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Answers by Roman C.

solve. What does w equal (answer)

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

probability Question (answer)

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

Calculus - Continuity Problem (answer)

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...

sin(x-6)=cos(3x-4) (answer)

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,...

Find the integral? (answer)

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   =...

the ecentricity of the ellipse 4x^2+y^2-8x+2y+4 (answer)

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...

Did I solve factoring with a zero product property correctly (answer)

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...

Find the integral? (answer)

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

Find the set of values? (answer)

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

Is a number between? (answer)

∫-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

Method of least squares (answer)

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...