Try "LINEAR ALGEBRA WITH APPLICATIONS" by Otto Bretscher.

## Roman C.'s Resources

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.

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

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 =...

Assuming the smallest rectangle, there are two options. Arrange the circles in a line, or in a 2 by 2 square arrangement. Here they are: OOOO or OO OO In the former you can see that the rectangle's width is four diameters,...

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...

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 can use the angle difference formula for sin 15° sin 15° = sin(60° - 45°) = sin 60° cos 45° - cos 60° sin 45° = (√6 - √2) / 4 cos 15° = cos(60° - 45°) = cos 60° cos 45° + sin 60° sin 45° = (√6 + √2) / 4 tan 15° = sin 15°/cos 15°) = = (√6 -...

sec2x + csc2x / csc2x(1+tan2x) = sec2x +1/(1+tan2x) = sec2x +1/sec2 x = sec2 x + cos2 x

sec2 x = 1+tan2 x = 1+(4/11)2 = 137/121. sec x = (-1/11)√137 cot x = 1/tan x = 11/4 csc2 x = 1+cot2 x = 137/16 csc x = (-1/4)√137 sin x = 1/csc x = -4/√137 cos x = 1/sec x = -11/√137

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

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...