Describe the mechanism that orchids use to control their pollen distribution.

The lenght of the missing side is 29.41 ft.

To calculate the missing length of the triangle, we use pythagoras theorem.

Pythagoras theorem states that in a right angle triangle, the square the hypotenus is equal to the sum of the square of the two other sides.

These can be expressed mathematically as

From the question,

Substitute these values into equation 1

Hence, the lenght of the missing side is 29.41 ft.

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Answer:

d

Explanation:

I remember it was right

a) Force exerted by blue team  = 1200N

b) Force exerted by red team=1250N

c) Resultant =50N in the direction of red team

d) Red team will win as they are pulling with greater force

There are 6 people on blue team and 5 people on red team

so here it is given that in blue team a person exerts a force of 250N and number of people is 6 , then total force will be 200x6=1200N

so here it is given that in red team a person exerts a force of 200N and number of people is 5 , then total force will be 250x5=1250N

the unbalance force here is 1250-1200=50N

from the above we know that red team have an extra force of 50N so they will win the match as they are pulling with greater force.

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The distance covered by the runner after starting from rest is 39.74 m/s².

The real route length of a moving particle or object is referred to as distance. The shortest distance between a body's initial and final positions is referred to as displacement. Speed is the amount of distance a particle travels in one unit of time.

The constant acceleration of a runner is 1.1 m/s².

The runner maintains the constant acceleration for 8.5 seconds.

So,

a = 1.1 m/s²

t = 8.4 seconds

Since the runner starts from the rest.

Therefore, the initial velocity u = 0 m/s

Using the equation of motion,

s = ut + (1/2) × a × t²

s = 0 × 8.5 + ( 1/2 ) × 1.1 × 8.5 × 8.5

s = ( 1/2 ) × 79.475

s = 39.737 m/s²

s = 39.74 m/s²

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If a person swims at a constant speed of 1 meter per second, than the linear function will be used to model the distance travelled by the swimmer.

The parent function is "the principal's of ice"

A linear function is a function that forms a straight line on a graph. It is generally a polynomial function whose degree is at most 1 or 0. Although linear functions are also represented in terms of calculus and linear algebra.

Here Y-axis represents Distance and X-axis represents Time.

Also speed is the rate of change of distance with respect to time i.e. distance is changing linearly with time

Mathematically it is  [tex]Speed = \frac{distance}{time}[/tex].

Change in Distance = Change in time and hence speed is constant.

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A happiness that is full of significance and delight as well as a sense of vitality and freedom results from this kind of all-consuming desire. This is your chance to live a more fulfilled life where finding joy in what you do instead of pursuing the one thing you love is the goal.

Passion fuels our motivation. It aids us in constructing our dreams and goals. It's how we decide what our life's job is, and why we put in the effort to get there. Our lives are useless and unfulfilling without passion—for our friends and family, for creating beauty, for giving back, or for fulfilling a higher purpose.

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The final velocity of the plane at the end of the railway is:

V2f=v2i+2a(x)

v2f=(55m/s)2−(2)(2.5m/s2)(600m)

vf=5m/s.

Since the final velocity is not equal to zero, the plane would not be able to stop at the end of the runway.

Technically, there may be the most effective manner for the aircraft to stay putting motionless inside the air if weight and raise cancel every other out perfectly, and at the equal time thrust and drag cancel every different out too. but this is exceptionally uncommon. To live within the air and sustain its flight, a plane wishes to be moving forward.

In addition to wing spoilers, airplanes use disc brakes. aircraft disc brakes are just like the braking system in automobiles. They consist of a pair of calipers that, while engaged, squeeze pads towards the rotors of an aircraft's landing gear. Disc brakes are designed to stay static at all times. maximum planes use a long runway earlier than takeoff to gain enough velocity for the aircraft to raise up into the air. most airplanes can take off handiest if they are moving rapidly sufficient.

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The height of the cliff from the ground is 19.6 meters.

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity.

Given is the initial speed of soccer ball kicked horizontally off a cliff which is 8 m/s. It cover a horizontal distance of 16 m. From this, we can write -

Horizontal initial velocity = u [h] = 8m/s

Horizontal distance covered = S [h] = 16m

For horizontal direction, of motion, we can write -

u [h] = 8m/s

S [h] = 16m

From second equation of motion applied for the horizontal direction -

S[h] = u[h] x t + 1/2 a[h] x t²

Since horizontal acceleration a[h] is zero, we can write -

t = S[h]/u[h]

t = 16/8

t = 2 seconds

Since the ball is kicked horizontally, the initial vertical velocity u[v] will be 0 m/s.

The acceleration in the vertical direction a[v] is directed vertically downwards and is equal to 9.8 m/s².

