Why do the lowest eigenvalues and eigenfunctions of an infinite square well provide the best approximation to the corresponding eigenvalues and eigenfunctions of a finite square well?

The total area of this shape is 44 square inches. The area of the triangle is 20 square inches. Write and solve an equation to find the area of the rectangle.

Harriet used 100 square floor tiles with sides 1 foot long to cover the floor of a square room. What was the perimeter of the room?

(a) Identify which of the following functions are eigenfunctions of the operator d/dx; (i) cos(kx); (ii) $e^{ibx};$ (iii) kx; (iv) $e^{-a x^{2}}.$ Give the corresponding eigenvalue where appropriate. (b) Identify which of the following functions are eigenfunctions of the operator $\mathrm{d}^{2} / \mathrm{d} x^{2};$ (i) cos(kx); (ii) $e^{ibx};$ (iii) kx; (iv) $e^{-a x^{2}}.$ Give the corresponding eigenvalue where appropriate.

Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

$$x ^ { 2 } - \frac { 4 } { 3 } x + c$$

Answer the question. The area of a square is 810 units. What is the length of a side of the square? Can you find the exact length of the side? Explain.

Complete each system for the given number of solutions. one solution

$$\left\{\begin{aligned} x+y+z &=7 \\ y+z &= \square \\ z &= \square \end{aligned}\right.$$

Four objects with the same charge $-q$ are placed at the corners of a square of side $d$. Determine the values of the $\vec{E}$ field and $V$ field in the center of the square.

The perimeter of square PQRS is 84 . Find the length of each side of square PQRS under the given conditions.

$$Q R=3(R S)$$

Complete each system for the given number of solutions. one solution

$$\left\{\begin{aligned} x+y+z &=7 \\ y+z &=\square \\ z &=\square \end{aligned}\right.$$

Find the unknown digit.

$$\square \times \frac { 5 } { 6 } = \frac { 20 } { 6 } , \text { or } 3 \frac { 1 } { 3 }$$

$$\square =$$

A rectangle and a square have equal areas. The rectangle has length 9 cm and width 4 cm. What is the perimeter of the square, in centimeters?

Find the value of c that makes the expression a perfect square trinominal. Then write the expression as the square of a binomial.

$$s ^ { 2 } - 26 s + c$$

The volume of the square prism is $96x^3+48x^2+6x$. Find an expression that could describe the perimeter of one of the prism's square faces.