The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?
The inequality x² + 2x - 168 ≤ 0 can be used to determine the possible lengths of the base of a triangle when the height is 4 inches greater than twice the base and the area is no more than 168 square inches.
To find the possible lengths of the base of a triangle where the height is 4 inches greater than twice the base and the area is no more than 168 square inches, we start with the formula for the area of a triangle:
Area = (1/2) × base × height.
Let the base be x. Thus, the height can be expressed as 2x + 4. Therefore, the area equation becomes:
(1/2) × x × (2x + 4) ≤ 168
To simplify this, multiply both sides by 2:
x(2x + 4) ≤ 336
Expanding and rearranging the terms gives:
x² + 4x ≤ 336
Subtract 336 from both sides to form a quadratic inequality:
x² + 4x - 336 ≤ 0
Divide the entire inequality by 2 to simplify:
x² + 2x - 168 ≤ 0
This is the inequality that can be used to find the possible lengths of the base of the triangle.
A rectangular pool has a volume of 375 m3. the pool is 10 m long and 5 m wide. how deep is the pool? 7.5 m 3,750 m 75 m
two vectors A and B have components (0,1) and (-1,3), respectively. What is magnitude of the sum of these two vectors?
a) 3.2
b) 4.1
c) 3.9
d) 2.8
Which best supports the idea that the surface of the moon has changed very little?
a) If photographs of the moon were taken millions of years ago, the surface would look the same.
b) Because the moon does not have a large iron core, it is not possible for geologic events to occur on the moon.
c) Because the moon has no atmosphere, it is not possible for geologic events to occur on the moon.
d) If one considers the history of the moon, there is only one distinct phase of its development.
a baseball pitcher throws a fastball at 42 meters per second. if the batter is 18 meters from the pitcher, approximately how much time does it take for the ball to reach the batter?
The time taken by the ball to reach the batter is 0.42 seconds
The baseball pitcher throws a fastball at 42 m/s
The batter is about 18 meters from the pitcher
Therefore the time for the ball to reach the batter can be calculated as follows;
= 18/42
= 0.42 secs
Hence the time taken by the ball to reach the batter is 0.42 seconds
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Which voice can produce a pitch that has a speed of 343 m/s and a wavelength of 0.68m?
A soccer player kicks a soccer ball at +10.0 m/s at an angle of 60°. What are the horizontal and vertical components of velocity of the kick?
Answer:
Horizontal component: [tex]V_{x}=+5m/s[/tex]
Vertical component: [tex]V_{y}=+8.66m/s[/tex]
Explanation:
We have the launch speed [tex]V =+ 10m/s[/tex] and the angle of 60°, so the components of the speed [tex]V_{x}[/tex] and [tex]V_{y}[/tex] are those shown in the attached image.
[tex]V_{x}[/tex] which is the horizontal component of the velocity can be found by multiplying the cosine of the angle by the initial velocity:
[tex]V_{x}=+10m/s(cos60)\\V_{x}=+10m/s(0.5)\\V_{x}=+5m/s[/tex]
[tex]V_{y}[/tex] which is the verticalcomponent of the velocity is found by multiplying the sine of angle by the initial velocity
[tex]V_{y}=+10m/s(sin60)\\V_{y}=+10m/s(0.866)\\V_{y}=+8.66m/s[/tex]
In summary:
Horizontal component: [tex]V_{x}=+5m/s[/tex]
Vertical component: [tex]V_{y}=+8.66m/s[/tex]
Suppose a planet has twice the mass of the earth and twice the earth's radius. What is the acceleration of an object in free fall on this planet?
2.5 m/s2
4.9 m/s2
9.8 m/s2
4.9 × 106 m/s2
...?
The acceleration of an object in free fall on a planet that has twice the mass of the Earth and twice the Earth's radius is 4.9 m/s², half of the acceleration on Earth.
