### Show that a rule is a metric

Show that a rule is a metric. See attached file for full problem description.

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Show that a rule is a metric. See attached file for full problem description.

1. If f(x) = -3x + 7, find f(a + 1). 2. Explain how we can obtain the graph of -|x + 4| + 2 from the graph of |x|. 3. If f(x) = 3x - 4 and g(x) = x - 1, find (f - g)(x) and f(g(x)). 4. Find the inverse of the function f(x) = 2x + 8.

Two vibrations, x1 = 3 sin(10t + pi/6) and x2 = 2 cos(10t - pi/6) where t is in seconds, are superimposed. determine the time at which the amplitude of the resultant vibration, x1 + x2, first reaches a value of 2.

Please see attached file. If lines A, B and C are parallel and length a=2.8, c=3, b=3.2, what is length d? a. 1.88 b. 3.43 c. 3 d. 3.2

See attached

G(x) =ksqrt(x+1) if 0<=x<=3 mx+2 if 3<x<=5 Find the values of k and m so that g'(3) exists.

From fire tower A, a fire with bearing N 75° E is sighted. The same fire is sighted from tower B at N 49° W. Tower B is 55 miles east of tower A. How far is it from tower A to the fire?

Using one of the tests for convergence (comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges: ∞ ∑ (e^n)/ 1 + (e^2n) n=1

Please give a detailed solution to the attached problem.

Show that the alternating series converges and use the partial sum S9 o estimate the error made as an approximation to S of the series.

Let X be a space which has a universal covering space. If (X1, p1) is a covering space of X and (X2, p2) is a covering space of X1, then (X2, p1p2) is a covering space of X.

Attachment file. Let X be a normed space and . Show that if for every bounded linear functional f on X , then .

Please explain step by step how to complete the following: In the following determine graphically whether the equation could possibly be an identity. If it could, prove that it is. 5. sin^4 t - cos^4 t = 2 sin² t -1 ans. - sin^4t - cos^4 t = (sin²2t - cos²t) (sin²t + cos²t) = (sin²t-(1-sin²t)) (1) = 2 sin²t -

A rectangular storage unit has dimensions 1 m by 2 m by 3 m. If each linear dimension is increased by the same amount a) what increase would create a new storage unit with a volume 10 times the original b) how many solutions are there to this problem? please explain why?

Attached file.

24. Graph the following parabola clearly labeling exact points for the vertx, x-intercepts(s), and y-intercept(s): y=2xsquare+4x-3

Please see the attached file for the fully formatted problems. We are using the book Methods of Real Analysis by Richard R. Goldberg.

Please solve the following with as much explanation of each step as possible. Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0. Find an interval for the function g over which Rolle's

Find the points guaranteed by the mean value theorom for F(x) = x^.5 - 2x on the closed interval [ 0 , 4 ]

Use the equation s=rO for the following: 1. Find the number of degrees in the central angle of a circle with radius of 20 inches if the angle subtends an arc of 13 inches. 2. Find the length of a degree on the equator considering the diameter of the equator to be 7912 miles. 3. A bicycle has a 28 inch wheel. How man

Let A = union ( i from 1 to infinity) of M_i, Mi's are disjoint, show that m*(A) = sum (i from 1 to infinity) of |M_i| m*(A) is the outer measure of A, that is, m*(A) = inf sum (i from 1 to infinity) of M_i. PLEASE NOTICE THE = SIGN, A = the union, not a subset of the union.

Determine if the following conforms to the intermediate value theorem. Clearly give the conditions and, if appropriate, find an appropriate value for c. f(x)=10/((x^2)+1) [0,1] k=8

Find the rectangular cordinates of the point (r,degrees)= (-5,-55 degrees)

Find the volume of the object rotated by the given points. 1. y=1/x, y = 0, x = 1, x = 3; about y = -1 2. y = x, y = 0, x = 2, x = 4; about x = 1

What is the fifth term in the following sequence? asubcript n =n+asubscript n-1. if a1 equals -2, for n greater than or equal to 2.

Classify the behavior at infinity (analytic, pole, zero, or essential singularity; if a zero or pole, give its order) of the following functions: f1(z) = (z^3 + i)/z f2(z) = e^(tan(1/z))

Find a horizontal line that divides an area between y=x^2 and y=9 into two equal parts. I need help in approaching this problem. I know how to calculate the area. I divided the area by two and through trial and error I found the horizontal line to be close to y=5.6. I don't know how to get an exact answer.

X and y represents rectangular coordinates. What is the given equation using polar coordinates (r, theta). x^2 = 4y

The polar coordinates of a point (-1, -pi/3), find the rectangular coordinates for that point.

Write the following parabola in standard form: x - y + y^2 = 0