Tilda

A curve is defined by the parametric equations x = 3 + cos t and y = -2 + sin t.

At what two points on the curve are the tangent lines horizontal?

An airplane, flying in the direction 35 degrees west of north at 425 mph in still air, encounters a 55 mph wind blowing from the west (the wind direction is due east). 

The airplane maintains its air speed and compass heading, but, because of the wind, acquires a new ground speed and direction. What are they?

The derivative of a function is 𝑔′(𝑥)=19−6𝑥2 and the graph of g(x) passes through the point P(3, 7). Find g(x).

Two boats are moving toward a buoy along paths that makes a 90 degree angle. The first boat is 165 ft from the buoy and is traveling at a rate of 25 ft/sec. The second boat is 110 feet from the buoy and is traveling at a rate of 35 ft/sec. Find the rate of change of the distance between the boats after one second.

The base of a cone-shaped tank is a circle of radius 5 feet, and the vertex of the cone is 12 feet above the base. The tank is filled to a depth of 7 feet, and water is flowing into the tank at a rate of 3 cubic feet per minute. Find the rate of change of the depth of the water in the tank.

(V = 1/3Bh) where B is the area of the base

Suppose the revenue, in dollars, for producing x chairs is given by 𝑟(𝑥) = 90𝑥 and the cost to produce the chairs is given by 𝑐(𝑥) = 0.002𝑥^3 − 0.1𝑥^2 + 20𝑥 + 6000.

Find the production level that will maximize profit.

Let 𝑓(𝑥)=𝑒3𝑥−5

a . Find an expression for dy.

b. Estimate dy for x = 2 and dx = 0.04

Let 𝑓(𝑥)= 𝑎𝑥4+100𝑥2 . What is the value of a if

a. f(x) has a local minimum at x = 5?

b. f(x) has a point of inflection at x = 2?

Thank you!

The derivative of a function is 𝑔′(𝑥)=19−6𝑥2 and the graph of g(x) passes through the point P(3, 7). Find g(x).

The derivative of a function is f’(x) = x(x + 2)(x – 4).

Find the value of x at each point where f(x) has a:

a. local maximum

b. local minimum

c. point of inflection

I can find them graphically, but am having problems finding them analytically. Thank you!

I'm interested to do some electrosis on copper using copper acetate as an electrolyte, with copper anodes and cathodes. So far the videos I've seen are all trying to grow crystals and they have been quite successful getting crystals. But the diagrams I've looked at all suggest that they will grow in a block form. The articles I've seen dont say how the resulting copper will look like only that it purifies the copper.

So I'm curious, does copper grow through electrosis grow in the shape of crystals or nice blocks?

Find the parametrization for the curve.

Given the line through the points (5, -2) and (8, 2)

Thanks

Light from a distant galaxy has an apparent wavelength of 452 nanometers.

If the galaxy is known to be moving away at a speed of 5.00x107 meters per second, what is the actual wavelength of the light?

Light from a distant galaxy has an pparent wavelength of 452 nanometers. If the galaxy is known to be moving away at a speed of 5.00x107 meters per second, hat is the actual wavelength of the light?

A 0.250 kilogram mass is attached to the end of a 1.20 meter string and swung in a horizontal circle. The mass makes one revolution in 1.15 seconds. What is the tension in the string? Express your answers in newtons. a) 10.3 newtons b) 8.96 newtons c) 143 newtons d) 0.908 newtons

1: A bolt needs to be tightened. Jill uses a wrench that is 58 centimeters long and applies a force of 85 newtons at an angle of 75 degrees from the wrench handle. What torque does the wrench exert on the bolt? Express your answer in newton-meters.

a) 4800 newton-meters

b) 49 newton-meters

c) 48 newton-meters

d) 4900 newton-meters

2: A force with a magnitude of 552 newtons is used to stop an object with a mass of 56.0 kilograms moving at a velocity of 135 meters per second. How long will it take to bring the object to a full stop? Express your answer in seconds.

a) 13.7 seconds

b) 134 seconds

c) 23.4 seconds

d) 0.073 second

A toy rocket is shot straight up into the air with an initial velocity of 42 meters per second. How high does the rocket rise above the ground? The acceleration due to gravity is -9.8 meters per second squared. Express your answer in meters.

a) 4.3 meters

b) 410 meters

c) 90. meters

d) 2.1 meters

A skater and his skateboard have a combined mass of 50.0-kilograms. From a stationary start at the top, the skater descends a steep ramp. If the top of the ramp is 8.50-meters above the bottom, how fast is the skater traveling when he reaches the bottom of the ramp? Express your answer in meters per second. You may assume that friction effects are negligible.