The measurment of the radius of the end of a log is found to be 28 inches, with a possible error of 1/4 inch. Use differentials to approximate the possible propagated error in the computing the area of teh end of the log. Then determine the relative error (as a %). Round to 2 decimal places.

Q: A ship started at a certain port and travelled N 48° E at the rate of 32 kph. After 1.5 hours, a…

A:

Q: The measurement of the side of the cube is 6 cm long. If this length has an error of 1/12 cm. Find…

A: Topic = Derivative

Q: A ladder is 27 feet long and is leaning against the side of a house. The base is moved away at 3 ft…

A: Solution is given below:

Q: The radius of a circular disk is given as 24 cm with a maxi -mum error in measurement of 0.2 cm.(a)…

A: Given data:

Q: .A ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

Q: Use differentials to estimate the value of V1.3. Compare the answer to the exact value of V1.3.

A:

Q: Find the rate of change of area of the square in m/s with respect to its side when the sides, s, is…

A:

Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom

A:

Q: Suppose that the acceleration of a vehicle at time t (in s) is given by a(t) = 2t+ 1 (mph/s).If the…

A:

Q: The measurements of an edge of a cube is found to be 15cm with a possible error of 0.01 cm. Use the…

A: We have a cube whose edge is 15 cm. The error in calculating the edge is 0.01 cm Now, this error can…

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

A:

Q: One side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°,…

A: Part (a):To estimate the error in the length of hypotenuse.

Q: A 17 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: Given, length of ladder = 17 ft But given that ladder is leaning against a wall ⇒  the ladder and…

Q: A vehicle purchased for $29800 depreciates at a constant rate of 5%. Determine the approximate value…

A: Given that , The value of vehicle, (P) = $29,800, Rate of depreciation, (r) = 5% = 0.05 Time (t) =…

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

Q: If the area of a healing wound changes at a rate given approximately by dA 4 for 1 <t<10 is in days…

A:

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

A:

Q: The altitude of a certain circular cone is the same as the radius of the base, and is measured as 5…

A:

Q: One side of a right triangle is known to be 45 cm long and the opposite angle is measured as 30°,…

A: a) Given that one side is 45 cm long and the opposite angle is measured as 30° with a possible error…

Q: The base of the Great Pyramid at Giza is a square that is 20 m on each side. (a) As illustrated in…

A: Answer is mentioned below

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

Q: (A1) A ladder 11 feet long rests againt a certical wall. if the bottom of the ladder slides away…

A:

Q: 1. If the motor on a motorboat is started at t = 0 and the boat consumes gasoline at the rate of 6 –…

A:

Q: A circle has a radius of 5 cm, if the radius is increased by 0.1 mm., what is the estimated increase…

A: Let's find.

Q: If a rock is dropped from a 200 ft building, its posi- tion (in feet above the ground) is given by…

A: Given-  st=-16t2+200, where t is the time in seconds since it was dropped. To Find- (a) The velocity…

Q: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: As an object cools, its rate of cooling slows. Explain how this follows from Newton’s Law of…

A:

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: A ladder is 36 feet long and is leaning against the side of a house. The base is moved away at 2 ft…

A:

Q: The base of the Great Pyramid at Giza is a square that is 230 m on each side. (a) As illustrated in…

A:

Q: The hour hand of a clock is 4 inches long and the minute hand is 6 inches long. At the moment the…

A: The hour hand of clock is 4 inches long and the minute hand is 6 inches long. At that time angle…

Q: If the sides of a square increase in length at a rate of 3 in/s, then the rate of change of the…

A: Let the side length of a square be x Now, Side length increases at a rate of 3in/s. That is, dxdt=3…

Q: A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: Topic:- calculus

Q: S. A searchlight is trained on an object falling under the in- fluence of gravity from a height of…

A:

Q: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week.…

A: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week…

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

A:

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: From the given problem the representative diagram is as shown below. Apply the Pythagorean theorem:…

Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: We need to use the formula for differential to estimate the change in volume when side of the cube…

Q: A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A: Let y be the distance from top of the ladder to the ground And X be the distance from foot of the…

Q: A man walks along a straight path at a speed of 4ft/s. A spotlight is located on the ground 20ft…

A:

Q: the

A:

Q: In the Newton's Law of Cooling, at small differences of temperatures between the body and the…

A: Recall:  The rate of loss of heat is directly proportional to the difference in the temperatures…

Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

A:

Q: One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°,…

A: Part (a) Side of the triangle is 15 cm, and opposite angle 30 degree with possible error of ± 1…

Q: Use differential to approximate the value e1.01.

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A: Given, a One side of right triangle = 20c.m longand the opposite angle=30°=xpossible error=±1°Let…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: We need to choose correct option.

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.