# Recent questions tagged prove

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that there are infinitely many positive integers which are not representable as a sum of cubes of two other positive integers.
Prove that there are infinitely many positive integers which are not representable as a sum of cubes of two other positive integers.Prove that there are infinitely many positive integers which are not representable as a sum of cubes of two other positive integers. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that the difference $d=a_{2}-a_{1}=a_{3}-a_{2}=\cdots=a_{p}-a_{p-1}$ is divisible by $p$.
Prove that the difference $d=a_{2}-a_{1}=a_{3}-a_{2}=\cdots=a_{p}-a_{p-1}$ is divisible by $p$.Given an increasing sequence of prime numbers $a_{1}, \ldots, a_{p}$ forming an arithmetic progression, let $p$ be a prime number and let $a_{1}&gt;p ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How can I prove that a matrix$S_{ij}$is positive semi-definite? 1 answer 56 views How can I prove that a matrix$S_{ij}$is positive semi-definite?How can I prove that a matrix$S_{ij}$is positive semi-definite? ... close 0 answers 35 views Show that the inequality $$\sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}-x_{j}\right|} \leqslant \sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}+x_{j}\right|}$$ holds for all real numbers$x_{1}, \ldots, x_{n}$.Show that the inequality $$\sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}-x_{j}\right|} \leqslant \sum_{i=1}^{n} \sum_{j=1}^{n} \sqrt{\left|x_{i}+x_ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write the elements of a_{13}, a_{21}, a_{33}, a_{24}, a_{23} 1 answer 20 views Write the elements of a_{13}, a_{21}, a_{33}, a_{24}, a_{23} In a matrix \left\begin{array}{cccc} 2 &amp; 5 &amp; 19 &amp; -17 \\ 35 &amp; -2 &amp; \frac{5}{2} &amp; 12 \\ \sqrt{3} &am ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The individual quantities like a_{11}, a_{22}, a_{13} \ldots . . a_{m n} are called the ________________ of the matrix. 1 answer 58 views The individual quantities like a_{11}, a_{22}, a_{13} \ldots . . a_{m n} are called the ________________ of the matrix.The individual quantities like a_{11}, a_{22}, a_{13} \ldots . . a_{m n} are called the ________________ of the matrix. ... close 0 answers 62 views The multiplicity of a root of characteristic polynomial is known as the algebraic multiplicity. The dimension of the eigenspace of that root is known as the geometric multiplicity.The multiplicity of a root of characteristic polynomial is known as the algebraic multiplicity. The dimension of the eigenspace of that root is known ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove polar decomposition using singular value decomposition. 0 answers 30 views Prove polar decomposition using singular value decomposition.Prove &nbsp;polar decomposition using singular value decomposition. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if \lambda is a root of the characteristic polynomial, then there exist at least one eigenvector for \lambda. 0 answers 32 views Prove that if \lambda is a root of the characteristic polynomial, then there exist at least one eigenvector for \lambda.Prove that if \lambda is a root of the characteristic polynomial, then there exist at least one eigenvector for \lambda. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Can you give an example to denote the working of the central limit theorem? 1 answer 54 views Can you give an example to denote the working of the central limit theorem?Can you give an example to denote the working of the central limit theorem? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the solution for the following linear equation: 1 /(4 x-2)=5 / 6 1 answer 27 views Find the solution for the following linear equation: 1 /(4 x-2)=5 / 6Find the solution for the following linear equation: 1 /(4 x-2)=5 / 6 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the solution for the following linear equation: 5 x / 2=(3 x+24) / 6 1 answer 52 views Find the solution for the following linear equation: 5 x / 2=(3 x+24) / 6Find the solution for the following linear equation: 5 x / 2=(3 x+24) / 6 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Subtract polynomials 4 x^{3}-2 x^{2}-10 and 5 x^{3}+x^{2}+x+5 1 answer 28 views Subtract polynomials 4 x^{3}-2 x^{2}-10 and 5 x^{3}+x^{2}+x+5Subtract polynomials 4 x^{3}-2 x^{2}-10 and 5 x^{3}+x^{2}+x+5 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 12 t-10=14 t+2. Find t 1 answer 19 views 12 t-10=14 t+2. Find t$$12 t-10=14 t+2$. Find $t$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the unit circle?
A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at $\mathrm{A}$ enclosing an angle of $60^{\circ}$. The area enclosed by these tangents and the arc of the circle isA pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at $\mathrm{A}$ enclosing an angle of $60^{\circ} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The product of two positive numbers is 391 and their difference is 6 . What is their sum? 0 answers 67 views The product of two positive numbers is 391 and their difference is 6 . What is their sum?The product of two positive numbers is 391 and their difference is 6 . What is their sum? ... close 0 answers 52 views The first two terms of a sequence are 3 and 4. Each of the following terms in the sequence is the sum of all the preceding terms. Which of the following is not a term in the sequence?The first two terms of a sequence are 3 and 4. Each of the following terms in the sequence is the sum of all the preceding terms. Which of the followi ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Using a right-angled triangle how can we derive the trigonometric identity$1+\cot ^{2} \theta=\csc ^{2} \theta$1 answer 85 views Using a right-angled triangle how can we derive the trigonometric identity$1+\cot ^{2} \theta=\csc ^{2} \theta$Using a right-angled triangle how can we derive the trigonometric identity$1+\cot ^{2} \theta=\csc ^{2} \theta$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the following equation for$r:-2 r-2.25=3.75-8 r$1 answer 41 views Solve the following equation for$r:-2 r-2.25=3.75-8 r$Solve the following equation for$r:-2 r-2.25=3.75-8 r$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Deduce that the choice$a_{2}=1-a_{1}$gives$E[T]=\mu$In this case prove that the variance of$T$is a minimum if$a_{1}=a_{2}=\frac{1}{2}$. 1 answer 56 views Deduce that the choice$a_{2}=1-a_{1}$gives$E[T]=\mu$In this case prove that the variance of$T$is a minimum if$a_{1}=a_{2}=\frac{1}{2}$.Let$T=a_{1} X_{1}+a_{2} X_{2}$, where$X_{1}$and$X_{2}$are uncorrelated random variables with mean$\mu$and variance$\sigma^{2}$, and$a_{1}$an ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true? 0 answers 68 views Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true?Which of the following statements about the series $$\sum_{n=1}^{\infty} \frac{(-1)^{n}}{1+\sqrt{n}}$$ is true? ... close 0 answers 224 views The lengths of two sides of a triangle are$b$and$c$. Let$s$be the length of the angle bisector of the angle between the two given sides. The length of the third side of the triangle is:The lengths of two sides of a triangle are$b$and$c$. Let$s$be the length of the angle bisector of the angle between the two given sides. The leng ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The measure of the angle$\angle C B D$is: 0 answers 47 views The measure of the angle$\angle C B D$is:In the triangle$\triangle A B C$measures of angles$\angle A=46^{\circ}$and$\angle C=60^{\circ}\$ are given. The angle bisector intersects the circ ...