Recent questions tagged p216

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xv)\;(32.15)^{\Large\frac{1}{5}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(3.968)^{\Large\frac{3}{2}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xiii)\;(81.5)^{\Large\frac{1}{4}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xii)\;(26.57)^{\Large\frac{1}{3}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xi)\;(0.0037)^{\Large\frac{1}{2}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(x)\;(401)^{\Large\frac{1}{2}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(ix)\;(82)^{\Large\frac{1}{4}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(255)^{\Large\frac{1}{4}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(vii)\;(26)^{\Large\frac{1}{3}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(vi)\;(15)^{\Large\frac{1}{4}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(0.999)^{\Large\frac{1}{10}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(0.009)^{\Large\frac{1}{3}}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(iii)\;\sqrt{0.6}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(ii)\;\sqrt{49.5}$

asked Aug 5, 2013 by sreemathi.v

1 answer

Find the equation of the ellipse if the centre is $(3 , -4 ), $one of the foci is $(3+\sqrt{3},-4)$ and $e=\large\frac{\sqrt{3}}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(\pm 3 , 0 )$ and the vertices are $(\pm 5 , 0)$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(2 , -1 ) , (0 , -1 )$ and $e=\large\frac{1}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if One of the foci is$(0 , -1 )$, the corresponding directrix is $3x+16=0$ and $e=\large\frac{3}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.

asked Jan 17, 2013 by sreemathi.v

1 answer

Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate change in the volume V of a cube of side $x$ metres caused by increasing the side by $1\%$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate value of $f (5.001)$, where $f (x) = x^3 – 7x^2 + 15.$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate value of $ f (2.01)$, where $f (x) = 4x^2 + 5x + 2$.

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xv)\;(32.15)^{\Large\frac{1}{5}}$

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(3.968)^{\Large\frac{3}{2}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xiii)\;(81.5)^{\Large\frac{1}{4}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xii)\;(26.57)^{\Large\frac{1}{3}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(xi)\;(0.0037)^{\Large\frac{1}{2}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(x)\;(401)^{\Large\frac{1}{2}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(ix)\;(82)^{\Large\frac{1}{4}}$

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(255)^{\Large\frac{1}{4}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(vii)\;(26)^{\Large\frac{1}{3}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(vi)\;(15)^{\Large\frac{1}{4}}$

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(0.999)^{\Large\frac{1}{10}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(0.009)^{\Large\frac{1}{3}}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(iii)\;\sqrt{0.6}$

Using differentials, find the approximate value of each of the following up to 3 places of decimal. $(ii)\;\sqrt{49.5}$

Find the equation of the ellipse if the centre is $(3 , -4 ), $one of the foci is $(3+\sqrt{3},-4)$ and $e=\large\frac{\sqrt{3}}{2}$

Find the equation of the ellipse if the foci are $(\pm 3 , 0 )$ and the vertices are $(\pm 5 , 0)$

Find the equation of the ellipse if the foci are $(2 , -1 ) , (0 , -1 )$ and $e=\large\frac{1}{2}$

Find the equation of the ellipse if One of the foci is$(0 , -1 )$, the corresponding directrix is $3x+16=0$ and $e=\large\frac{3}{5}$

The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is

If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$.

Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.

Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3\%$ is

If $f(x) = 3x^2 + 15x + 5$, then the approximate value of $f (3.02)$ is

If the radius of a sphere is measured as $9 \: m$ with an error of $0.03 \: m$, then find the approximate error in calculating its surface area.

If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1\%$.

Find the approximate change in the volume V of a cube of side $x$ metres caused by increasing the side by $1\%$.

Find the approximate value of \(f (5.001)\), where $f (x) = x^3 – 7x^2 + 15.$

Find the approximate value of $ f (2.01)$, where $f (x) = 4x^2 + 5x + 2$.

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$