Mathematics

Finding 1st and 2nd derivatives

Im confused, I cant figure out how to find derivatives. I am asked to find the 1st & 2nd derivative of Y=3x^2-12x-5x^-3 Could someone show me how to do this step by step please? The formulas aredy/dx

Find the indefinite integral x^3 sqrt(x^2 -25)dx using the substitution x=5sec

x = 5secθ dx = 5tanθ secθ dθ ∫ x ³ √(x ² - 25)dx = ∫ 125sec³θ √(25sec²θ - 25) 5tanθ secθ dθ = ∫ 625sec⁴θ √[25(sec²θ - 1)] tanθ dθ = ∫ 625sec⁴θ √[25(tan²θ)] tanθ dθ = ∫ 3125sec⁴θ tan²θ dθ = ∫ 3125sec²

Move one digit to make equation correct 62-63=1

Dear Ramasamy,Heres how u do it...62-63=1,insteadof 62 I write it as,2 raised to the power of 6-63=1,that is,64-63=1-O boyo, this is confusin O.O One digit am not sure Buh, ef ye can move two digits

Find the total number of matrices that can be formed with the elemements 0,1,2,3 each matrix having 4 elements

Im getting 4^4 but my book says 3*(4^4) .-The book is counting 2*2, 1*4 and 4*1 matrices. Personally I think theyre being a bit too sneaky. The section is presumably probability, so why are they ask

HOW Do YOU Solve DERIVATIVES Through A Point

Find the slope of the folium of Descartes x^3+y^3-9xy=0 at the points (4,2) and (2,4). Slope at (4,2)=Slope at (2,4)= At what point other than the origin does the folium have a horizontal tangent? T

Calculus and Integrals

Let: Definite integral f(x) dx=1 from x=3 to 12,Definite integral f(x) dx=3 from x=3 to 6Definite integral f(x) dx=3 from x=9 to 12 I found the definite integral f(x) dx=-5 from x=6 to 9 Now I need t

Find a formula for f^(100)(x) if f(x)=x^(100)

I assume you want to find the 100th derivative of f(x) = x^100 f(x) = 100x^99 = nPr(100, 1) * x^(100 - 1) f(x) = 100 * 99x^98 = nPr(100, 2) * x^(100 - 2) f(x) = 100 * 99 * 98x^97 = nPr(100, 23) * x^(

Setup a Differential equation with water tanks

Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining.the tank initially contains 175 liters and 23 l

Simple question on set notation

What is the difference between 13 ∈ { n² + n⎮n ∈ Z} and 13 ∈ {n ∈ Z⎮n² + n} and is 13 ∈ { n² + n⎮n ∈ Z} true? (Z is the set of all integers) There was a question on my exam today asking if 13 ∈ { n²

How to find the absolute value of this function

f(x)=I3x^2-6I Im supposed to write it as a piece wise function. help?-solve 3x^2 - 6 = 0 3x^2 = 6 x^2 = 2 x = √2 or x = -√2 If x 0. If -√2 If x > √2, then 3x^2 - 6 > 0. Therefore, f(x) = { 3x^2 - 6

Math Help Please?! (algebra)

Solve Equation 6(x-0.8)-0.2(5x-4)=6-6 (x - 0.8) - 0.2 (5x - 4) = 6 Multiply: 6x - 4.8 - x + 0.8 = 6 Add:5x - 4 = 6 Add 4 on both sides: 5x = 10 Divide by 5: x = 2-Distribute the numbers 6(x-0.8)=

Algebra.....problem solving!

Together two pipes can fill a small reservoir in 2hours.Working alone Pipe1 can fill a reservoir in 1hour and 40minutes less time than Pipe2 can.How long would each pipe need to fill the reservoir by

INITIAL VELOCITY , CALCULUS HELPP!!

An object is moving in a straight line such that its position x meters from a fixed point O in the line at any time t seconds is given by x=t^2-6t+8 Find the objects initial velocity-Find d/dt x = t

Graphing a quadratic function without using a graphing calculator

Ok i was given f(x)= 2x^2 - 8x + 3 I had to use completing the square to get it into vertex form AKA 2(x-2)^2 - 1 So the vertex is (2, -5) -5 from plugging back in etc etc How would I find the x an

ANOTHER QUESTION ON CALCULUS, VELOCITY !

An object is moving in a straight line such that its position x meters from a fixed point O in the line at any time t seconds is given by x=t^2-6t+8 At what time(s) is the object at O? Last question