. A trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough is 10 m long. Water is being pumped into the trough at a rate of 5 m/min. At what rate does the height of the water change when the water is 1 m deep? I. 10

Q: Coffee is draining out of a conical filter at a rate of 2.25 in3>min. If the cone is 5 in tall…

A: Given: The change in volume for the filter is -2.25 in3/min The change in volume for the coffee pot…

Q: B. How rapidly will the water level inside a vertical cylindrical tank if we pump the water out at…

A:

Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

A:

Q: Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section…

A: The situation is as shown below: Consider a small differential element of water at a height of h…

Q: 01/Water poured into a conical tank through a faucet, this tank has a base radius of 5 ft and 10 ft…

A:

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m/s a. At what rate is the…

A: Let, l be the length of a legth of a leg of an isosceles right triangle, h be the length of the…

Q: . A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking…

A: We make diagram of the situation .

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

A:

Q: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of a…

Q: A conical tank with an upper radius of 4 m and a height of 5 m drains into a cylindrical tank with a…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

A:

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 5 ft across at…

A: Similar triangles property is used as the height and width of the water level is proportional to the…

Q: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: A large conical tank of height H being filled with water by a hose at the top of the tank at a rate…

A: given: A large conical tank of height H=9 feet and radius R=3 feet is being filled with water by a…

Q: If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what…

A: (a)Given:

Q: 5. A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows…

A:

Q: The cone is 12 cm tall and has a radius of 4 cm. If the ice cream fills the cone evenly at a rate of…

A:

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm/min, find the rate (in…

A: Given  Decreasing rate of surface area = 3cm2/min To find: the rate of decreasing of diameter when…

Q: The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is…

A:

Q: A softball diamond is a square whose sides are 60 ft long. Suppose that a player running from first…

A: Suppose , y is the distance from the home and x is the distance from first base. Given that ,…

Q: A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the…

A: Given :                     The height of the ladder = 3.9m                     Let x…

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

A:

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A: 1) Let A be the surface area  r = radius of the sphere D = diameter of sphere = 10 cm…

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate at…

A: To find the rate at which the diameter decreases when the diameter is 12 cm and surface area…

Q: 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second…

A:

Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

Q: 14. If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at…

A: To find the rate

Q: A baseball diamond is a square with with side 90 feet (between the bases). A batter hits the ball…

A: Roughly draw the situation first Where x= Distance covered by batter at time t D= Distance of the…

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

A:

Q: A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoíd that is 40…

A:

Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

Q: The legs of an isosceles right triangle increase in length at a rate of 4 m/s. a. At what rate is…

A:

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

A:

Q: 5 If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at…

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.