Explanation:The acceleration of an object in free fall on a planet depends on the mass and radius of the planet. In this case, the planet has twice the mass of the Earth and twice the Earth's radius. To calculate the acceleration, we can use the formula for gravitational acceleration:
g = (G * M) / R^2
Where g is the acceleration, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Since the planet has twice the mass and twice the radius of the Earth, we can substitute those values into the formula:
g = (G * 2M) / (2R)^2 = (2 * G * M) / (4 * R^2) = G * M / (2 * R^2)
So the acceleration of an object in free fall on this planet is half of the acceleration on Earth, which is 4.9 m/s².
How is light used to study space? IN YOUR OWN WORDS
Conceptual Question 8.09osama wadi
Part A
In a perfectly ELASTIC collision between two perfectly rigid objects
the momentum of each object is conserved.
both the momentum and the kinetic energy of the system are conserved.
the kinetic energy of the system is conserved, but the momentum of the system is not conserved.
the kinetic energy of each object is conserved.
the momentum of the system is conserved but the kinetic energy of the system is not conserved.
...?
What process occurs when all of the energy from light waves is transferred to a medium?
Answer:
absorption
Explanation:
When exiting the highway, a 1100-kg car is traveling at 22 m/s. The car's kinetic energy decreases by 1.4×105J The exit's speed limit is 35 mi/h. Did the driver reduce its speed enough?
Answer: The final velocity is 33.78 mi/h, so the driver did reduced his speed enough.
Explanation: The kinetic energy of an object can be calculated as:
K = (1/2)m*v^2
We know that the mass of the car is m=1100kg
and the initial velocity is 22m/s
The initial kinetic energy is:
K = (1/2)*1100*(22)^2 = 266,200 joules.
Now, if the kinetic energy decreases by 1.4x10^5 J, the new kinetic energy is:
K = 266,200j - 140,000j = 126,200j
So we now can find the new velocity in m/s.
126,200 = (1/2)*1100*v^2
126,200*2/1100 = v^2
229.45 = v^2
v = (229.45)^(1/2) = 15.1 m/s
We know that the limit is 35 mi/h, so we need to transform our result into miles per hour.
We know that in one hour, there are 3600 seconds, so the velocity per hour is:
15.1*3600 m/h = 54,360 m/h
and we know that one mile is 1609.34 meters, so we need to divide by 1609.34.
v = (54,360/1609.34) mi/h = 33.78 mi/h
this is less than the speed limit, so the driver reduced his speed enough.
After losing kinetic energy, the car's final velocity was approximately 18.99 m/s, exceeding the exit's speed limit of 15.64 m/s, hence the driver did not reduce their speed adequately.
Explanation:To determine whether the driver reduced their speed enough when exiting the highway, we must calculate the car's speed after its kinetic energy decreases by 1.4×105J. The initial kinetic energy (KE) of the 1100-kg car traveling at 22 m/s can be calculated using the equation KE = ½ mv². Plugging in the values, we can find the initial kinetic energy:
KEinitial = ½ (1100 kg)(22 m/s)² = 5.28×105J
After losing 1.4×105J of energy, the remaining kinetic energy will be:
KEfinal = KEinitial - 1.4×105J = (5.28 - 1.4)×105J = 3.88×105J
We can solve for the final velocity (vfinal) using the remaining kinetic energy:
½ (1100 kg)vfinal² = 3.88×105J
vfinal = √((2×3.88×105J) / 1100 kg)
vfinal ≈ 18.99 m/s
To compare to the speed limit, we convert 35 mi/h to meters per second:
35 mi/h × 0.44704 (conversion factor) = 15.64 m/s
Since the final velocity of the car is 18.99 m/s, which is greater than the exit's speed limit of 15.64 m/s, the driver did not reduce their speed enough.
The crankshaft in a race car goes from rest to 3540rpm in 2.6s. What is the crankshaft's angular acceleration? How many revolutions does it make while reaching 3540rpm?
What would a drummer do to make the sound of a drum give a note of lower pitch?
a. hit the drum skin with a larger force b. hit the drum skin with a smaller force
c. hit the drum skin nearer the edge d. loosen the drum skin ...?
