Solve each quadratic inequality by using a graph, a table, or algebraically.

$$-3x^2+10x<5$$

An expression that describes the relationship between each input and output

A mass weighing 0.4 lb stretches a spring by 3 inches. Ignore damping. External vibrations create a force of $F(t)=2 \sin \omega t$ lb. Find the natural frequency, the value of $\omega$ that produces resonance and a value of $\omega$ that produces beats.

Solve the following initial value problem.

$$f^{\prime}(x)=\frac{2}{x^{2}}-\frac{x^{2}}{2}, f(1)=0$$

A typical flashlight battery will produce a $0.50-A$ current for about $3 \mathrm{h}$ before losing its charge. Determine the total number of electrons that have moved past a cross section of wire con necting the battery and lightbulb.

Use a calculator to help you solve each equation. Round each approximate answer to three decimal places.

$$0.25(2x-1.6)^2=(x-0.9)^2$$

Write the standard form of the equation of the circle with the given center and radius. Center (-2 , 4) , r = 6

write the first five terms of the geometric sequence.a1 = 2, r = π

Display each set of data in a frequency table and a line plot. test scores: 100 90 70 60 95 65 85 70 70 75 80 85 75 70 100 90

The value of each U.S. coin is a fractional part of one dollar. A quarter is $\frac { 1 } { 4 }$ dollar, a dime is $\frac { 1 } { 10 }$ dollar, a nickel is $\frac { 1 } { 20 }$ dollar, and a penny is $\frac { 1 } { 100 }$ dollar. Simplify the following expressions and describe any patterns you see: $\frac { 1 } { \frac { 1 } { 4 } } , \frac { 1 } { \frac { 1 } { 10 } } , \frac { 1 } { \frac { 1 } { 20 } } , \frac { 1 } { \frac { 1 } { 100 } }$

a) Solve the given integro-differential equation by using the Laplace transform.(b) By differentiating the integro-differential equation a sufficient number of times, convert it into an initial value problem.(c) Solve the initial value problem in part (b), and verify that the solution is the same as the one in part (a). φ'(t)+φ(t)=∫t0sin(t−ξ)φ(ξ)dξ,φ(0)=1

Is the statement true or false ? Nuclear fission is the process by which the nuclei of smaller atoms combine to form a new, more massive nucleus.

Suppose that the functions u and v are harmonic in a domain D. a) Is the sum u + v necessarily harmonic in D? b) Is the product uv necessarily harmonic in D? c) Is $\partial u / \partial x$ harmonic in D? (You may use the fact—which we will prove in

Verify each identity.

$$\frac { \cos 3 x + \cos 5 x } { \cos 3 x - \cos 5 x } = \cot x \cot 4 x$$