From second equation of motion applied for the vertical direction -

S[v] = u[v] x t + 1/2 x a[v] t²

S[v] = 1/2 x a[v] t²                      {u[v] = 0}

S[v] = 1/2 x 9.8 x 4

S(v) = 9.8 x 2

S[v] = 19.6 m

Therefore, the height of the cliff from the ground is 19.6 meters.

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[ The given question is not complete, the complete question is -

A soccer ball is kicked horizontally off a cliff with an initial speed of 8 m/s and lands 16 m from the base of the cliff: What is the time of flight of the soccer ball? What is the height of the cliff? ]

The ball rise 18.42 m from its original position.

Height is the vertical distance between two points.

To calculate the height of the ball, from the original position, we use the formula below.

Formula:

Make h the subject of the equation

Where:

From the question,

Substitute these values into equation 2

Hence, the ball rise 18.42 m from its original position.

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There are few points given to us in this question.

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

What is a light year?

Many might confuse it with time because of the presence of term “year” this term is actually used for space objects to measure distance. Light Year is the distance travelled by light in one Earth year.

It’s a term named by German scientist Friedrich Bessel who first used it in 1838.

One light year is about 6 trillion miles or 9.46 trillion kilometers.

To solve part A, we will first multiply V(light) with time (in seconds) in a year and multiply the product with 1.5 light year per light year.

Now let us understand what is Astronomical Unit AU?

AU is also used to measure distance but within our solar system. It is usually the average distance between Sun and Earth. It is about 93 million miles or 150 million kilometers.

To solve part B, we first convert the light year to AU and we do this by using the final value from part A and then convert it in significant figure to obtain a proper value for the answer.

The calculations are shown in the figures below.

Hence,

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

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The gravitational potential energy of an object depends on  mass of the object, gravitational field and height of the object.

The gravitational potential energy of an object is the energy possessed by the object due to the object's position above the ground level.

P.E = mgh

where;

The factors affecting gravitational potential energy of an object include;

Thus, the gravitational potential energy of an object depends on  mass of the object, gravitational field and height of the object.

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Area and Speed are derived Units Because they are derived from the Fundamental Units

By proceeding using the dimensional analysis,

We can see,

Area = Length of object x Breadth of object

As we know, both the length and the breadth of the object are measured as Meter(M),

Area = M x M

Now, for Speed,

Speed = distance/time

unit of distance is Meter(M) and unit of time is Second(S), both of these are fundamental quantities.

Speed = Meter/second

Speed = M/S

As we can see, the unit of area is a composition of a fundamental unit and speed is also a composition of fundamental unit and any unit which is composition of one or more fundamental unit is called derived Unit.

Hence it is proved that Area and Speed are Derived Units.

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The perimeter of the pool is measured as 30 feet.

We know that a rectangle is a four sided polygon recall that a polygon is any figure that has n sides. The number of sides in a  polygon could move from three to infinity. The polygons come in different shapes and are solids with definite values of surface areas and volumes.

The rectangle is four sided which each of the angles of the rectangle adding up to give 360 degrees. It must be noted that the opposite sides of the rectangle are equal to each other.

We have the following information;

Length of the pool = 4(3 feet) = 12 feet

Width of the pool = 3 feet

Since perimeter = 2 ( length + width)

Perimeter = 2( 12 + 3)

Perimeter = 30 feet

Hence, the perimeter of the pool is measured as 30 feet.

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An auto's velocity increases uniformly from 6.0 m/s to 20 m/s while covering 70 m in a straight line, its acceleration is 2.6 [tex]m/s^2\\[/tex] and the time taken is 5.4 s.

The probable rate at which an object’s velocity changes with respect to time is referred to as its acceleration in mechanics. They are vector quantities and accelerations.

The direction of the net force acting on an object determines the direction of its acceleration.

The meter per second ([tex]m/s^2\\[/tex]) unit of acceleration is used to measure speed. The square meter is a measure of area ([tex]m^2[/tex])

The auto's velocity increases uniformly from 6m/s to 20m/s while it is covering the total of 70m.

Since it increases uniformly, thus we can use equation of motion

[tex]V^2 - U^2 =2as[/tex]

U = 6m/s

V = 20m/s

s = 70 m

Thus,

[tex](20)^2 - (6)^2 = 2*a*70[/tex]

a = 2.6 [tex]m/s^2\\[/tex]

Then for the time, we have

a = [tex]\frac{(V-U)}{t}[/tex]

2.6 = [tex]\frac{20 - 6}{t}[/tex]

t = 5.4 s

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The characteristic that is used to measure light radiated by a star is luminosity. The correct option is C.

