The length, width, and height of a box are measured as 5 ft, 4 ft, and...

The length, width, and height of a box are measured as 5 ft, 4 ft, and 8 ft, respectively, with an error in measurement of at most 0.3 ft in each. Use differentials to estimate the maximum error (in feet) in the calculated volume of the box.

Expert Solution

milcah answered 2 years ago

The length ℓ, width w, and height h of a box change with time. At a...

The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 4 m and w = h = 1 m, and ℓ and w are increasing at a rate of 8 m/s while h is decreasing at a rate of 2 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume. (b) The surface area. (c) The length of a diagonal....

The length l, width w, and height h of a box change with time. At a...

The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 2 m and w = h = 3 m, and l and w are increasing at a rate of 7 m/s while h is decreasing at a rate of 5 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume. m3/s (b) The surface area. m2/s (c) The length of...

The length, width, and height of a room are measured to be 4.1 meters, 3.2 meters,...

The length, width, and height of a room are measured to be 4.1 meters, 3.2 meters, and 2.4 meters, respectively. Each measurement is subject to a 1% error. Find the volume of the room and it’s uncertainty in cubic meters. Assume that the percentage errors add. Express the answer with the appropriate number of significant digits.

Design a rectangular milk carton box of width w, length ll, and height h which holds...

Design a rectangular milk carton box of width w, length ll, and height h which holds 540 cm^3 of milk. The sides of the box cost 1 cent/cm^2 and the top and bottom cost 3 cent/cm^2. Find the dimensions of the box that minimize the total cost of materials used.

if you a square that is 3' 5" in width, length and height. How many five...

if you a square that is 3' 5" in width, length and height. How many five point stars (2" in size) filled with air will fit into the square? Please show all work.

A rectangular box has a length of 1 in, width of 2 in, and height of 3 in. Find the cosine of the angle between the diagonal of the box and the diagonal of its base.

A rectangular box has a length of 1 in, width of 2 in, and height of 3 in. Find the cosine of the angle between the diagonal of the box and the diagonal of its base. what is the volume of the parallelepiped by <-5; 2; 1>, <1; -1; -3> and<-1; -1; -4>? (a) 9 (b) 10 (c) 11 (d) 12 (e) None of the above

The breaker wave height and alongshore current are measured as 5.5 ft and 2.7 ft/s, respectively....

The breaker wave height and alongshore current are measured as 5.5 ft and 2.7 ft/s, respectively. For a beach slope of 1 :20 with straight and parallel depth contours, determine the angle of wave approach at the breaker zone.

An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length.

An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length. The length of the box is labeled x in the picture. You have 100 in2 of cardboard to use. Find the length x and the height y that maximize the volume of the box. (a.) Find a formula for the volume V in terms of x and y. (b) Use the constraint given by the amount of cardboard available...

A wood burning stove is box shaped with a height of 30.7”, width 26.25” and depth...

A wood burning stove is box shaped with a height of 30.7”, width 26.25” and depth 25.5”. The front surface is glass (Ԑ= 0.9) and the other surfaces are cast iron (Ԑ= 0.7). The fire keeps the stove surface at a constant 202 °C. a.Calculate the rate at which the stove’s one glass surface (30.7” by 26.25”) radiates heat into the surrounding space. b.Calculate the rate at which the cast iron sides radiate heat into the surrounding space. Add this...

Write a PHP program using HTML form. It will take Length, Width and Height of a...

Write a PHP program using HTML form. It will take Length, Width and Height of a box as input. When a button is pressed, it will calculate the Volume. If Volume is less than 25 then display the message “Small box”. If Volume is from 25 to 50, it will display the message “Medium box”. When the Volume is greater than 50, then display the message “Large box”.

Question