A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the point B diametrically opposite on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 5 kilometer per hour and row a boat at 3 kilometer per hour. 1- Find the total distance she must travel if she rows from A to C and walks from C to B.

Q: A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height…

A: Given radius = 5.2cm Height = 13cm Total surface area of cone shaped container and cylindrical…

Q: B4. Find the dimensions of the right circular cylinder of maximum lateral surface area which can be…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: A company wishes to manufacture a boxwith a volume of 36 ft3 that is open on top and is twice as…

A: Let the dimensions of the box be, length=lwidth=wheight=h It is given that length is twice its…

Q: Two containers designed to hold water are side by side, both in th shape of a cylinder. Container A…

A: The volume of a cylinder is equal to the product of the area of the circular base and the height of…

Q: 5. Design a 4m³ open-top box shaped like a circular cylinder as shown in Figure. What dimensions…

A:

Q: A piece of cardboard measuring 11 inches by 9 inches is formed into an open-top box by cutting…

A: A piece of cardboard measuring 11 inches by 9 inches.

Q: One train leaving a train station is travelling east at a rate of 50 km/h. Another train starting…

A:

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: 3) Determine the speed of change of volume of a rectangular parallelepiped, knowing that the edges…

A: Let the length of base edges and vertical edge are x, y and z respectively such that dxdt = +2…

Q: An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to…

A:

Q: find the maximum valume of a cone given that the sum of the radius and height of the cone is 15 cm.

A:

Q: a. A water tank has the shape of an upright cylinder with radius r = 1 meter and height 10 meters.…

A: Work needed = 37500 N m

Q: 1. Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: A right circular closed cylinder with radius r cm and height h cm is placed on a square block with…

A:

Q: A force is applied to a particle, which moves in a straight line, in such a way that after each…

A: A geometric series is convergent if common ratio is less than 1. Sum of infinite geometric series is…

Q: 1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of its…

A: A roof gutter is to be made from a long strip of sheet metal L units wide, by bending up equal…

Q: (c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will…

A:

Q: In constructing an open rectangular box from 75 ft² of material, what dimensions will result in a…

A:

Q: A reservoir is 90m long and its cross section is an isosceles trapezoid having equal sides of 11m,…

A: Given that a reservoir is 90 m long whose cross section is an isosceles trapezoid. The dimensions…

Q: A spherical party balloon is being inflated with helium pumped in at a rate of 6 cubic feet per…

A: to find the rate of change of radius

Q: 2. A right triangle with hypotenuse of 5V3 cm. is revolved about one of its legs to generate a cone.…

A: Given,          Let r, h, and V be the radius, height, and volume, respectively

Q: By using the disk method, find the volume of a circular cone of radius r and height h. Initially,…

A: Given: ri=12m;hi=6m y=mx+b b=0m=r-0h=rhy=rhxf(x)=y Disk method Formula for volume:…

Q: A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the…

A:

Q: Suppose that for the tank in Exercise 23 the pump breaks down after 4.7 X 10° J of work has been…

A:

Q: 3. A rectangle with a fixed perimeter of 64 units is rotated about one of its sides, thus sweeping…

A:

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

Q: A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: An open-top box is to be made by cutting congruent squares of side length x from the cor- ners of a…

A: The box is in the shape of cuboid whose sides are x , 20-2x and 25-2x

Q: A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of 10m,…

A: Given that the reservoir is 80m long whose cross-section is an isosceles trapezoid with sides of…

Q: A spherical scoop of ice cream sits on top of a waffle cone. The diameter of the ice cream sphere is…

A: Cone Shaped ice cream scoop: diameter d1 =10 cm (sphere) diameter d2 = 10cm (cone) and height h = 20…

Q: A company applies a clear glaze finish on the outside of the ceramic bowls it produces. The bowl…

A:

Q: An open box is to be made from a square piece of cardboard whose sides are 10 inches long, by…

A:

Q: 14. A system of storm sewers in a coastal city is designed to capture water runoff during heavy…

A:

Q: The side of a cube increases at the rate of 1 m/sec. The rate at which the volume of the cube…

A:

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 25 feet high. If…

A:

Q: A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions…

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

Q: A piece of wire 13 m long is cut into two pieces. One piece is bent into a square and the other is…

A: We will use derivative test to solve this.

Q: A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the…

A:

Q: (23) A right triangle with a hypotenuse of 6 inches is rotated about one of its legs to generate a…

A:

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 30 feet high. If…

A: Given,            A conical water tank with vertex down has a radius of 13 feet at the top and is 30…

Q: A baseball diamond has equal sides of 90ft in length and each pair of adjacent sides are…

A:

Q: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls…

A: SOLUTION-

Q: 3. The commercial jets at 40 000 ft are flying at 520 mph along straight-line courses that cross at…

A: Here both intersect at right angle  So if we take the interesection is O  So OA = 5       OB = 12…

Q: Find the total distance traveled by a particle that has velocity V(t) = 2t -4 over [0,5]

A:

Q: A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/ sec.…

A: Please see the answer in Step 2.

Q: Find the total length of the cable. L = 2y + 3√² +6² + constant Differentiate both sides.

A: the solution next step..

Q: 3) Water is being poured at the rate of 2TT m3/min. into an inverted conical tank that is 12-meter…

A:

Q: 2. Soybeans, pouring down from a chute at a constant rate of 2 m3/min, form a conical hil. Assuming…

A:

Q: - Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = 2 (all…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.