The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm

Q: If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in…

A:

Q: Solve the following time rates problems: A softball diamond has the shape of a square wide sides 60…

A: Consider the given information. Let's draw a figure according to the given figure.

Q: SOLVE FOR THE FOLLOWING RELATED RATES PROBLEMS. SHOW YOUR SOLUTIONS 1. A cylindrical tank with…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled away…

A: Given: A ladder 10 meters long leans against a wall. If the bottom of the ladder is being pulled…

Q: 3. Answer the following problems. Show your complete solutions. 1. If a stone is thrown vertically…

A: 1.h=10t - 0.83 t2Velocity is the derivative of the height.V=dhdt=10-1.66 ta. Velocity after 3…

Q: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: (b) Use the given formulas for the volume and area (displayed above the diagram) to rewrite the…

A:

Q: The length of a rectangle is given by 4t - 3 and its height is 2t, where t is time in seconds and…

A: Given the rectangle whose length and height are given L=4t−3H=2t3

Q: A 25-foot ladder is leaning against a house, as shown in the figure below. 25 ft sec +X→ If the base…

A: a). Put x = 15, we get b). Put x = 24, we get

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate (in…

A:

Q: For the following problems, consider a pool shaped like the bottom half of a sphere, that is being…

A: The radius of pool is r=10 ft If V is the volume of pool, dVdt=25 ft3/min The depth of the water is…

Q: A car traveling at the rate of 20m/s is approaching an intersection. When the car is 100 meters from…

A: Given: dadt=20 m/s and   dbdt=100m/s at   t=2 sec first we convert m into ft so, 20m/s×3.281=65.62…

Q: (1) An ultrasound imaging device measures a time of 5.2 × 10$ seconds for sound waves to return to…

A: Given, Speed=1540 m/s time=5.2* 10-5 Distance=?

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A: dv/dt = 45 cm3/second side is 2 cm height is 5 cm side/height = 2/5 side (s) = 2h/5 volume of…

Q: Analyse and solve the following problems and explain the reasons for each element of your solutions.…

A: Given:  --------------------------------------------------------------------------------- Relation…

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: Topic:- application of derivatives

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: we have to find the rate change in diameter

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in…

A:

Q: Solve the following problems. 1. A ladder 7.5 meters long is leaning against the wall of a house.…

A: In the question we have to find the rate at which ladder is sliding down.

Q: Solve the following. 1. Water flows into a vertical cylindrical tank at 12 ft3/min, the surface…

A: As per bartleby guidelines we only give first three questions answers.

Q: A triangle with constant base b and height h is changing with time where h(t) = 2t – 3. What is the…

A:

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 half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: We use half life equation here.

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: 1. A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m3/min. How fast is…

A: 1. Given that the radius of the cylindrical tank is 5 m. Let the height of the tank be h. Then the…

Q: Solve the following related rates problems. 4. The radius of a circle is increasing at the rate of…

A: We have to find the rate of change of area of circle where radius of a circle is increasing at the…

Q: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is…

A: Given equation is PV=8.31T Also given that, dTdt=0.21dPdt=0.05P=17T=304 So,…

Q: SOLVE FOR THE FOLLOWING RELATED RATES PROBLEMS. SHOW YOUR SOLUTIONS 1. (a) If A is the area of the…

A: a) dAdt in terms of drdtwhere A is the area of the circle & r is the radius of the circle. b)…

Q: Analyse and solve the following problem and explain the reasons for each element of your solutions.…

A: Given: A tank partially filled with gasoline is seeping through the sides, at a rate proportional to…

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A: Topic-basic maths

Q: SOLVE FOR THE FOLLOWING RELATED RATES PROBLEMS. SHOW YOUR SOLUTIONS  1. Each side of a square is…

A:

Q: 1. The side of a cube increases at a rate of 2.5m/s. Find the rate at which the surface area…

A: Let x be the legth of a side and S be the surface area of the cube We know that   S=6x2 Given that…

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A:

Q: Water is being drained from a conical reservoir (vertex down) at the rate of 3 cubic feet per…

A: Given the volume flow rate of water is: 3 cubic feet per second. Consider the height of the cone is…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Initial mass of the sample=moHalf side of pd-100 is y days . So , h=4relative decay rate…

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: (t) s(t) xt)

A:

Q: Solve the following related rates problems. 3. A tank of water in the shape of a cone is being…

A: The cone is a solid which has a circular base and comes to a point at the top similar in shape to an…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Let's find rate of the increasing the  volume.

Q: The height of a triangle is increasing at a rate of 2 [cm/min] and its area at a rate of 2 [cm²/…

A: It is given that height of triangle is increasing with a rate 2 cm/min and area with a rate 2…

Q: On a rainy day, a girl broken up with her boyfriend after being together for eight long years. They…

A: Given: The boy is due north crying and running at a rate of 5 ft/sec and the girl is walking due…

Q: Solve the following time rates problems. A girl starts at a point A and runs east at the rate of 10…

A: Given that, A girl starts at a point A and runs east at the rate of 10 ft/sec. One minute later,…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: To find the initial mass of the sample.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.