What is the gravitational force between two masses of 15kg each, when their centers are 0.25m? Could you detect this force with even sensitive equipment?
A 1000 kg car can accelerate from rest to a speed of 25 m/s in 10 s. What average power must the engine of car produce in order to cause this acceleration? Neglect friction losses
If a force of 10 n is applied to an object with a mass of 1kg the object will accelerate at
A large region of gas and dust that may contain as many as one million solar masses is called a _____.
a. galaxy
b. protostar
c. supernova remnant
d. giant molecular cloud
Answer:
a giant molecular cloud.
Explanation:
A ball is dropped from a height of 100 ft. one second later another ball is dropped from a height of 75 ft, which one hits the ground first? ...?
Both balls will hit the ground simultaneously because the time it takes to fall is based on the height, not the initial velocity.
Explanation:The time it takes for an object to fall to the ground depends only on its height and is independent of its initial velocity. In this case, both balls are dropped, so they have an initial velocity of 0 m/s. The ball dropped from 100 ft and the ball dropped from 75 ft will both hit the ground at the same time. This is because the only factor affecting the time it takes to fall is the height, not the initial velocity. Therefore, both balls will hit the ground simultaneously.
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Will a solid metal sphere hold a larger elaectric charge than a hollow sphere of the same diameter?Where does the charge reside in each case? ...?
A roller coaster car is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the value of its centripetal acceleration at that point?
a. The value for the centripetal acceleration is g downward.
(correct answer on plato just did the mastery for this one)
At the top of the loop, where a roller coaster car is just maintaining contact with the track, its centripetal acceleration equals the acceleration due to gravity, which is 9.8 m/s².
Explanation:The value of the centripetal acceleration at the top of the loop, where a roller coaster car just maintains contact with the track, is equal to the acceleration due to gravity, which is 9.8 m/s². This can be deduced from the balancing forces at the top of the loop. In this situation, the force due to gravity is acting downwards while the centripetal force is also acting downwards - directed towards the center of the circular path. Therefore, these forces must match at the top of the loop for the car to just maintain contact with the track. This gives us the equation for centripetal acceleration, ac = g , where ac is the centripetal acceleration and g is the acceleration due to gravity.
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You want to be shielded from all three types of nuclear radiation. If you find shielding that blocks radiation, then it will most likely also block the other two types.
The correct answer to the question is gamma radiation . Therefore shielding that blocks gamma radiation, then it will most likely also block the other two types.
Radiation shielding is crucial to protect against the three types of radiation emitted by radioactive elements: alpha, beta, and gamma rays. Different materials are used for shielding based on the type of radiation and its penetrating power. For example, a sheet of paper can stop alpha particles, while thick lead or concrete is needed to absorb gamma rays.
Complete question:
You want to be shielded from all three types of nuclear radiation. If you find shielding that blocks ______ radiation, then it will most likely also block the other two types.
A cold beer initially at 35ºF warms up to 40ºF in 3 min while sitting in a room of temperature 70ºF. How warm will the beer be if left out for 20 min
Final answer:
Using Newton's law of cooling, we can calculate that the beer will be approximately 60.4ºF if left out for 20 minutes.
Explanation:
To calculate the final temperature of the beer after being left out for 20 minutes, we can use Newton's law of cooling. This law states that the rate of heat loss of an object is proportional to the temperature difference between the object and its surroundings. In this case, the initial temperature of the beer is 40ºF and the room temperature is 70ºF. Let's determine the constant of proportionality, k, first:
k = (T2 - T1) / t = (70 - 40) / 3 = 10
Now we can use the formula to find the final temperature, T3, after 20 minutes:
[tex]T3 - 70 = (40 - 70)e^(-10(20/3))[/tex]
[tex]T3 - 70 = -30e^(-20/3)[/tex]
[tex]T3 = 70 - 30e^(-20/3)[/tex]
Using a calculator, we can find that T3 is approximately 60.4ºF.
