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(a)
To Find: The formula for
(a)
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Answer to Problem 3P
The required formula is
Explanation of Solution
Given:
The given diagram is shown in Figure 1
Figure 1
Calculation:
Consider the table shown in Table 1
Table 1
Consider the stage each side is replaced by the shorter sides each of the length of
Thus, the required formula is
(b)
To Prove: The value
(b)
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Explanation of Solution
Calculation:
Consider the formula for
Since,
Hence, proved.
(c)
To Find: The sum of the infinite series to find the area enclosed by the snow flake curve.
(c)
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Answer to Problem 3P
The area enclosed by the snowflake is
Explanation of Solution
Calculation:
The area of each of the small triangles added at the given stage is one fourth of the area of the triangle added at the preceding stage. Consider the area of the original triangle and then, the area
Since, the small triangle is added to the sides at every stage so it follow that the area is added to the figure of the next stage as,
Then, the total area is of the form,
Then, the area of the original equilateral triangle with sides is,
Thus, the area of the enclosed by the snowflake curve is,
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Question 2. i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) = P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer. ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer.arrow_forwardProblem 4. Let f(x, y) = { Find P(X <1/2|Y = 1/2). c(x + y²) 0arrow_forwardQize f(x) x + 2x2 - 2 x² + 4x² - 4 Solve the equation using Newton Raphsonarrow_forwardSolve please thanks!arrow_forwardSolve please and thank youarrow_forwardAccording to Newton's law of universal gravitation, the force F between two bodies of constant mass GmM m and M is given by the formula F = , where G is the gravitational constant and d is the d² distance between the bodies. a. Suppose that G, m, and M are constants. Find the rate of change of force F with respect to distance d. F' (d) 2GmM b. Find the rate of change of force F with gravitational constant G = 6.67 × 10-¹¹ Nm²/kg², on two bodies 5 meters apart, each with a mass of 250 kilograms. Answer in scientific notation, rounding to 2 decimal places. -6.67x10 N/m syntax incomplete.arrow_forwardSolve please and thank youarrow_forwardmv2 The centripetal force of an object of mass m is given by F (r) = rotation and r is the distance from the center of rotation. ' where v is the speed of r a. Find the rate of change of centripetal force with respect to the distance from the center of rotation. F(r) b. Find the rate of change of centripetal force of an object with mass 500 kilograms, velocity of 13.86 m/s, and a distance from the center of rotation of 300 meters. Round to 2 decimal places. N/m (or kg/s²) F' (300)arrow_forwardSolve work shown please and thanks!arrow_forwardGiven the following graph of the function y = f(x) and n = = 6, answer the following questions about the area under the curve from x graph to enlarge it.) 1 (Round your answer to within two decimal places if necessary, but do not round until your final computation.) a. Use the Trapezoidal Rule to estimate the area. Estimate: T6 G b. Use Simpson's Rule to estimate the area. Estimate: S6 - ID = 0 to x = 6. (Click on aarrow_forward"Solve the following differential equation using the Operator Method and the Determinant Method:" Solve by dr no ai """'+3y"" + 3y+y=arrow_forward(4,4) M -4 2 2 -4 (-4,-4) 4 8 10 12 (8,-4) (12,-4) Graph of f The figure shows the graph of a piecewise-linear function f. For −4≤x≤12, the function g is x defined by g(x) = √ƒ (t)dt . . Find the value of g(6). Find the value of g'(6). |arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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