Dan Sp.
• Member for 3 years, 10 months
• Last seen more than 1 year ago
• Norther Virginia

It crosses itself where, for two different values of t, you get equal x and y values. So letting $t_1 = u$ and $t_2=v$: $$u^3-u+3 = v^3-v+3$$ $$u^2-3 = v^2-3$$ These simplify to: $$u(u^2-1) = v(v^2-1)... View answer 1 votes Yes, dim(S)=2. Here is a basis for B: \begin{bmatrix}0\\1\\0\end{bmatrix}, \begin{bmatrix}2\\0\\-1\end{bmatrix} The basis does not span R^3 but it is a basis for S. To complete B for ... View answer Accepted answer 1 votes You need more than just the slopes to be equal. At these points, y must also be equal. So you also have:$$px=x^4-x^3p=x^3-x^2$$This, with your equation, is a system of 2 equations and 2 ... View answer Accepted answer 1 votes The Huygens' formulas change the size of the bet as time goes on. This is not the best model for your description. You should look into Random Walk. Your problem is directly related to a 1-D random ... View answer 1 votes None of this is correct! For a function, Big-O describes how a function grows as it approaches infinity or some value. In your case, as x goes to 0 so:$$ f(x)= O(1) \text{ as } x \rightarrow 0$$... View answer 1 votes First die can be 2, 4, or 6. Second any roll 1-6. So the sample space is 3 \cdot 6= 18 Only two positive outcomes: {2,4} and {4,2}. Probability = \frac{2}{18} = \frac{1}{9} View answer 1 votes I do not believe your approach is the simplest. The height of the jump is:$$ 2R = \frac{\dot y_0^2}{2g} $$So:$$ \dot y_0 = \sqrt{Rg} $$Now take each component separately. First, what is the ... View answer 1 votes Seems accurate. Life expectancy in the US is about 80 years. So 330,000,000 / 13,000 / 80 \approx 317. View answer Accepted answer 1 votes Start with \nabla f = (z+yz)\hat{i} + (-2y+xz)\hat{j}+ (x+xy)\hat{k}. Lets apply the divergence theorem and see what we have to work with.$$ \iint_S \left[(z+yz)\hat{i} + (-2y+xz)\hat{j}+ (x+xy)\...

I would first eliminate the parametric equations. The first one: $$x=\cos(t) + 1$$ $$\cos(t) = x - 1$$ And using the right triangle trick: $$\sin(t)=\sqrt{2x-x^2}$$ So, $y=\sqrt{2x-x^2}-1$ is the ...

Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex. Here is the ...

You confused one of your rates. The height of the water is increasing at a rate of 0.2 feet per second. This one would be $$\frac{dh}{dt} = 0.2$$ You equated $0.2$ to $\frac{dV}{dt}$. This is ...

Did you go ahead and take arccos$\left(\frac{-3}{7\sqrt{6}}\right)$? I get about 100$^o$. So your answer is no. The acute angle is 180 - 100 or about 80$^o$.

Keep taking derivatives until the first non-zero derivative at the point of interest. So for $x^3$: $$f'(x)=3x^2$$ $$f''(x)=6x, f''(0) = 0$$ $x^3$ is peculiar, it has an inflection point here so ...

Well, lets say you are evaluating how much money you have vs how much money your friend has. You have 4 - \$5 dollar bills. Your friend has 2 -$10 bills. After thinking about it, you conclude you ...

Use two Taylor series for $f'$ at $0$ using steps $h$ and $-h$. $$f(h) = f(0) + h \cdot f'(0) + \frac{h^2 \cdot f''(0)}{2!} + \frac{h^3 \cdot f'''(0)}{3!} + \frac{h^4 \cdot f''''(0)}{4!} ...$$ $$f(-h)... View answer 0 votes Your initial velocity vector is correct but your v(t) is incorrect. It should be:$$v(t)=(0.627273, -1.31655t+ 1.96578)$$Yes, the velocity in the y direction changes over time. At the initial ... View answer Accepted answer 0 votes Hint: apply the quadratic formula. a = 1, b = -3\mu, and c = \mu^2. \mu is in fact, just a number. Your two energy values will just pop out as a function of \mu. View answer 0 votes On this line:$$E^2 O^2 2 \cdot 4 \cdot 6 \cdots N = E^2 O^2 \cdot (2 \cdot 2) \cdot (2 \cdot 3) \cdot (2 \cdot 4) \cdots (2 \cdot (N/2))$$I believe you missed the first 2. It should be:$$E^2 O^2 ...

You replace $u_{j-1}$ with $u_n$ and replace $u_{j+1}$ with $u_0$ because your box does not have overlap. i.e. $u_0$ is not the same point as $u_n$. These two points are 'next' to each other across ...

One way to get an equation of a line is with a point and a slope. This is the appropriate way with the equation you give: $y-y_1 = m(x-x_1)$. You indicate the easy way to get the point yourself, plug ...

The interpretation is as follows. There is one combination of 5 men. 5 men here. There are 5 combinations of 4 men and 1 woman. +20 men. Thats 25 men and 5 women. If you keep going like this, you ...

Not necessarily. As a counterexample, consider the function $$y = |x|$$ $y$ is differentiable at $x = 0^-$ and at $x = 0^+$. However, note that $y = 0$ at $x = 0$, but it is not differentiable.
Use the Divergence Theorem for the whole thing. This converts the surface integral to a volume integral: $$\iint_T F\cdot \hat{n} dS = \iiint_V (\nabla \cdot F) dV$$ This is much more doable to ...