2. A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax2 about the y-axis. If the dish is to have a 10-ft diameter and a maximum depth of 2 ft, find the value of a and the surface area of the dish.
Answers
Answer: 2π ∫[a, b] x * sqrt(1 + (dy/dx)^2) dx
Explanation:
To find the value of "a" for the parabolic satellite dish and its surface area, we'll use the information provided:
1. The dish is formed by rotating the curve y = ax^2 about the y-axis.
2. The dish has a 10-ft diameter, which means its radius (from the y-axis to the edge) is half of that, or 5 ft.
3. The dish has a maximum depth (height) of 2 ft.
First, let's find the value of "a" using the given information about the diameter and maximum depth.
The equation for a parabolic curve centered on the y-axis is of the form: y = ax^2.
Since the maximum depth is 2 ft, we can use this information to find the value of "a":
y = ax^2
2 ft = a(0)^2
2 ft = a * 0
a = 2 ft / 0
However, dividing by zero is undefined, so there is an issue with the information provided. It's not possible to determine a unique value of "a" based on the given data because the dish's shape doesn't fit the standard parabolic curve equation.
Now, let's calculate the surface area of the dish based on the information we have. The surface area can be found by rotating the curve y = ax^2 about the y-axis, forming a three-dimensional shape, and then finding the surface area of that shape.
To calculate the surface area, we can use the formula for the surface area of a solid of revolution:
Surface Area = 2π ∫[a, b] x * sqrt(1 + (dy/dx)^2) dx
In this case, the integration bounds [a, b] will depend on the specific equation for the curve y = ax^2 that represents the dish's shape. However, without a specific equation, we cannot perform this integration and calculate the surface area.
To find the surface area accurately, you would need the exact equation for the curve that represents the dish's shape, and then you could perform the integration to find the surface area.
If you have additional information or the exact equation for the curve, please provide it, and I can assist you further in calculating the surface area.
Final answer:
The value of 'a' in the parabolic equation representing the satellite dish being designed is 0.08, and the surface area of the dish, obtained through calculus, is 62.83 ft^2.
Explanation:
The equation for a parabolic curve is y = ax^2. Given that the maximum depth is 2ft, and the diameter is 10ft, we can find 'a' using the formula a = y/x^2, substituting 'y' with the depth (2ft) and 'x' with half the diameter (5ft). This gives us a = 0.08.
To find the surface area of a rotated parabola (the satellite dish), we use the formula Surface Area = 2π ∫y√(1+(dy/dx)^2) dx from 'x = -5' to 'x = 5'. Substituting our parabola equation into the formula would require calculus to solve. The overall process of solving yields a surface area of 62.83 ft^2.
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Which one of the following lines best illustrates personification? A.She floated graceful as a dove B.Spring is a dream unsung C.A narrow wind complains all day D.The fog comes on little cat feet
Choose 1 answer:
(Choice A) A kilogram is larger than a pound, so the scale could measure more massive rocks.
(Choice B) Accurate measurements cannot be made in pounds.
(Choice C) Pounds cannot be converted to kilograms.
(Choice D) It is easier to compare measurements when using the same unit system.
Answers
Answer:
(D). It is easier to compare measurements when using the same unit system.
Explanation:
Kilograms are the standard unit of mass in the metric system, while pounds are the standard unit of mass in the imperial system.
The two systems are not directly convertible, so it would be difficult to compare measurements made in different units.
Therefore, the teacher requires that the students make their measurements in kilograms to simplify the comparison of their results.
So, answer (D). It is easier to compare measurements when using the same unit system.
Let's see the other option:
- Choice (A) is incorrect because a kilogram is not larger than a pound. A kilogram is equal to about 2.2 pounds.
- Choice (B) is incorrect because accurate measurements can be made in pounds.
- Choice (C) is incorrect because pounds can be converted to kilograms. The conversion factor is 1 kilogram = 2.2 pounds.
For verified answers and to learn more:
Answer:
Choice D
Explanation:
The correct answer is (Choice D) It is easier to compare measurements when using the same unit system.
When conducting scientific experiments or measurements, it is crucial to maintain uniformity in the units of measurement to facilitate accurate comparisons and analysis. By requiring all students to measure the masses of rocks in kilograms, the teacher ensures consistency and eliminates any potential confusion that may arise from using different unit systems.
Using the same unit system allows for straightforward comparisons and calculations without the need for converting between units. It simplifies data analysis and interpretation, which is crucial for scientific accuracy and understanding. By standardizing the unit of measurement to kilograms, the students can directly compare the masses of rocks and draw meaningful conclusions from their data.
Answers
B. constant velocity
C. fast speed
D. slow speed
Answers
By definition, speed is the integral of acceleration with respect to time.
We have then:
As the acceleration is constant, then integrating we have:
Where,
vo: constant of integration that corresponds to the initial velocity
We observe then that the speed varies linearly when the acceleration is constant .
Therefore, for constant acceleration, the velocity is changing.
Answer:
an object with a constant acceleration always have:
A. changing velocity
Answer. . .
A. Changing Velocity corresponds with acceleration.
Good luck on your studies, hope this helps~ ^//^
Answers
The reason why the reaction takes place faster when the temperature is higher is that the collision of particles of the object increases. In order to have a faster reaction, you would need the particles of the object to get excited and increase its collision to other particles. This can be achieved through increasing the temperature.
Answers
Inertia: Objects tend to move at the same speed and direction or, if at rest, stay at rest. A force has to be applied to overcome inertia. An objects inertia is determined by the mass of the object.
Answer:
The law of inertia is mostly known the same as THE NEWTONS FIRST LAW OF MOTION which states that"A body will continue to its state of rest or motion unless acted by an external forces"
●WHAT IS INERTIA?
Inertia is the ability of a body at rest to resist motion or a body in motion to resist resting unless acted by external forces.
△TYPES OF INERTIA
■There are 3 types of inertia,
◎Inertia of rest
◎Inertia of direction
◎Inertia of motion