } = 52151.89\)
The pressure drop per unit length ΔP/L = 52,151.89 Pa
ii) The pressure, ΔP, drop along 10 cm (0.1 m) length of aorta = ΔP/L × x;
∴ ΔP = 52,151.89 Pa × 0.1 m = 5,215.189 Pa
Given that the atmospheric pressure, \(P_{atm}\) = 10⁵ Pa, we have;
\(P_{atm}\)/ΔP = 10⁵/5,215.189 ≈ 19.175
Therefore, the atmospheric pressure is approximately 19.175 times the pressure drop along 10 cm length of aorta
b. i) The power, P = Q × ΔP
Therefore, the power required for the heart to push blood along a 10 cm length of aorta, is P₁₀ = 0.0005 m³/s × 5,215.189 Pa = 2.6075945 Watts
ii) Therefore compared to the basal metabolic rate of, 'P', 100 W, we have;
P/P₁₀ = 100 W/2.6075945 Watts = 38.349521 ≈ 38.35
The basal metabolic rate is approximately 38.35 times more powerful than the power to push the blood along a 10 cm length
c. i) The velocity profile across the aorta is given as follows;
\(v_m = \dfrac{1}{4 \cdot \mu} \cdot \dfrac{\Delta P}{L} \cdot R^2\)
Where;
\(v_m\) = The velocity at the center
We get;
\(v_m = \dfrac{1}{4 \times 1} \times 52,151.89 \times 0.0125^2 \approx 2 .04\)
The velocity at the center, \(v_m\) ≈ 2.04 m/s
ii) The velocity profile, v(r), is given by the following formula;
\(v(r) = v_m \cdot \left[1 - \dfrac{r^2}{R^2} \right]\)
Therefore, we have;
\(v(r) = 2.04 - \dfrac{2.04 \cdot r^2}{0.0125^2} \right] = 2.04 - 163\cdot r^2\)
The velocity profile of the pipe is created with Microsoft Excel
A fishing boat uses an ultrasound of frequency 4.0×10²Hz to detect a fish blow it. two echo's of the ultrasound are received after 0.09s coming from the shoal of the fish and the other after 0.12s coming from the sea bed .if the sea bed is 64m below the ultrasound transmitter and the receiver, calculate; a. the speed of the ultrasound in water b. the wavelength of ultrasound in water. c. the depth of the fish below the boat.
a. the speed of the ultrasound in water is 1480 m/s
b. the wavelength of the ultrasound in water is 37 m
c. the depth of the fish below the boat is 89.76 m
How to calculate?a.
v = fλ
v = fλ = (4.0 x 10^2 Hz)(λ)
the speed of the ultrasound in water is given as :
v = v_water = 1480 m/s
substitute v_water into the equation above and solve for λ:
λ = v_water / f = (1480 m/s) / (4.0 x 10^2 Hz) = 37 m
Therefore, the speed of the ultrasound in water is 1480 m/s and the wavelength is 37 m.
c. The depth of the fish below the boat ia found using,
d = v_water * t / 2
The first echo came back after 0.09 s:
d = (1480 m/s) * (0.09 s) / 2 = 64.32 m
This is the depth of the sea bed, which is already known to be 64 m. So the fish must be deeper than the sea bed, and the second echo must have come from the fish. The second echo came back after 0.12 s:
d = (1480 m/s) * (0.12 s) / 2 = 89.76 m
So the depth of the fish below the boat is 89.76 m
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choose inertial frames. check all that apply. choose inertial frames.check all that apply. a carousel rotates at a constant speed. a vertically tossed ball is at the highest point of its trajectory. a plane moves at a constant speed of 254 m/s . at the instant the traffic light turns green, a bus starts from rest
The highest point in a ball's trajectory is when it is thrown vertically. The average speed of a plane is 254 m/s/s. A carousel rotates continuously.
What is the unit for speed?seconds per metre Miles per hour (mph), kilometres per hour (km/h), and metres per second (m/s) are the three most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed equals distance x time is the speed equation.
Who defined speed?Galileo Galilei, an Italian physicist, is typically attributed with being the first to quantify speed by taking into account the distance travelled and the time required. Galileo defined speed as the amount of distance travelled in a given amount of time.
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In Newtonian ring observation equipment, the space between the lens and the glass plate is filled with liquid. Calculate the refractive index of the liquid if the radius of the third bright ring is 3.65 mm. Observations are made in transmitted light. The radius of curvature of the lens is 10m. The wavelength of light is 0.0000589 cm.
The answer is 1.33, but how?????
To calculate the refractive index of the liquid, we can use the formula for the radius of the nth bright ring in Newton's rings: \(r_n\) = √(n × λ × R). Therefore, the refractive index of the liquid is approximately 1.378.
