# Tagged Questions

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### Problem about moving sides of triangle

Imagine a triangle XOY which sides lie on x-axis and y-axis with hypotenuse XY of length 5 m. Suppose the point X moves away from the (0,0) along x-axis with speed = 1 m per second. What speed the ...
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### How to find the volume of a solid [closed]

Suppose the solid $E$ is given by $$E=\{(x,y,z): (x^2+y^2+z^2+8)^2 \leq 36(x^2+y^2)\}.$$ Find the exact volume of $E$.
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### Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
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### What if the cow could fly?

See grazing cow. Now keep the restriction that the length of the rope is $l\leq\pi r$ where $r$ is the radius of the barn, (I like to think of this as a goat tied to a silo) but now suppose the cow ...
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### Area of the field that the cow can graze.

How do we find the area that the cow can graze? The question goes as follows-- There is a circular barn house surrounded by a huge grazing field. A cow is tied to the rope ($AB$) at the end $A$ as ...
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### Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
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### Determine Center Point based on 2 separate elipses

First timer here. I've been digging back into my good old maths days but am extremely rusty (beyond belief). I got a really tricky question that i want to determine formula for so that my mate can ...
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### What does the secant value represent?

What does the secant value represent? I know that $$\sec = 1/\cos(\theta)$$ but really I do not know what this value represents, so I need your help. A clear example with images would be appreciated. ...
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### what does secant mean in mathematics?

I need your help. pleas I need some one to explain for me what does secant mean in mathematics? Clear example with images would be appreciated.
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### How to calculate the number of lattice points in the interior and on the boundary of these figures with vertices as lattice points?

We define a point $(x,y)$ in the plane to be a lattice point if both $x$ and $y$ are integers. Now let $$S\colon= \{ (x,y) \ | \ 0 \leq x \leq m, \ 0 \leq y \leq \frac{nx}{m} \},$$ where $m$ and ...
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### How to establish the formula for area of a triangle using the axioms of area?

We have the following definition: AXIOMATIC DEFINITION OF AREA We assume there exists a class of $M$ of measurable sets in the plane (i.e. subsets of the plane whose area can be defined) and a set ...
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### These two definitions of a hyperplane are equivalent?

My book first defines a hyper plane in $R^n$ as set $H= \{p^tx=\alpha \}$ where $p$ is a nonzero vector and $\alpha$ is scalar, or equivalently as the set $H=\{x:p^t(x-\bar{x })=0$. Next it ...
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### How to find iso function value points without exploring all points in 2D space

Consider a 2D graph with dim1 and dim2 represented as X and Y respectively. The range of X and Y are 1 to 100. Hence there are 10000 points in the 2D space. Each point in the space is some function of ...
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### how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
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### Equation of the plane that passes through a line and it's parallel with another line

What is the equation for plane $P$ that passes through $D_1:( x = 1+2t, ~y=t,~ z=t )$ and its parallel with $D_2 : ( x = -t,~ y=t, ~z = 2+3t )$? I'm just learning this. I think that if $P$ plane ...
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### Transformation shifts parallelogram to trapezoid - fairly simple

We are given the region $D= {\{(x,y) | 1 \leq x-y \leq 2, x \leq 0, y\leq 0\} \subseteq \mathbb R^2}$ I drew this region on a piece of paper, it resembles an infinite parallelogram on the third ...
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