The radiant power emitted by a light-emitting object with respect to time is measured as luminosity, which is an absolute measure of radiated electromagnetic power.

The total amount of electromagnetic energy radiated per unit of time by a star, cosmos, or other celestial object is referred to as luminosity in astronomy.

The amount of light emitted by a star is measured using luminosity. It is the total amount of emery or light emitted by a star per unit of time. Or it is the total energy produced by a star in one second from its surface.

Thus, the correct option is C.

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Your question seems incomplete, the missing options are:

Size

color

luminosity

temperature

Only when the average speed of the heavy particles is lower than that of the light particles will the average kinetic energy of the light particles equal the average kinetic energy of the heavy particles.

Only when the average speed of the heavy particles is lower than that of the light particles will the average kinetic energy of the light particles equal the average kinetic energy of the heavy particles.

As the temperature rises, the particles accumulate kinetic energy and quicken. The actual average speed of the particles is influenced by both their mass and temperature; at a given temperature, larger particles travel more slowly than lighter ones.

Given that the formula for calculating a particle's kinetic energy is

Ek = 1/2 mu²,

The formula for particle speed is [tex]$$c = [3RT/M]^{1/2[/tex].

The graphs of kinetic energy and particle speed show that the heavier particles only have higher peaks, whilst the lighter particles only have lower peaks.

It is clear from the graphs and the temperatures employed that the graphs' shapes were nearly identical. It does not appear to be significantly impacted by temperature.

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The balancing level that we are when standing at a normal posture is the Normal balancing level. That is option D.

Posture is defined as the bearing of one's body while at rest or while moving.

Normal posture can be defined as the normal position of the body while standing which involves standing straight and tall with shoulders back and the hands by the sides with the head kept in line with the body level.

The balancing level of posture is that level where the body is being positioned in such a manner as to reduce the amount of work done by the muscles.

Therefore, the balancing level that we are when standing at a normal posture is the Normal balancing level.

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When 68.5 g of sucrose is dissolved in 500.0 g of water, the freezing point of the water decreases by -0.744°C.

The correct option is C.

The temperature at which a liquid freezes is known as the freezing point. The freezing point normally rises with increased pressure, much like the melting point does. Combinations and some organic materials, such lipids, have freezing points that are lower than melting points.

The following formula is used to determine the freezing point depression:

ΔT = i m

where ,

ΔT is the change in freezing point,

i is the van't Hoff factor,

is the freezing point depression constant, and

m is the molality of the solution.

It is given in the question that the

of water = -1.86°C/mol

molar mass sucrose = 342.30 g/mol

i value of sugar = 1

500.0 g of water and 68.5 g of sucrose are dissolved in it.

ΔT  = 1 * -1.86° *m

molality = (68.5/342.3)/(500/1000)= 0.200116857/.5

m = 0.400

ΔT  = 1 * -1.86° * 0.400

ΔT  = - 0.744°C

The change in the freezing point of water when 68.5g of sucrose is dissolved in 500.0 g of water is - 0.744°C .

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Answer:

Assuming the height at which the wrench was dropped is 336 feet,

the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

Explanation:

Without knowing the exact height at which the 24th floor is located, it would be difficult to determine whether the wrench will hit the ground before the sound hits the ground

Realistically, we can assume each floor of the building is 14' high

So the height at which the 24th floor is located is 24 x 14 = 336 feet

To travel 336 feet at 1100 feet per second, sound will take 336/1100 seconds which is 0.30 second

Let's compute the time taken for the wrench to hit the ground

The acceleration due to gravity is usually taken to be 16 feet/second²

The displacement which is the distance traveled by an object with an initial velocity of u in time t is given by the equation:
s = ut + (1/2)t²

Here the initial velocity is 0

So the equation is
s = 1/2 x 32 x t² = 16t²

To cover 336 feet we substitute 336 for s and get

336 = 16t²

t² = 336/16

t = ±√(336/16) ≈ 4.58 seconds (we only take the positive root)

So the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

In general, we can state that if the height from which the wrench was dropped is h then time t taken for wrench too hit the ground is

t = √(h/16) seconds

If this is greater than the time taken for sound to travel the same distance then the person can get out of the way

The dimension of the amplitude, A is L.

The amplitude of a wave is the maximum displacement of the wave.

The amplitude of a wave is measured in the units of meters.

The given displacement of the light wave;

x = A sin(2πft)

where;

Since amplitude of a wave measures the wave's displacement, then amplitude will have the same dimension as displacement.

A = meters = L

Thus, the dimension of the amplitude, A is L.

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Given :

How to calculate average speed?

Average speed is calculated by Distance travelled / time taken.