\(r_n\) = √(n × λ × R) (formula )
Where: \(r_n\) is the radius of the nth bright ring,
n is the order of the ring,
λ is the wavelength of light,
and R is the radius of curvature of the lens.
the third bright ring (r_3 = 3.65 mm = 0.365 cm), the radius of curvature of the lens (R = 10 m = 1000 cm), and the wavelength of light (λ = 0.0000589 cm).
n = \(r_n\) / √(n × λ × R)
Substituting the given values:
n = 0.365 / √(3 × 0.0000589 × 1000)
Calculating the value:
n ≈ 1.378 ( refractive index)
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A flat sheet of paper of area 0.450 m2 is oriented so that the normal to the sheet is at an angle of 600 to a uniform electric field of magnitude 18 N C-1. What is the magnitude of the electric flux through the sheet? A. 3.22 N m2 C-1 B. 21.42 N m2 C-1 C. 5.04 N m2 C-1 D. 11.72 N m2 C-1 E. 4.05 N m2 C
The magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹ (Option E).
The electric flux through a surface is given by the product of the electric field strength and the area of the surface projected perpendicular to the electric field.
In this case, the electric field strength is 18 N C⁻¹, and the area of the sheet projected perpendicular to the electric field is 0.450 m²
(since the normal to the sheet makes an angle of 60° with the electric field). Multiplying these values gives the electric flux:
Electric flux = Electric field strength × Area
Electric flux = 18 N C⁻¹ × 0.450 m²
Electric flux = 8.1 N m² C⁻¹
In summary, the magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹. This value is obtained by multiplying the given electric field strength by the projected area of the sheet perpendicular to the electric field.
The angle of 60° is taken into account to determine the effective area for calculating the flux.(Option E).
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estimate the work you do to mow a lawn 10m by 20m with a 50 cm wide mower. Assume you push with a force of about 15 N.
Answer:
W = 6000 Joule
Explanation:
Work is defined as force times distance
W = F * d
We know that F = 15N, we just need the distance (d)
Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.
The width of the mower is only 50 cm = 0.5 m.
This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,
d = 10 (meter) * 40 (times) = 400 meter
Therefore:
W = (15) * (400) = 6000 J
Ben, a psychology student, decides to examine masking behaviors, now that more people are vaccinated. He goes to his local grocery store, finds a specific spot to sit, and counts the number of people he sees with masks or without masks across 2 weeks. Ben is most likely conducting a(n) ____________________ study.
Ben as a psychology student is most likely conducting a behavioral study.
What is psychology?
Psychology can simply be defined as the study of human mind, conscious and unconscious, thoughts and feelings.
In conclusion, Ben as a psychology student is most likely conducting a behavioral study.
Some few branches of psychology are:
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Energy from the sun comes to Earth as radiant energy. Which of these is an example of radiant energy being converted to heat energy?
A Turning windmills transform mechanical energy into electrical energy.
B Black shirts feel hotter than light-colored shirts on a sunny day.
C Solar cells convert sunlight into electrical energy.
D Green plants use sunlight in photosynthesis.
Answer:
B
Explanation:
The radiant energy form the sun is absorbed by the black shirt and is converted to heat energy.
Answer:
B Black shirts feel hotter than light-colored shirts on a sunny day.
Explanation:
The energy from the sun also called solar energy is an energy source which reaches the earth as a form of radiant energy, that is it is transmitted without the movement of mass. Solar cells absorbs radiant energy from the sun into electrical energy for powering electrical devices.
During photosynthesis, sunlight absorbed by the chlorophyll of green plants is converted into chemical energy.
In black body, radiant energy abosrde are stored and converted to heat energy, reason dark colored clothes feels hotter than light colored on sunny days.
The kinetic energy of a moving car is less than the amount of chemical
potential energy that is released when fuel is burned in the engine. Which
statement best explains why this is so?
A. More of the car's energy is transformed into potential energy the
faster it goes.
B. Friction causes some of the energy released by the fuel to be
transformed into thermal energy,
C. Some chemical energy is transformed into potential energy as the
particles in the fuel are rearranged.
D. The force of gravity transforms some kinetic energy into
gravitational potential energy.
Answer:
A
Explanation:
Because it makes sense
In the 3rd step of the experiment, the scientist heated sugar and water, until the sugar
was completely dissolved.
What type of mixture was created from the water and sugar solution?
Answer:
Homogenous Mixture
Explanation:
When the scientist heated sugar and water, until the sugar was completely dissolved, then the mixture is a homogeneous mixture, also known as a solution.
What is a mixture?A mixture is a combination of two or more substances that are physically combined in a way that each retains its own identity and properties. The substances that make up a mixture are called components or constituents, and they can be either elements or compounds.
Mixtures can be classified as homogeneous or heterogeneous, depending on whether the components are uniformly distributed or not.
In a homogeneous mixture, the components are evenly distributed throughout the mixture, resulting in a uniform composition and appearance.
In a heterogeneous mixture, the components are not uniformly distributed, and the mixture may contain visible boundaries or phase separations.
