Maths-
General
Easy
Question
In ![straight triangle A B C comma sum fraction numerator open parentheses b squared minus c squared close parentheses over denominator a end fraction cos space A equals](data:image/png;base64,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)
- S
- 0
- Δ
- 2Δ
The correct answer is: 0
Related Questions to study
physics-
One solid sphere A and another hollow sphere B are of the same mass and same outer radii. The moment of inertia about their diameters are respectively IA and IB such that....
One solid sphere A and another hollow sphere B are of the same mass and same outer radii. The moment of inertia about their diameters are respectively IA and IB such that....
physics-General
maths-
maths-General
maths-
If ![L subscript x not stretchy rightwards arrow 0 end subscript open parentheses fraction numerator cos begin display style space end style 4 x plus a cos space 2 x plus b over denominator x to the power of 4 end fraction close parentheses](data:image/png;base64,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)
If ![L subscript x not stretchy rightwards arrow 0 end subscript open parentheses fraction numerator cos begin display style space end style 4 x plus a cos space 2 x plus b over denominator x to the power of 4 end fraction close parentheses](data:image/png;base64,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)
maths-General
physics-
One circular rig and one circular disc both are having the same mass and radius. The ratio of their moment of inertia about the axes passing through their centers and perpendicular to their planes, will be,.....
One circular rig and one circular disc both are having the same mass and radius. The ratio of their moment of inertia about the axes passing through their centers and perpendicular to their planes, will be,.....
physics-General
physics-
A circular plate of uniform thickness has a diameter of 56 . A circular portion of diameter 42 cm . is removed from +ve x edge of the plate. Find the position of center of mass of the remaining portion with respect to center of mass of whole plate
A circular plate of uniform thickness has a diameter of 56 . A circular portion of diameter 42 cm . is removed from +ve x edge of the plate. Find the position of center of mass of the remaining portion with respect to center of mass of whole plate
physics-General
maths-
If f(x) =
x then ![lim for x not stretchy rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,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)
If f(x) =
x then ![lim for x not stretchy rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,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)
maths-General
physics-
From a uniform circular disc of radius R, a circular disc of radius R/6 and having center at a distance +R/2 from the ceater of the disc is removed. Determine the center of mass of remaining portion of the disc.
From a uniform circular disc of radius R, a circular disc of radius R/6 and having center at a distance +R/2 from the ceater of the disc is removed. Determine the center of mass of remaining portion of the disc.
physics-General
maths-
maths-General
physics-
Four particles A,B,C and D of masses m,2 m,3 m and 5 m respectively are placed at corners of a square of side x as shown in figure find the coordinate of center of mass take A. at origin of x-y plane
![](data:image/png;base64,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)
Four particles A,B,C and D of masses m,2 m,3 m and 5 m respectively are placed at corners of a square of side x as shown in figure find the coordinate of center of mass take A. at origin of x-y plane
![](data:image/png;base64,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)
physics-General
maths-
maths-General
maths-
If
and ![f left parenthesis 5 right parenthesis equals 2 comma f to the power of straight prime left parenthesis 0 right parenthesis equals 3](data:image/png;base64,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)
If
and ![f left parenthesis 5 right parenthesis equals 2 comma f to the power of straight prime left parenthesis 0 right parenthesis equals 3](data:image/png;base64,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)
maths-General
physics-
Consider a two-particle system with the particles having masses M1, and m2. If the first particle is pushed towards the center of mass through a distance d, by what distance should the second particle be moved so as to keep the center of mass at the same position?
Consider a two-particle system with the particles having masses M1, and m2. If the first particle is pushed towards the center of mass through a distance d, by what distance should the second particle be moved so as to keep the center of mass at the same position?
