Caroline

Consider the function f(x)=9−x^2.

Let T(x) equal the area of the shaded isosceles trapezoid that has two vertices on the x-axis and two vertices on the graph of f, as shown.

What is the maximum value of T(x) ?

An open-topped glass aquarium with a square base is designed to hold 62.5 cubic feet of water. What is the minimum possible exterior surface area of the aquarium?

Given △ABC with b=10 and c=12 , what is the measure of ∠A (in degrees) that will maximize the area of the triangle? I would love if anyone could help me solve this!

A sailboat 3 miles west of Point Stuart sails toward Point Stuart at 4 miles per hour. At the same moment, a motorboat 4 miles north of Point Stuart travels due south toward Point Stuart at 12 miles per hour.

At that moment in time, what is the rate of change in the distance between the sailboat and the motorboat in miles per hour?

I would please like to know how to solve this problem, thank you

Four resistors are connected to a battery with a terminal voltage of 12 V, as shown in the figure below. (Assume R1 = 39.0 Ω and R2 = 79.0 Ω.)

this is the figure http://www.webassign.net/sercp9/18-p-022-alt.gif

(a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit.

(b) Find the current delivered by the battery to this equivalent resistance.

(c) Determine the power delivered by the battery.

(d) Determine the power delivered to the 50.0-Ω resistor.

What minimum number of 150 W lightbulbs must be connected in parallel to a single 150 V household circuit to trip a 40.0 A circuit breaker?

A heating element in a stove is designed to dissipate 3,110 W when connected to 240 V.

(a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120 V.

(b) Calculate the power it dissipates at that voltage.

An electron is fired at a speed v0 = 4.50 106 m/s and at an angle −45° between two parallel conducting plates that are D = 3.5 mm apart, as in the figure below. The voltage difference between the plates is ΔV = 95 V.

(a) Determine how close, d, the electron will get to the bottom plate.

(b) Determine where the electron will strike the top plate. (State how far the electron travels to the right before striking the top plate.)

The potential difference between the accelerating plates of a TV set is about 25 kV. If the distance between the plates is 1.8 cm, find the magnitude of the uniform electric field in the region between the plates.

Two small metallic spheres, each of mass 0.35 g, are suspended as pendulums by light strings from a common point as shown in the figure below. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of θ = 3.0° with the vertical. If each string has length L = 36.0 cm, what is the magnitude of the charge on each sphere?

This is the figure: http://www.webassign.net/sercp9/15-p-015.gif

This is the figure: http://www.webassign.net/sercp9/15-p-010.gif

and for each force, (6+, 1.5+, and 2-) we're supposed to calculate the magnitudes of the forces and i know youre supposed to use coulomb's law but im not really sure how to go about it. any help would be much appreciated

The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons).

(a) What is the force between the two alpha particles when they are 3.20 10-15 m apart?

(b) What is the initial magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is 4.0026 u.

An estimated force vs. time curve for a baseball struck by a bat is shown in the figure below.\

figure: http://www.webassign.net/sercp9/6-p-008.gif

(a) From the curve, determine the impulse delivered to the ball.

(b) From the curve, determine the average force exerted on the ball.

Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 14.9 m/s toward the east, and the other is traveling north with velocity v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 51.6° north of east.

What was the initial speed of the northward-moving vehicle?

An astronaut in her space suit has a total mass of m1 = 74.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her oxygen tank of mass m2 = 12.0 kg away from her spacecraft with a speed v = 9.00 m/s to propel herself back toward it .

(a) Determine the maximum distance she can be from the craft and still return within 1.80 min?

Why does this work in terms of Newton's laws of motion?

A 0.302-kg volleyball approaches a player horizontally with a speed of 16.7 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s.

(a) What impulse is delivered to the ball by the player?

(b) If the player's fist is in contact with the ball for 0.0600 s, find the magnitude of the average force exerted on the player's fist.

When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the mechanical energy loss due to frictional forces exerted on the car by the air and the road. If the power developed by the engine is 189 hp, estimate the total friction force acting on the car when it is moving at a speed of 27 m/s. One horsepower equals 746 W.

An older-model car accelerates from 0 to speed v in 11 s. A newer, more powerful sports car of the same mass accelerates from 0 to 2v in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars. (Take Pnew and Pold as the powers of the new car and old car, respectively.)

A 2.90-kN piano is lifted by three workers at a constant speed to an apartment 22.0 m above the street using a pulley system fastened to the roof of the building. Each worker is able to deliver 183 W of power, and the pulley system is 75.0% efficient (so that 25.0% of the mechanical energy is lost due to friction in the pulley). Neglecting the mass of the pulley, find the time required to lift the piano from the street to the apartment.

A 7.80-g bullet moving at 660 m/s penetrates a tree trunk to a depth of 6.30 cm.

(a) Use work and energy considerations to find the average frictional force that stops the bullet.

(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.