Find the index of refraction of a medium for which the angle of incidence of a light beam is 31.5 and angle of refraction is 25.6

Determine the partial fraction decomposition of the expression below. Show all work in an easy-to-read solution.That might mean working the problem out on a separate page and transferring your organized work below.Double checkyour calculations. 16x+16/x(x-2)^2(x^2+4)

Explain how earth is made up of material supernovae

4. The ice fish lives under the polar ice cap where the water temperature is -4°C. This fish doesn't freeze at that temperature due to the solutes in its blood. The solute concentration of the fish's blood can be related to a sodium chloride solution that would have the same freezing point. What is the minimum concentration of sodium chloride solution that would not freeze at -4°C Assume idela behavior and complete dissociation of NaCl.

A boy starts from walking North at a speed of 1.5m/s and a girl starts walking West at the same point P at the same time at a speed of 2.0m/s. At what rate is the distance between the boy and the girl increasing 6s later?

Sketch the graph of the function f(x) = xe^x

The table below lists body temperatures obtained from randomly selected subjects (based on Data Set 3 “Body Temperatures” in Appendix B). Using a 0.05 significance level, test for an interaction between gender and smoking, test for an effect from gender, and test for an effect from smoking. What do you conclude?

factor f(x)=2x^4-15x^3+44x^2-79x+60 completely into a product of linear factors in standard form.

Determine the partial fraction decomposition of the expression below. Show all work in an easy-to-read solution.That might mean working the problem out on a separate page and transferring your organized work below.Double checkyour calculations. 16x+16/x(x-2)^2(x^2+4)

Determine the partial fraction decomposition ofthe expression below. Show all work in an easy-to-read solution.That might mean working the problem out on a separate page and transferring your organized work below.Double check your calculations. 48x-24/x(x-1)(x-3)(x+2)(x+1)(x-2)

Two charged spheres are 8.45cm apart. They are moved, and the force on each of them is found to have been tripled. How far apart are they now?

What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.

factor f(x)=2x^4-15x^3+44x^2-79x+60 completely into a product of linear factors in standard form.

how do you solve this

Determine the partial fraction decomposition of the expression below. Show all work in an easy-to-read solution.That might mean working the problem out on a separate page and transferring your organized work below.Double checkyour calculations. 16x+16/x(x-2)^2(x^2+4)

Determine the partial fraction decomposition ofthe expression below. Show all work in an easy-to-read solution.That might mean working the problem out on a separate page and transferring your organized work below.Double check your calculations. 48x-24/x(x-1)(x-3)(x+2)(x+1)(x-2)

Use Cramer’s Rule to solve the system of equations: {3x+y =-1 {2x+y-z=-4 {-x +2z=3

If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation $a=9.81\left[1-v^{2}\left(10^{-4}\right)\right] \mathrm{m} / \mathrm{s}^{2}$ where $v$ is in $\mathrm{m} / \mathrm{s}$ and the positive direction is downward. If the body is released from rest at a very high altitude, determine (a) the velocity when $t=5 \mathrm{s}$, and (b) the body's terminal or maximum attainable velocity $(\text { as } t \rightarrow \infty)$

When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down slightly before going up. Explain why.

A machine at a post office sends packages out a chute and down a ramp to be loaded into delivery vehicles. (a) Calculate the acceleration of a box heading down a $10.0^{\circ}$ slope, assuming the coefficient of friction for a parcel on waxed wood is $0.100 .$ (b) Find the angle of the slope down which this box could move at a constant velocity. You can neglect air resistance in both parts.

A fireman has mass $m$; he hears the fire alarm and slides down the pole with acceleration $a$ (which is less than $g$ in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is $90.0 \mathrm{kg}$ and he accelerates at $5.00 \mathrm{m} / \mathrm{s}^{2},$ what is the magnitude of his applied force?

A diver bounces straight up from a diving board, avoiding the diving board on the way down, and falls feet first into a pool. She starts with a velocity of $4.00 \mathrm{m} / \mathrm{s}$ and her takeoff point is $1.80 \mathrm{m}$ above the pool. (a) What is her highest point above the board? (b) How long a time are her feet in the air? (c) What is her velocity when her feet hit the water?

While sliding a couch across a floor, Andrea and Jennifer exert forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathbf{J}}$ on the couch. Andrea's force is due north with a magnitude of $130.0 \mathrm{N}$ and Jennifer's force is $32^{\circ}$ east of north with a magnitude of $180.0 \mathrm{N}$. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force $\overrightarrow{\mathbf{F}}$ DS should they push so that the couch does not move?

A telephone pole has three cables pulling as shown from above, with $\quad \overrightarrow{\mathbf{F}}_{1}=(300.0 \hat{\mathbf{i}}+500.0 \hat{\mathbf{j}})$ $\overrightarrow{\mathbf{F}}_{2}=-200.0 \hat{\mathbf{i}},$ and $\quad \overrightarrow{\mathbf{F}}_{3}=-800.0 \hat{\mathbf{j}} .$ (a) Find the net force on the telephone pole in component form. (b) Find the magnitude and direction of this net force.

A car is 2.0 km west of a traffic light at $t=0$ and 5.0 km east of the light at $t=6.0$ min. Assume the origin of the coordinate system is the light and the positive $x$ direction is eastward. (a) What are the car's position vectors at these two times? (b) What is the car's displacement between 0 min and 6.0 min?