physics-General
Maths-
For ![x element of R Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x minus 3 over denominator x plus 2 end fraction close parentheses to the power of x equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAAnCAYAAABAFqmbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABPlJREFUeNrtXW9EXWEYfyWZZCRJJpEkmUQmyTVjJslkJJmZieR+mMy+TCZJzD5MMn1JkklkZiYZM8nsQ0ySyYzsUx8SM5lc1+Xuedzn6uzcc895n/ec7r3n3OfHj86558/7nvc5z/v8eZ+TUgJBYfAF2El/VwA/ApvlsUQHceDrELd/gfrghkHgOv39CnhPhj06iAH3gZUl0p5bwC3gOTAB/AmcB9a5nINtPwDe9Lg29nMSuCTDHh1UA38Bu0qoTdukJass+7po+nfDdepLjYfG/mG7tiDkmAUuhqStZ5pmxWye326TOXEIrJehjwZwIP8Ar2kcOwZ8keclGCtAW1tIg3qhkYTdLqRNwB3S0nEXQReEDFPAN4zj94ANlu1HBXAGG+g+aBcPaJ6zDHxu2a6iyESbZfvIw+wQhASH5NTpop+8+uzU/PkS25a2cZJxbp+m1haEHKiVTg3O+0QRgH2PaIGTIDrRC7XAIeCuRuTBihNguwxztIFT9JrBeagRk+oiaVAo1JAg62KN+iiIMFaBE8xzcJp+SybFaBHanGAcO0Z9FEQYmwxHKRsd+KAycWXUit80zIkg0UnOHcd+35JhjjbQHtaNldaTQFiFdpAZ2eAAQ2HDKpOFwzUOmMHDJMZDpvlxWi6DmSAH45hsri2HwU1HsN/nJCBewHDUO+UcS14njRc0YjRTJIjb9NJwUEF9DBXQE8X8+h41PqkhfK3kZVsxB3zJFOLfIRTiKL6YdiTD1FjMs38nR6Vb6efFhxw89BHgCnPA0yLE0kerR8lNbTaR9q02uN808Klt34zKDaynPR4UJ+4pQlwGfeSmNhdIo5pgA3jXsn1VZTI9DaKJy1qIfSdpuKnNY00HxQkYsmkkL7ifXqBhg4chQix9zAEntZk0fGNQ8FO2Y2OGDyOKQpwOCUt2XDipTVNN3EOhmyx6HaISoonFnDAyJ7ipzXlDm3jUIQqBM0CzCLGYE35gktpsouO4a0PRIRy37UNtvGrwMJI+7HIR4gj10U9qE2O72Thxl9IreMQslNPaAXQkO5gPY99l1vBTJr7i8XI+UZms2aL6v0YOZ6ZlelHbRYgLgyBSm/aMXcqjE5hlu+Kwv1flLhzxso0wt3+S535+ysSXKILS4/DbFEVS2khY8d5xEt4HNkGvEyEW+IVXmXjc40VJqYvSmiwe27Zn6NhZhyjMiMM9UyX8vLJ+0RmZavj87htcJymiFxxMy8RR6LEW7IbDb/a1wB00u5yTEGTRqJxj37oLgIqBHTLPaix9+6p4a5grVQgXAJUq/JSJu9nEw6Rh0VTArOYGXX+DBm+ONPxaHmHF0GRtiKZ39CMOGMfjczkV8fOPyy4TR1sZ19jaa8+6af+Ii/bfVLxllEGU7Pu1UTmVHQNKFsUH4qyWcpn4iuLXoPkt2fcjxL1kUuhiXOXmAQQRA0YwuJUZfkv2TYUYo0i7NlvfC+tKCkUjD5whTgzOK0bJ/nvgHWY70R6Wkv0ywAFN0xz4KdnnauIWEuBW5nkYt5ePp5QJsCBgmXG835J9jhCjFsUQo0mxA5pJz2R4ywNoDuh+UDCIkn1dIUbnEUOFJt9LxojQX1XYzwkIioxpjQhDUCX7ukK86cOeRe09I8NaXkDNeuRi4xajZN/UEcRFUF4f2RZEFH2qtP7dgQmqyFGNyXCWLzA5sBji9qNJNFGsm/8DkEaU4UU0fWkAAAGZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPng8L21pPjxtbz4mI3gyMjA4OzwvbW8+PG1pPlI8L21pPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtcm93PjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48L21yb3c+PG1yb3c+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MjwvbW4+PC9tcm93PjwvbWZyYWM+PC9tZmVuY2VkPjxtaT54PC9taT48L21zdXA+PG1vPj08L21vPjwvbWF0aD6DhiSgAAAAAElFTkSuQmCC)
There are seven indeterminate forms which are typically considered in the literature:
For ![x element of R Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x minus 3 over denominator x plus 2 end fraction close parentheses to the power of x equals](data:image/png;base64,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)
Maths-General
There are seven indeterminate forms which are typically considered in the literature:
physics-
Three particles of the same mass lie in the (X,Y) plane, The (X,Y) coordinates of their positions are (1,1),(2,2) and (3,3) respectively. The (X,Y) coordinates of the center of mass are
Three particles of the same mass lie in the (X,Y) plane, The (X,Y) coordinates of their positions are (1,1),(2,2) and (3,3) respectively. The (X,Y) coordinates of the center of mass are
physics-General
Maths-
given that ![f to the power of † left parenthesis 2 right parenthesis equals 6 text and end text f to the power of † left parenthesis 1 right parenthesis equals 4](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
given that ![f to the power of † left parenthesis 2 right parenthesis equals 6 text and end text f to the power of † left parenthesis 1 right parenthesis equals 4](data:image/png;base64,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)
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or