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Calculus

The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.

500 Questions

5 mm is how many inches?

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There are 25.4 mm in 1 inch, therefore 5 mm = .2" (actually a hair less)

Direct Conversion Formula5 mm*

1 in

25.4 mm

=

0.1968503937 in

What is produced when you slice a cone with a plane that is parallel to the base of the cone?

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That conic section is a circle.

When you slice a cone with a plane parallel to the base of the cone, the sliced section is a circle, and the portion of the original cone on the side of the vertex is again a cone.
An isosceles cone would be the out come

More differences between simple harmonic motion and periodic motion with practical examples?

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Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. Practical examples include a swinging pendulum or a mass-spring system. Periodic motion, on the other hand, refers to any repeated motion that follows the same path at regular intervals, such as the motion of a wheel rotating. So, while all simple harmonic motion is periodic, not all periodic motion is necessarily simple harmonic.

What is 76 cm in inches?

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An inch is 2.54 centimeters, so 7.6 centimeters converts to 2.99 inches.

3 inch equal how many cm?

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3 inches is equal to 7.62 centimeters.

Ten cm equals how many inches?

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One centimeter is approximately equal to 0.3937 inches. Therefore, 10 centimeters is roughly equal to 3.937 inches.

What is 8x -9 equals 9x -5?

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8x - 9 = 9x - 5

8x - 8x - 9 = 9x - 8x - 5

-9 = x - 5

-9 + 5 = x - 5 + 5

-4 = x

What is a times x minus b equals c for x?

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ax - b = c

Add 'b' to both sides

ax = c + b

Divide both sides by 'a'

x = (c + b) / a

The answer!!!!!

Why was Newton outraged when in 1684 German mathematician Wilhelm Leibniz published a calculus book?

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Newton was outraged because he believed that Leibniz had stolen his ideas on calculus. Newton and Leibniz both independently developed calculus, but Newton felt that Leibniz had plagiarized his work. This led to a bitter dispute between the two mathematicians known as the "calculus priority dispute."

Why is 1000cm squared equals 1m squared?

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Linearly 100 cm = 1 m

Area = 100cm X 100 cm = 1 m x 1m

=>

10000 cm^(2) = 1 m^(2)

So 1000 cm^(2) does NOT equal 1 m^(2)

How many milliliters are equal to cubic meters?

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1 cubic meter = 1000 liter = 10 6 cubic centimeter
1 liter = 1000 milliliter

1 cubic meter = 10 6 milliliter

8000 meters x 20 meters equals how many cubic meters?

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8000 meters multiplied by 20 meters equals 160,000 square meters.

Why did limit invented?

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Limits were developed in mathematics to describe the behavior of functions as they approach specific values or points. They allow us to analyze and understand the behavior of functions at points where they may not be defined or may have discontinuities. Limits are fundamental in calculus for defining concepts like derivatives and integrals.

What is y x y?

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Y*Y would equal y2 in algebra, however there is no specific value to the variable y. If that question also said "Y=2," then 2*2 would equal 22 or 4.

What is 3 over 8 plus 1 over 2 equal?

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3/8 + 1/2 =

3/8 + 4/8 =

7/8

What is 4000 x 600?

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It is 2400000.

What are avena sativa 1x double strength ferrum phosphoricum 3x magnesia phosphorica 3x gum Arabic inactive lactose nf natrum phosphoricum 3x calcarea phosphorica 3x active passiflora incarnata 1 x?

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This appears to be a homeopathic remedy formulation containing Avena sativa, Ferrum phosphoricum, Magnesia phosphorica, Natrum phosphoricum, and Calcarea phosphorica in low potencies. Gum Arabic and lactose are used as inactive ingredients. Passiflora incarnata is included as an active ingredient known for its calming properties, often used for conditions like anxiety and insomnia. Always consult with a healthcare provider before taking any new supplement or homeopathic remedy.

What is the square root of 361?

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The square roots are -19 and +19.

What is the value of y when the value of x is 3?

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It depends on the relationship between x and y.

How many mililiters in a cenimeter?

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None, since there can be no conversion.

A centimetre (not cenimeter) is a measure of length in 1-dimensional space while a millilitre is a measure of volume in 3-dimensional space. The two measure different characteristics and, according to the most basic principles of dimensional analysis, any attempt at comparisons or conversions between the two are fundamentally flawed.

What is finite math?

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Finite math is a branch of mathematics that focuses on mathematical concepts that have finite, specific values or elements. It typically includes topics such as logic, set theory, probability, statistics, and linear algebra, which are applied to real-world problems with a limited number of possibilities. Finite math is often used in business, social sciences, and computer science to model practical situations.

What is the difference between partial derivative and derivative?

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Say you have a function of a single variable, f(x). Then there is no ambiguity about what you are taking the derivative with respect to (it is always with respect to x).

But what if I have a function of a few variables, f(x,y,z)? Now, I can take the derivative with respect to x, y, or z. These are "partial" derivatives, because we are only interested in how the function varies w.r.t. a single variable, assuming that the other variables are independent and "frozen".

e.g., Question: how does f vary with respect to y? Answer: (partial f/partial y)

Now, what if our function again depends on a few variables, but these variables themselves depend on time: x(t), y(t), z(t) --> f(x(t),y(t),z(t))? Again, we might ask how f varies w.r.t. one of the variables x,y,z, in which case we would use partial derivatives. If we ask how f varies with respect to t, we would do the following:

df/dt = (partial f/partial x)*dx/dt + (partial f/partial y)*dy/dt + (partial f/partial z)*dz/dt

df/dt is known as the "total" derivative, which essentially uses the chain rule to drop the assumption that the other variables are "frozen" while taking the derivative.

This framework is especially useful in physical problems where I might want to consider spatial variations of a function (partial derivatives), as well as the total variation in time (total derivative).

A beam of light in air is incident at an angle of 35 degrees to the surface of a rectangular block of clear plastic n 1.49 What is the angle of refraction?

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The angle of refraction can be calculated using Snell's Law: n₁sin(θ₁) = n₂sin(θ₂), where n₁ is the refractive index of air (1.00), θ₁ is the angle of incidence (35 degrees), n₂ is the refractive index of the plastic (1.49), and θ₂ is the angle of refraction. Plugging in the values gives: (1.00)sin(35) = (1.49)sin(θ₂). Solving for θ₂ gives an angle of refraction of approximately 23.6 degrees.