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3s=2t can also be written as 3y=2x or 3x=2y. Either way, it is linear.

To find out if it is linear, simply graph it. If you can draw a completely vertical line through any point of the graph without intersecting more than one point of the graph, then it is linear.

This equation (3s=2t), it is linear.

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Q: 3s equals 2t is this a linear equation or nonlinear?
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What is the integral of 2 times 1-x dx with limits 0 to t?

,/` 2(1 - x) dx,/` 2 - 2x dx2x - x2 ...evaluated from 0 to t gives us...2t - t2 - [2(0) - (0)2]2t - t2


What is the limit as t approaches 0 of 2t tan t?

That would be 0. (But that was too easy. Did you mean something else?)


How do you make a the subject of t equals 0.5 x a plus b x h?

To make the following relationship: t = (1/2)a +bh a function of "a" (a = ...) start by subtracting both sides by "bh": t - bh = (1/2)a then divide both sides by (1/2), which is the same as multiplying by 2: 2(t - bh) = a from here you can distribute the 2 if desired: a = 2t - 2bh


Integration of tangent cubed of x?

Find I = ∫ tan³ x dx. The solution is: I = ½ tan² x - log cos x. * * * Here is how we can obtain this result: First, let t = tan x, s = sin x, and c = cos x; then, dI = t³ dx, ds = c dx, dc = -s dx, and dt = (1 + t²) dx; and, of course, t = s / c. By algebra, t³ = t(t² + 1) - t; thus, we have dI = t³ dx = t(t² + 1) dx - t dx = t dt - t dx. Now, d (t²) = 2t dt; thus, t dt = ½ d(t²). On the other hand, we have d log c = dc / c = -s dx / c = -t dx; thus, t dx = -d log c. Combining these results, we have dI = t dt - t dx = ½ d(t²) - d log c. This integrates readily, giving I = ½ t² - log c, which is the solution we sought. * * * We may check our result, by differentiating back: dt / dx = 1 + t²; and d(t²) / dt = 2t; thus, (d/dx)(t²) = 2t dt / dx = 2t (1 + t²). Also, we have d log c / dc = 1 / c; and dc / dx = -s; whence, (d/dx)(log c) = (dc / dx) / c = -s / c = -t. Then, dI / dx = ½ (d/dx)(t²) - (d/dx)(log c) = t (1 + t²) - t = t + t³ - t = t³, re-assuring us that we have integrated correctly.


A hemi-spherical vessel has internal radius 0.5 m It is initially empty Water flows in at a constant rate of 1 liter per second Find an expression for the depth of the water after t seconds?

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