Find an equation of the circle that satisfies the given conditions. Center (7, -3); tangent to the x-axis

Find the coordinates of the center of a circle that is tangent to the y-axis and intersects the x-axis at (8, 0) and (18, 0).

A thin metal plate is insulated on the back and exposed to solar radiation on the front surface. The exposed surface of the plate has an absorptivity of 0.8 for solar radiation. If solar radiation is incident on the plate at a rate of 450 W/m^2 and the surrounding air temperature is 25$^\circ{}$C

Graph each linear function using the slope and y-intercept.

$$f(x) = -2x + 4$$

Consider the problem

$$\begin{array}{l}{\max z=f(x)} \\ {\text { s.t. } \quad a \leq x \leq b}\end{array}$$

a. Suppose f(x) is a convex function that has derivatives for all values of x. Show that x = a or x = b must be optimal for the NLP. (Draw a picture.) b. Suppose f(x) is a convex function for which f'(x) may not exist. Show that x = a or x = b must be optimal for the NLP. (Use the definition of a convex function.)

Answer the following question as a complete sentence using the word in parenthesis. ¿Qu^e anuncia el letrero? (un descuento)

Plot the points $(7,1)$ and $(12,-3)$. Draw a straight line through them. Name three points that are on the same line as each given pair of points.

Determine, with reasons, whether A is similar to B. If

$$A \sim B,$$

give an invertible matrix P such that

$$P ^ { - 1 } A P = B.$$

$$A = \left[ \begin{array} { l l } { 4 } & { 2 } \\ { 3 } & { 1 } \end{array} \right] , B = \left[ \begin{array} { l l } { 2 } & { 2 } \\ { 3 } & { 2 } \end{array} \right]$$

What is the difference between demand and aggregate demand?

Define what we mean by “power-factor correction.” For power-factor correction of an inductive load, what type of element should we place in parallel with the load?

Graph each equation, and determine the domain and range. Determine whether the equation is a function, is one-to-one, onto. both, or neither. Then state whether it is discrete or continuous.

$$y=-5x^2$$

A meteorologist says that there is a $50\%$ greater chance of rain than no rain on Wednesday. What is the probability that it will rain on Wednesday?

Evaluate the expression. 15 - b when b = 9

Use the cofactor expansion theorem to evaluate the given determinant along the specified row or column.

$$\left| \begin{array} { c c } { - 8 } & { 6 } \\ { - 4 } & { 9 } \end{array} \right| , \text { column } 2.$$