Mixtures can be created by mixing substances together using physical methods, such as stirring, shaking, or heating. Unlike chemical reactions, which involve the formation of new substances with different properties, mixtures can be separated back into their individual components by physical means, such as filtration, evaporation, or distillation.
Here in the question,
The mixture created from the water and sugar solution is a homogeneous mixture, also known as a solution. In a homogeneous mixture, the components are uniformly distributed throughout the mixture, resulting in a uniform composition and appearance. In this case, the sugar molecules are evenly dispersed throughout the water molecules, creating a clear and transparent solution.
Therefore, The mixture created from the water and sugar solution is a homogeneous mixture,
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Find the surface of each pyramid round to nearest tenth if necessary
12.2m
16m
10.6m
12.2m
12.2m
Surface area of pyramid 1 539.2 \(m^{2}\) Pyramid 2: 370.9 \(m^{2}\) Pyramid 3: 446.4 \(m^{2}\)
To find the surface area of a pyramid, we need to know the dimensions of its base and its slant height. Assuming the base of each pyramid is a square, we can calculate the surface area using the formula:
Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height)
Let's calculate the surface area for each pyramid using the given dimensions:
1. Pyramid 1: Base = 12.2 m Slant Height = 16 m Base Area = (12.2 \(m^2\)= 148.84 \(m^2\)Perimeter of Base = 4 × 12.2 m = 48.8 m
Surface Area = 148.84 \(m^2\)+ (0.5 × 48.8 m × 16 m) = 148.84 m^2 + 390.4 \(m^2\) = 539.24 \(m^2\) (rounded to nearest tenth)
2. Pyramid 2: Base = 10.6 m Slant Height = 12.2 m Base Area = (10.6 \(m^2\))= 112.36\(m^2\) Perimeter of Base = 4 × 10.6 m = 42.4 m
Surface Area = 112.36\(m^2\)+ (0.5 × 42.4 m × 12.2 m) = 112.36 \(m^2\)+ 258.56 \(m^2\) = 370.92 \(m^2\)(rounded to nearest tenth)
3. Pyramid 3: Base = 12.2 m Slant Height = 12.2 m Base Area = (12.2 \(m^2\)= 148.84 \(m^2\)Perimeter of Base = 4 × 12.2 m = 48.8 m
Surface Area = 148.84 m^2 + (0.5 × 48.8 m × 12.2 m) = 148.84 \(m^2\)+ 297.52 \(m^2\) = 446.36 \(m^2\) (rounded to nearest tenth)
Therefore, the surface areas of the given pyramids are approximately: Pyramid 1: 539.2 \(m^2\)Pyramid 2: 370.9 \(m^2\) Pyramid 3: 446.4 \(m^2\).
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After initially picking the stone up off the ground, a man exerts a 148 N force upwards on a 10 kg stone. What is the acceleration of the stone?
Answer:
5m/s²
Explanation:
The force exerted on an object is calculated using the formula ;
F = ma
Note that the upward force (F) is 148N
Where;
F = force (N)
m = mass (kg)
a = acceleration (m/s²)
The downward force towards gravity is F' = mg
F' = 10 × 9.8m/s²
F' = 98N
Net force (F - F') = m × a
148 - 98 = 10 × a
50 = 10a
a = 50/10
a = 5m/s²
A truck is traveling at an initial velocity
of +39m/s and it starts slowing down smoothly for 3.3s. It covers a distance of 45m while slowing down. What is the acceleration?
Answer:
Approximately \(-15.37m/s^2\)
Explanation:
The acceleration can be found using the formula:
\(x_{f} = x_{i} + v_{i} (t)+\frac{1}{2} (a)(t^{2} )\)
The work is as shown:
\(45m = 0 + 39 m/s (3.3s)+\frac{1}{2} a(3.3s)^2\)
\(45m=128.7m + 5.445s^2 a\)
\(-83.7m=5.445s^2a\)
\(a = -15.37190083m/s^2\)
a is about -15.37\(m/s^2\)
A ball with a mass of 65 g flies with a velocity of 25 m/s. It is hit with a bat, whereby it gets a velocity of 35 m/s in the opposite direction. What is the average force that the bat acts on the ball with if the ball touches the bat for 4.0 ms?
The average force the bat exerts on the ball when it touches it for the given period of time is 975 N.
The given parameters:
mass of the ball, m₁ = 65 ginitial velocity of the ball, v₁ = 25 m/sfinal velocity of the ball, v₂ = 35 m/s opposite directiontime of action, t = 4 msThe average force the bat exerts on the ball when it touches it for the given period of time is calculated by applying Newton's second law as follows;
\(F = ma\\\\F = \frac{M(v_2 - v_1)}{t} \\\\F = \frac{0.065(35 - (-25))}{4 \times 10^{-3}} \\\\F = \frac{0.065(35 + 25)}{4 \times 10^{-3}} \\\\F = 975 \ N\)
Thus, the average force the bat exerts on the ball when it touches it for the given period of time is 975 N.
Learn more about Newton's second law here: https://brainly.com/question/19887955