Give a linear equation that expresses volume,V,in terms of Temperature, T

This is the first question of a 4 part problem. I just need help with how to start it. above is the 1st question to below problem: In some experiments, tathered data suggest that volume of gas and temperature are related quantities. In one particular experiment, at a temp. of -30 degrees C, the volume of a gas was measured t ...continues

Find the angle in a triangle

Suppose that the triangle ABC has three edges a=BC=4sqrt(3) , b=AC=4 and c=AB=4. Find angle ABC and BAC.

Area of Rectangle under a Parabola and Sectors in an Arc

Proving the area of a shaded rectangle under a parabola and then differentiating the expression. Minimizing the perimeter of sectors in an arc. Please see the attached file for the fully formatted problems.

Proof By Induction

Prove by induction (or any other method): For any natural n the following statement is true: (2n+1)+(2n+3)+(2n+5)+.....(4n-1)=3n^2

Word Problem - How many Cookies?

Dad made cookies. Dad ate 1 cookie. Dave ate 1/2 dozen cookies. Kate ate 1/2 of what Dave ate. Henry & Julie each ate 1/3 of what was left. Then Jake ate 1/2 of what was left. Mom ate 1 cookie. There was 1 cookie left. How many cookies were baked?

Functions: Variable Replacement Problem

The problem reads: If a @ b = 3a - b^2 find 2 @ (3 @ 1)

Summation Equality: Prove by Induction

I would be grateful if someone could show me how to prove by induction the attached formula.

The Maximum of the function

Find the maximum of f(x,y)=xy such that x+3y=12

Velocity

a mo-ped can travel 60 miles in 2 hours less time than a bicycle can travel 50 miles. the mo-ped is traveling at a rate of 10 miles per hour faster than the bicycle. 1. how fast in mph is each traveling? 2. how long will it take each to travel their respective distance?

Inequality

Prove that (a1b1+a2b2+...+anbn)^2<=(a1^2+a2^2+...+an^2)(b1^2+b2^2+...+bn^2) where ai, bi are real numbers, i=1,2,...,n