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What is the hottest temperature reached?

The temperature inside a kiln used to bake clay pottery is given by T(x) = -0.4x^2 + 32x + 73 degrees F where x is the number of minutes the kiln is on and 0 <= x <=80. (see equation in attached file)

Solving Equations

Find all real and imaginary solutions to the equation. 49x^2 + 9 = 42x

Finding the Equation of a Circle

Find the equation of the circle that passes through the origin and has intercepts equal to 1 and 2 on the x- and y- axes, respectively.


Factor: 3x^2 - 11 xy - 20 y^2 keywords: factoring expressions

Solving Equations

Solve y^2=30 where y is a real number. Simplify your answer as much as possible. (If there is more than one solution, separate them with commas).

Solving Equations

Find all values of w which satisfy the equation w+2 w-1 --------- = --------- + 1 w-1 w+5 (If there is more than one solution, separate them with commas)


Multiply: (4u - w + 3)(3u + 3w - 2) Simplify your answer as much as possible

Writing in a + bi Form

Question: Consider the following expression: -3i(4i - 1), a and b are real numbers. Write in the form a + bi.


-3/2 -25 Simplify each expression. Write your answers with positive exponents. Assume that all variables represent positive real numbers.

The Stabilization Ratio (births/deaths) for South and Central America

The stabilization ratio (births/deaths) for South and Central America can be modeled by the formula y = -0.0012x^2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x a) use a graph to estimate the year in which the stabilization ratio was at its maximum. b) use the formula to

Exponential Growth Word Problems

A colony of 1000 bacteria is introduced to a growth-inhibiting environment and grows according to the formula n = 1000 + 50t + t^2 How many bacteria are present after 3 hours?

Solving Equations

Solve for t. Where t is a real number. Divide with commas, if there is more than one solution. principle square root t + 19=4

Substitution of "v" in a 2nd order d.e.

I have been tasked with solving y'' - 3y^2 =0 using the technique used substituting v for y', therefore substituting v dv/dy for y''. (Equation with "x" missing) I broke it down as follows Y'' -3y^2 =0 Y'' =3y^2 Substituting I get v dv/dy = 3y^2 Separating variables, I get v dv =3y^2dy Integrating I get 1/2v^2 +c = y^3 +c

Word Problem: Distance

Anne is pulling on a 60 foot rope attached to the top of a 48 foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing?