Four cards are drawn in succession, without replacement, from a standard deck of 52 cards. How many sets of four card are possible?

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Answer 1

Answer: The answer I that u are looking for is 13

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Solve 2w2–64 = 0, where w is a real number.

-9=2x-5
Please help me now.....

Answers

-9= 2x-5

Add 5 to both sides

-4= 2x

Divide by 2

-2=x or x=-2

Finding the work done in stretching or compressing a spring. Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.

In this problem we assume that the force applied doesn't distort the metal in the spring.

A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.

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Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Final answer:

To find the force function of a spring using Hooke's Law, you first identify the spring constant 'k' using the given work done and extension. In this case, we found 'k' to be 137.5 N/m. Hence, the force function F(x) for the spring comes out to be 137.5x N.

Explanation:

The problem revolves around Hooke's Law, which is used to determine the force needed to stretch or compress a spring by a certain distance away from its equilibrium position. This law can be mathematically represented as F(x)=kx, where 'F(x)' represents the force applied, 'k' is the spring constant, and 'x' is the distance.

In this question, the work done (W) to stretch the spring is given as 11 J, and the extension (Δx) is 0.4 m (from 2 m to 2.4 m). The work done on a spring is calculated by the equation W = 1/2 * k * (Δx)^2. From this, you can solve for 'k' value. Once you have 'k', you can find the force function F(x) for the spring.

1. Calculate 'k' using the work done equation:

11 J = 1/2 * k * (0.4 m)^2 ➔ k = 137.5 N/m

2. Substitute 'k' in F(x):

F(x) = 137.5 N/m * x

Hence, the force function F(x) = 137.5x N is required to extend the spring by 'x' metres.