Here, we know distance is 140 m and time is 5 seconds. Substituting the values,

=) Distance / Time

=) 140 m / 5 s

=) 28 m/s.

Therefore, the average speed (in m/s) of a cheetah that runs 140 meters in 5 seconds is 28m/s.

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The total heat supplied by the plant to convert the water to steam is 596.7 kcal.

Heat capacity is the quantity of heat required to raise the temperature of entire mass of a substance.

Q = Heat supplied to the water to the boiling point + Heat supplied to vaporize the water.

Q = mc₁Δθ + mc₂Δθ + mLv

where;

Substitute the given parameters and solve for the heat supplied in the process.

Q = (1)(1)(100 - 58.6) + (1)(0.48)(131.8 - 100)  + 540(1)

Q = 41.4 + 15.264 + 540

Q = 596.7 kcal

Thus, the total heat supplied by the plant to convert the water to steam is 596.7 kcal.

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The speed of the archer is 0.15m/s

The weight of the arrow compared to the man is

60/0.03 = 2000.

Thus, the man is 2000x heavier than the arrow.

Momentum is defined as P = m v or mass times velocity.

This must always be conserved. Since they stand at rest, the total momentum is zero.

The momentum of the arrow once shot is

50 x 0.03,

and thus the momentum of the archer is given by

60 x speed = 50 x 0.03

This rearranges into speed = (50 x 0.03) / 60

=0.15m/s

The speed of the archer is

=(speed of the arrow x mass of the arrow) / mass of the archer

=(50 × 0.030)/60

=0.15m/s

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a. Her x position at t = 0.80 s is 0.0832 m

b. Her y position at t = 0.80 s is -28.8 m

c. Her x velocity component at t = 0.80s is 2.08 m/s

d. her y velocity component at t = 0.80s is -3.6 m/s

Since the skateboarder travels on a horizontal surface with an initial velocity of 3.6 m/s toward the south and a constant acceleration of 2.6 m/s² toward the east.

Now since she starts from the origin, to find her x position after 0.80 s, using the equation of motion for the x - components of motion,

x = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

x = ut + 1/2at²

x = 0 m/s × 0.8 s + 1/2 × 2.6 m/s² × (0.8 s)²

x = 0 m + 1.3 m/s² × 0.64 s²

x = 0 m + 0.832 m

x = 0.832 m

So, her x position at t = 0.80 s is 0.0832 m

Using the equation of motion for her y - components of motion, her y position is y = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

y = ut + 1/2at²

y = -3.6 m/s × 0.8 s + 1/2 × 0 m/s² × (0.8 s)²

y = -3.6 m × 0.8 s + 0

y = -28.8 m

So, her y position at t = 0.80 s is -28.8 m

Using the equation of motion for her x - component of motion, her x velocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = 0 m/s + 2.6 m/s² × 0.8 s

v = 0 m/s + 2.08 m/s

v = 2.08 m/s

So, her x velocity component at t = 0.80s is 2.08 m/s

Using the equation of motion for her y - component of motion, her xyvelocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = -3.6 m/s + 0 m/s² × 0.8 s

v = -3.6 m/s + 0 m/s

v = -3.6 m/s

So, her y velocity component at t = 0.80s is -3.6 m/s

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The magnitude of velocity of the ball dropped from a 91 m tall building at the point of impact is 42.8 m / s

s = ut + 1 / 2 at²

a = v / t

s = Distance

u =Initial velocity

a = Acceleration

t = Time

s = 91 m

a = 10 m / s²

s = ut + 1 / 2 at²

91 = 0 + ( 1 / 2 * 10 * t² )

t = √ ( 18.2 )

t = 4.27 s

v = 10 * 4.27

v = 42.7 m / s

The position-time graph and the velocity-time graph that represents the problem is drawn in the image attached.

Therefore, the magnitude of velocity of the ball is 42.7 m / s

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The coefficient of volume expansion is given as  1.5012 x10^-4

What is volume?

A volume can simply be defined as the amount of space occupied by any three-dimensional solid. The solids can take the shape or form of a cube, a cuboid, a cone, a cylinder or a sphere

Volume of water that is lost

= (0.35) * (0.98324) mL

= 0.3441 mL

The original volume of

55.50 mL will increase to

55.8441 mL

V(t) = Vo [1 + γ(60.0 - 18.7)]

=> coefficient of volume expansion,

γ = (Vt - Vo) / [Vo * 41.3]

= (0.3441) / [(55.50) (41.3)

= 1.5012 x10^-4

The coefficient of the volume expansion can be the measure of the fractional change of size per unit change in the temperature with the surrounding pressure being constant.

In conclusion, the coefficient of volume  is most applicable to the fluids.

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