Alternating current (AC) circuits use complex numbers to represent impedance in ohms. To find the total impedance in a circuit, you need to find the sum of the impedances from each part of the circuit. A circuit has partial impedances of 4.2 + 3i and 5 - 2.2i. What is the total impedance for the circuit?

How can you check that your quotient is correct?

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even.

Sketch the graph of the equation using extrema, intercepts, symmetry, and asymptotes. y = 1 - 1/x

Multiply

$$\sin ^ { 2 } \theta + \cos ^ { 2 } \theta = 1 \text { by csc } \theta$$

to find another form of the trigonometric identity.

solve the logarithmic equation algebraically. Approximate the result to three decimal places. ln√x+8 = 3

Solve the given initial-value problem.

$$\mathbf{X}^{\prime}=\left(\begin{array}{rrr}{1} & {-12} & {-14} \\ {1} & {2} & {-3} \\ {1} & {1} & {-2}\end{array}\right) \mathbf{X}, \quad \mathbf{X}(0)=\left(\begin{array}{r}{4} \\ {6} \\ {-7}\end{array}\right)$$

Find T(t) and N(t) at the given point. r(t)=

$$\frac { 1 } { 2 } t ^ { 2 } \mathbf { i } + \frac { 1 } { 3 } t ^ { 3 } \mathbf { j }$$

t=1

The melting points and boiling points of two isomeric alkanes are as follows:

$$\mathrm { CH } _ { 3 } \left( \mathrm { CH } _ { 2 } \right) _ { 6 } \mathrm { CH } _ { 3 } , \mathrm { mp } = - 57 ^ { \circ } \mathrm { C } \text { and } \mathrm { bp } = 126 ^ { \circ } \mathrm { C }; \\ \left( \mathrm { CH } _ { 3 } \right) _ { 3 } \mathrm { CC } \left( \mathrm { CH } _ { 3 } \right) _ { 3 } , \mathrm { mp } = 102 ^ { \circ } \mathrm { C } \text { and } \mathrm { bp } = 106 ^ { \circ } \mathrm { C }.$$

(a) Explain why one isomer has a lower melting point but higher boiling point. (b) Explain why there is a small difference in the boiling points of the two compounds, but a huge difference in their melting points.

Meredith wants to go on a trip this summer that costs $375. She paid a deposit of$125 and will save an additional $25 per week to pay for the trip. The equation 125 + 25w = 375 can be used to find the number of weeks Meredith will need to save. Describe the steps needed to solve the equation.

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.

Calculate the probability P(E). You roll two dice, one red and one green. Losing combinations are doubles (both dice showing the same number) and outcomes in which the green die shows an odd number and the red die shows an even number. The other combinations are winning ones. E is the event that you roll a winning combination.

Occupants in a single space shuttle in orbit feel weightless. Describe a scheme whereby occupants in a pair of shuttles (or even one shuttle and another massive object in orbit) would be able to use a long cable to continuously experience a comfortably normal Earth-like gravity.

Use a calculator to find the value of the trigonometric function to four decimal places.

$$\cot \frac { \pi } { 18 }$$