Mathematics

Could you please help with vectors

If a = 3i - j +2k & b = 2i - 2j + 4kfind a+b, a-b, a・b, and a×b.Thank you for your help,Could you please show step by step?-a+b what you do here is just adding the different components individually: (

Simplify 1/x + 1/y / xy

Simplify 1/x +1/y all over xy. HELP.-Multiply the top and bottom by xy to get: (1/x + 1/y)/xy * xy/xy = (y + x)/x²y² I hope this helps!

Find the sum of the first 90 positive odd integers

how do I work this out?-The nth odd integer is 2n-1. 1 + 3 + 5 + ... + 179 = x 179 + 177 + ... + 1 = x ----------------------------------- 180 + 180 + ... + 180 = 2x 90·180 = 2x x = 8100

How to evaluate the composite function given that f(x)=5x+3 and h(x)=√(x+5)

(f o h)(4)=-Given: f(x) = 5x + 3 h(x) = √(x + 5) Find f(h(4)) First we have to find h(4) h(4) = √(4 + 5) h(4) = √(9) h(4) = +/-3 Next we find f(-3) and f(+3) because its +/- f(-3) = 5(-3) + 3 f

Simplify this please

PLEASE show step by step with explanations 1/7-1/y ----------- 7-y ----------- 7-= [(y - 7)/7y]/[(7 - y)/7==> LCD in top fraction = [(y-7)/7y][7/(7-y)]==>Invert and multiply = -1/y==>Cancel the 7s

Trigonometry: Dividing Polynomial Help!

Heres the problem: x^3 + 2x^2- 3x - 6 divided by x - (sqrt)3 How do you do this? Please help :( Thank you :D-Use synthetic division to simplify that expression. √3 | 1 + 2 . . . .- 3 . . . . . - 6

Rectangle Problems? I Can't Figure It Out, Please Help. Only 2 Problems.

1) The length of a rectangular courtyard is 3 yards longer than triple the width. If the perimeter of the courtyard is 62 yards, what is the length of the courtyard? A) 7 yards B) 10 yards C) 21 yards

Is this the proper way to set up the equation to answer this question

Heres the question: If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? Is this how

What does the "d" stand for in this question

Sn = (1/2)n[2a1 + (n - 1)d]-The common difference between each number in a sequence or series-d is common difference in 2 adjacent terms. e.g. even numbers 2, 4, 6, .. common difference is 4 – 2 = 2,

Calculus antiderivative problem

A canister is dropped from a helicopter hovering 500m above the ground. Unfortunately, the canisters parachute does not open. The canister has been designed to withstand an impact speed of 100 m/s. Wi

Simplify, express in simplest radical form: 3√(3/13)

Okay this is what I have so far: 3*√(3/13) =3*(√3/√13 *√13/√13) =3*(√3√13/(√13)^2) =3*√39/13 However, Im not even sure if this is correct especially since everybody else is getting 3+√39/13 So Id lik

Gradients and tangent lines

If the gradient of f(x,y) at the origin is (6,8), the slope of the tangent line to the level curve of f through the origin at (0,0) is ___? I know you have to use a dot product and set it equal to ze

Can someone help me solve this simultaneous equation please (with workings)

Y=x (squared)-3x Y=2x-6 THANKS!-As they are both equal to Y, they are also both equal to each other: x² - 3x = 2x - 6 x² - 5x + 6 = 0 (x - 3)(x - 2) = 0 x = 3 or x = 2

Find the mean and standard deviation of the following set of data. 4 6 8 10 12 14

(4 + 6 + 8 + 10 + 12 + 14) / 6 = 9 (4 - 9)^2 = 25 (6 - 9)^2 = 9 (8 - 9)^2 = 1 (10 - 9)^2 = 1 (12 - 9)^2 = 9 (14 - 9)^2 = 25 √[(25 + 9 + 1 + 1 + 9 + 25) / 6] √(70/6) √(35/3) 3.41565025531986612774034

If y = 2sin π - 5cos θ, then dy/dθ =

y = 2sin π - 5cos θ dy/dθ = 5 sin(θ)-I am assuming that the expression is: y = 2sin(πθ) - 5cos(θ) Note that d/dx sin(f(x)) = f(x)cos(f(x)) and d/dx cos(f(x)) = -f(x)sin(f(x)), so: dy/dθ = 2πcos(πθ)