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- Find all 2x2 matrices such that ad-bc=1 and A^-1=A
Find all 2x2 matrices such that ad-bc=1 and A^-1=A

- Hyperbolic function
Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshx

- limits (precise definition) will rate
I need to use thedelta epsilon definitionI can get but Idon't know what to do from here because I can'tfactor it any further.

- solve the initial value problem
y"+y=2+x y(0)=1, y'(0)=2

- Partial Derivatives
Find the indicated partial derivatives.41. f(x,y,z)= y/(x+y+z), fy(2,1,-1)

- average rate of change
Let f(x)=8x2. Find a value A such that the average rate of changeof f(x) from 1 to A equals 88i cantremember to do this. please help

- quick question
if a function has cusps, endpoints, jumps, holes or verticalasymtotes, the derivative does not exist.correct ?

- Intro to quadratic equations
Solve.

- how many different ways
A spymaster has a network of 11 operatives whom he pays out of a slush fund containing $24000. For accounting reasons, his service requires him to use up his entirefund and to pay his operatives in integer multiples of $1000.(a) How many different ways can he pay his operatives?(b) Since an unpaid operative is unreliable, the spymaster decides that every operative will get at least $1000. With this rule, how many different ways can he pay hisoperatives?How do I approach this problem?

- Normal distribution with change of variables
Temperatures in August are distributed normally with a mean of75 degrees and variance of 16 degrees squared. Using the change ofvariables technique, find the pdfof temperature measured inCelsius.F = 9/5 C + 32is the relation between Farenheitand Celsius

- Geometry
Explain why any complex number u with |u|=1 can be written in the form cos theta + i sin theta for some angle theta, and conclude that multiplication by u rotates thepoint 1 ( and hence the whole plane) through the angle theta

- Integration
What is the integral of f(x) between limits 1 and 2Where f(x) = (x^2 - x + 1) / xThank you.

- solve the initial value problems using the method of Laplace transforms...
y' + y = g(t) y(0)=1 g(t)={1, 0<x<12, x>1

- Central Limit Theorom and Confidence Intervals
Give the notation for the Central Limit Theorom and explain each symbol in it, and then carefully explain its connection with confidence intervals, and with hypothesistesting

- Stats Homework
An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $ 5,000. After introducing several plans to preventloss, it randomly samples 200 policyholders and finds the mean amount per claim was $ 4,800 with a standard deviation of $ 1,300.Use the .05 significance level.1. What is the population in this case? What is the sample? How big is the sample?2. State your null and alternative hypotheses.3. What kind of tests do you plan to use? Why?4. Calculate the required test statistics and find the p-value associated with it.5. Do you reject Ho or accept Ha ? Why?6. Does it appear the prevention plans were effective in reducing the mean amount of a claim?What should the insurance company do?

- Antiderivatives
The question is: Since raindrops grow as they fall, their surfacearea increases and therefore the resistance to their fallingincreases. A raindrop has an initialdownward velocity of 10m/s andits downward acceleration isa=9-0.9tif0if t > 10If the raindrop is initially 500m above the ground, how longdoes it take to fall?

- 10
find the tangent line of the curve y=1/2 at x=2

- math
Let Qo: R^2->R^2 be a reflection in the Xaxis,let Q1:R^2->R^2 be reflection in the line y=x,let Q-1:R^2-.R^2 be a reflection in the line y=x,and letRpi/2:R^->R^2 be counterclockwise rotation through pi/2 show that Q1 o Rpi/2 =Qo and show that Rpi/2 o Qo= Q1

- Discre
- transformations
graph it..y=-1/2f(1/2x+1)-1write all transformations step....