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Nigeria
A solid has a cross section perpendicular to the x-axis, which is a square with side length \(y\). If the function \(y = 2x + 1\) represents the upper boundary of the solid from \(x=0\) to \(x=3\), find its volume.
Calculus Dec 18, 2024
Selve the following Difterential Equations a. \( \frac{d y}{d x}=\frac{x^{2} y-y}{y+1} \) b. \( \left[x^{2} \cos 3 x^{2}-3 x^{3} e^{2 x}+\left(\frac{x^{2}-1}{x^{3}+x}\right) x^{2}\right] d x-x^{2} d y=0 \) Solve the following Equations a. If \( z=\sin x y \), Find \( \frac{\partial^{2} z}{\partial x^{2}} \) and \( \frac{\partial^{2} z}{\partial y \partial x} \) b. If \( z=\sin (3 x+2 y) \), show that \( 3 \frac{\partial^{2} z}{\partial y^{2}}-2 \frac{\partial^{2} z}{\partial x^{2}}=6 z \)
Calculus Dec 17, 2024
Expand each power of \( (3 p+q)^{5} \)
Algebra Dec 17, 2024
Simplify the express \( \frac{a^{2} b^{4}-b^{2} a^{4}}{a b(a-b)} \) A. \( a^{2}-b^{2} \) B. \( b^{2}-a^{2} \) C. \( a^{2} b-a b^{2} \) D. \( a b^{2}-a^{2} b \)
Algebra Dec 17, 2024
Let \( G=S_{4} \) be the symmetric group of permutations of four symbols \( 1,2,3,4 \). (a) (i) List all the elements of \( G \) in matrix and cycled form. (ii) State the order of \( G \). (b) It is given that \( p=(1234), q=(3142), r=(2431) \) and \( s=(4123) \). (i) Show by computation that ( \( p q r s)^{-1}=s^{-1} q^{-1} r^{-1} p^{-1} \). (ii) Solve for the elements \( x \) and \( y \) given that \( p^{2} x y r^{-2}=s^{2} \). (iii) Compute the element \( u \) given that \( \left.u=\mid\left(p^{-4} q^{2}\right)^{-4}\left(r^{2} s^{-4}\right)^{-1}\right]^{-4} \). (iv) Compute the orders of \( p, q, r \) and \( s \) and hence verify Lagrange's Theorem.
Other Dec 17, 2024
\( \lim _ { n \rightarrow 0 } \frac { \tan k i } { \tan \pi k } \)
Calculus Dec 17, 2024
DON'T USE CALCULATOR \( 2 \times 2-2+1 \times 10 \)
Arithmetic Dec 17, 2024
given That \( 356_{x}=B C_{16} \) find the value of \( x \).
Algebra Dec 16, 2024
Jillow Brook National Bank operates a rive-up teller window that allows ustomers to complete bank transactions ithout getting out of their cars. On eekday mornings, arrivals to the drive-up eller window occur at random, with an rrival rate of 24 customers per hour or 0.4 ustomers per minute. What is the mean or expected number o. ustomers that will arrive in a five-minute eriod?
Probability Dec 16, 2024
We hits to a Web site occur at the rate of 9 per minute between 7:00 P.M. and 8:00 P.M he random variable \( X \) is the number of hits o the Web site between 7:16 P.M. and 7:24 P. State the values of \( \lambda \) and \( t \) for this
Probability Dec 16, 2024
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