If two carts collide, what type of collision will conserve both momentum and kinetic energy?
a. head on
b. perfectly inelastic
c. none
d. perfectly elastic
A bullet is fired horizontally from the top of a building with a muzzle velocity of 150 m/s.A similar bullet dropped from the top of the same building, takes 4 sec to reach the ground. How far forward does the first bullet go before it hits the ground?
Final answer:
The horizontal distance traveled by the bullet before hitting the ground is 600 meters.
Explanation:
To determine how far forward the bullet goes before it hits the ground, we can use the fact that both the horizontally fired bullet and the dropped bullet hit the ground after a certain time. The dropped bullet takes 4 seconds to reach the ground, so we can consider its vertical motion using the equation h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time. Plugging in the values, we get 0 = 0.5 * 9.8 * 4^2, which gives us h = 78.4 meters.
Since the horizontally fired bullet has the same horizontal velocity as the dropped bullet, it would take the same time to reach the ground. This means that the horizontally fired bullet travels a horizontal distance equal to its horizontal velocity multiplied by the time it takes to reach the ground. Plugging in the values, we get d = 150 * 4 = 600 meters.
Therefore, the first bullet travels 600 meters forward before hitting the ground.
The bullet fired horizontally travels 600 meters before hitting the ground because it takes the same 4 seconds as the dropped bullet to reach the ground, and it travels at a horizontal velocity of 150 m/s.
Step-by-Step Explanation:
Calculate the horizontal distance using the formula: distance = velocity x time.Here, the muzzle velocity of the bullet is 150 m/s and the time is 4 seconds.Distance = 150 m/s * 4 s = 600 meters.Conclusion:
The bullet fired horizontally travels 600 meters before it hits the ground.
A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 2.00 m making 0.700 revolutions per second. What is the centripetal acceleration of the ball?
The centripetal acceleration of the ball will be 38.68 meter per sq.second.
What is centripetal acceleration?The acceleration needed to move a body in a curved way is understood as centripetal acceleration.
The direction of centripetal acceleration is always in the path of the center of the course.
The given data in the problem;
r is the radius= 2.00m
frequency (f) = 0.7 rev/s
The angular velocity is found as;
[tex]\rm \omega = 2 \pi f \\\\ \omega = 2 \times 3.14 \times 0.7 \\\\ \omega = 4.398 \ rad/sec[/tex]
The centripetal acceleration is given by;
[tex]\rm a_c= \omega^2r \\\\\ a_c= (4.398)^2 \times 2.00 \\\\ a_c=38.68 \ m/sec^2[/tex]
Hence, the centripetal acceleration of the ball will be 38.68 meter per sq.second.
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A football is kicked at an 50 degree angle to the horizontal , travels a horizontal distance of 20m before hitting the ground. what is the initial speed?
Answer:
Initial speed of football=14.11m/s
Explanation:
Range is the horizontal distance travelled. Therefore using formular for Range,R to determine the speed.
R=V^2Sin2theta/g
Given: R=20m
Theta=50°
20= V^2 Sin(2×50)°/ 9.8
Cross multiply
20×9.8 = V^2 Sin100°
196= V^2×0.9848
V=Sqrt(196/0.9848)
V= 14.11m/s
An electromagnet is a temporary magnet due to which of the following?
The magnet is only present when a current is present
The magnet is only present when the domains are not aligned
The magnet is only present when the current is turned off
The magnet is only present when the resistance is high
Most of the Earth's volcanoes occuWhen fossils or minerals form, certain unstable elements are sometimes locked into them. The proportion of these unstable elements gradually decreases over time as they decay into other materials in a predictable way. Scientists use the rate at which such unstable elements decay to determine when the fossils or minerals formed. The technique described above is known as as
Radioactive dating, is your answer.
Which of Newton's Three Laws does the following statement satisfy?
For every action there is an equal and opposite reaction.
A
Newton’s First Law
B
Newton’s Second Law
C
Newton’s Third Law