O H.W 1: Two cars leave from the same position at the same time. One travels due North at 30 km/h, while the other travels due East at 40 km/h. At what rate is the distance between the cars changing after 1 hour?

Q: A woltage V across a resistance R generates a current I = V/R. If a constant voltage of 17 volts is…

A: Given, Voltage, V=17 volts Resistance, R=5 ohms The rate of change of resistance with respect to…

Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the…

A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r…

Q: Of a rectangle are chonging at the tates of 1m/s and 2m/s. Sides its When its sides are 30 m and Ao…

A:

Q: If a cup of coffee has temperature 94°C in a room where the ambient air temperature is 19°C, then,…

A: To find: The average temperature of the drink C during the first 26 minutes.  Given: The temperature…

Q: SA Spherical ballon is ingiated With goas at the rate af 20 Cm3min. How fast is the fadtus af the…

A:

Q: b. A thermistor is being used to measure temperature. For a given resistance Rthe temperature is…

A: The temperature, T for a resistance R is given by, T=1T0+1βlnRR0−1

Q: 10. A boy is flying a kite at a constant height of 60 ft. If the kite is moving horizontally at the…

A:

Q: 1, ship A is 70 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at…

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Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A: We have to find out distance between the cars

Q: A light moving at 0.8 m/s approaches a man standing 4 m from a wall (Figure). The light is 1 m above…

A: Given : A light moving at 0.8 m/s approaches a man standing 4 m from a wall .also light is 1 m above…

Q: 4. A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A: To find the solutions of given statements

Q: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

A: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

Q: A man 2 meters tall walks at a rate of 1.2 meters per second away from a light that is 5 meters…

A: dy/dt = rate of moving of tip of shadow dp/dt = rate of change in length of shadow

Q: When a switch is closed in a circuit containing a battery E,a ersistance R and an inductance L,the…

A:

Q: West Z dt x North JOAN dx dt ANDRES = 25km/hr dy dt y 18km/hr

A: Given: Speed of Andres  = 18 km/hr Speed of Joan  = 25 km/hr

Q: O E. (4, ) Which of the following pair (r, ) is the radius and the rate of change of the radius at…

A: Given volume =4/3 πr^3  and Surface area=4πr^2 Then we have to find radius and rate of change at…

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: A detailed solution is given below.

Q: 3. If the temperature in a room is given by T(x, y, z) = xyz, at what rate will the temperature felt…

A:

Q: The lengths a, b, and c of the edges of a rectangular box are changing with time. At the instant in…

A: Volume= V=length*width*height  V=abc Find dV/dt using product rule and then plug the given values…

Q: A truck is 300 kilometers due East of a car and it's traveling west at a constant speed of 30km/he.…

A:

Q: betw A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off…

A: Given that,

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A: Given: Let A is the area of a circle with radius r Then we have A = πr2

Q: One side of a triangle is increasing at a rate of 6 cm/s and a second side is decreasing at a rate…

A:

Q: The radius of the first circle is modeled by w(t)=12-12e^-0.5t at what time t is the radius of the…

A: The given equation of circle is w(t)=12-12e-0.5tUpon differentiating: (As it is given rate, we…

Q: O H.W 2: Two cars, one going due East at a rate of 90 km/h and the other going due South at a rate…

A: Find the rate of approaching each other

Q: Question 2 2.1 A spotight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the…

A: The problems involves the differentiation to find the respective values. Differentiation is defined…

Q: A 10​-footladder is leaning against a vertical wall​ (see figure) when Jack begins pulling the foot…

A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find da/dt in…

A: Given that  Area of the circle =A  Radius of the circle =r  To find the rate of change of area

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 feet per second. A…

A: Let's draw the diagram first Given: dhdt = 15 ft/sec We have to find the value of dydt when h=40

Q: A man stands still on a moving walkway that is going at a speed of 0.2 m/s to the west. What is the…

A: The solution is given below.

Q: Car X is travelling west at 20 kph and Car Y is travelling south at 30 kph. Both are headed for a…

A:

Q: hen the distance of the plane from at the rate of 8,000 km/hr. At w

A: Given: Perpendicular distance between station and plane is 5,000 km. To find rate of distance of…

Q: s. How fast (in knots) is the distance between the ships changing at 4 PM? (Note

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Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A: We have to find distance between two car

Q: In a AABC, the sides AB and AC are 12 and 15 units long, respectively. the Z. changes at a rate of…

A: Consider ∆ABCBy law of cosines(BC)2=(AB)2+(AC)2-2×AB×AC×cos(A)Let length of side BC be…

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: Note : According to our guideline I can solve only 1st , please reroute the remaining question.

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the…

Q: An object with an initial velocity of 40 m/s undergoes an acceleration of a(t) = 12t – 10 m/s“, t…

A:

Q: A bl ems orol a staight Ime across level ground with an initial velocity of 20 feet per second…

A: Given  initial velocity = 20 feet / sec final velocity = 0 feet / sec Deacceleration = 6 feet / sec2…

Q: A man 1.8 m. tall is walking at the rate of 1.2 m/s away from a lamp post 6.7 m high. At what rate…

A:

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

A:

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: To solve the following problem.

Q: c) Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and…

A: (In this figure, P is the point mentioned in the question, which is at some distance from ship A and…

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the…

A: Solution is in step 2 Option A is correct answer.

Q: 6. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 40 km/hr and ship B is…

A: Given query is to find the rate of change of distance.

Q: When the side a of a cube increases with time t, the change in volume dt - O a. da За- dt O b. da…

A:

Q: the lengths a, b, and c of the edges of a rectangular box are changing with time. at the instant in…

A: Given:  a = 1m, b = 2 m, c = 3 m, da/dt = db/dt = 1 m/sec, and dc/dt = -3 m/sec

Q: O H.W 1: Two cars leave from the same position at the same time. One travels due North at 30 mph,…

A: To find the rate at which distance between the two cars changing after 1 hour

Q: Assume that a rocket is lifting off 10 miles away, with a position h(t) = 5t². What is the rate of…

A: Topic = Derivative

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.