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Answers by Roman C.

log7(w2) + 2log7(5w) = 2   2log7w + 2log7(5w)=2   log7w + log7(5w)=1   log7(5w2)=1   5w2=7   w=±√(7/5)

The following are the possible outcomes and their sums                                      Roll 1                  ...

To make it continuous, all you need is equate consecutive formulas at their boundaries.   (x3 - B) / (x - 2) and Ax+B must agree at x=0.   You get (03 - B) / (0 - 2) = A·0+B which is B/2 = B. This implies that B=0.   Ax+B and 2x2 must agree at x=4...

Assuming degrees, remember that if a±b=90±360n then, sin a = cos b.   Hence you have (x - 6) + (3x - 4) = 90 + 360n ⇒ 4x - 10 = 90 + 360n ⇒ x = 25 + 90n   or (x - 6) - (3x - 4) = 90 - 360n ⇒ -2x - 2 = 90 - 360n ⇒ x = 180n - 46.

statistics (answer)

a and c are numeric since their values are numbers. b is categorical, as you major in a subject, which is not a number.

statistics (answer)

a and b are continuous since within a reasonable interval (e.g. (0,20) for a), any real number is possible.   c is discrete as there are finite gaps between consecutive possible values, which in this case must be non-negative integers 0,1,2,3,...

This is just the area of a quarter of a circle of radius 2 so you get (1/4)*π*22=π   Or you can use trig substitution: x = 2 sin θ, dx=2 cos θ dθ.   ∫02√(4 - x2) dx = ∫0π/2 √(4 - sin2 θ) * 2 cos  θ dθ = ∫0π/2 4 cos2 θ dθ = ∫0π/2 (2+2 cos 2θ) dθ   =...

4x2 + y2 - 8x + 2y + 4 = 0   4x2 - 8x + 4 + y2 + 2y + 1 = 1   4(x - 1)2 + (y+1)2 = 1   We have: a = 1/2 (semiminor axis), b=1 (semimajor axis)   Compute c = √(b2 - a2) = (1/2)√3   Finally, ε = c/b...

Find f(e^-1). (answer)

Divide both sides by x2 and use the quotient rule with (u/v)' = (u'v-uv')/v2 where u=f(x) and v=x.   x·f'(x) - f(x) = x   (f'(x)·x - f(x)·1)/x2 = x-1   (f(x)/x)' = x-1   f(x)/x = ln |x| + C   f(x) = x ln |x| +Cx   Now...

You want to set each factor equal to zero and then solve   Step 1: z = 0 or z-1 = 0 or z+3=0 Step 2: z = 0 or z = 1 or z = -3   For the other problem, you must make the right side 0 by subtracting 2 from both sides to get   x2 - x - 12 = 0   Now...

The answer must be the same, 5, because you can use a u-substitution: u=x+c, du=dx.   It yields ∫12--cc f(x) dx = ∫12 f(u-c) dx = 5

You want f'(x) ≥ 0. You get   1-1/x2 ≥ 0   1 ≥ 1/x2   x2 ≥ 1   |x| ≥ 1   x ∈ (-∞,-1] ∪ [1,∞)

∫-13 f(x) dx = ∫-12 (8-x2) dx + ∫23 x2 dx = [8x - x3/3] -12 + [x3/3]23 = 65/3 + 19/3 = 84/3 = 28   Answer: D

What's f(x)? (answer)

Rewrite as f(x) = ∫ (2x sin x + x2 cos x) dx   Note that the integrand has the form d/dx (uv) = u'v+uv' where u(x) = x2 and v(x) = sin x.   Hence f(x) = uv = x2 sin x + C

Solution using R.   1. Copy and paste this data in Notepad and save. Let's say you saved it as "WellData.txt".   2. Launch RStudio.   3. On the menu bar, select Tools > Import Dataset > From Text File...   4. Select WellData.txt...