If a ball is thrown into the air with a velocity of 58 f'/sec , its height (in feet) after t seconds is given by H= 58t – 16t². Find the velocity when t=9 sec.

Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

Q: A 13-foot ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: A light is hung 6 meters above a straight horizontal path.  If a man 2 meters tall is walking toward…

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Q: The top of a 10 ft ladder slides down a vertical wall at a rate of 1 ft/sec. How fast is the…

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

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Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: A 46 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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Q: What is the velocity (in ft/s) of a sandbag 0.25 s after it is released from a hot-air balloon that…

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Q: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04…

A: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of  0.04…

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

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Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: A 10 ft ladder leans against a wall. If the top of the ladder slides down the wall at a rate of 2…

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Q: A 5​-foot-tall woman walks at 4ft/s toward a street light that is 25ft above the ground. What is the…

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Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: If the radius of a circle increases by 3%, use differentials to approximate the increase in the area…

A: radius of a circle increases by 3%,

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

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Q: use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in…

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Q: An object is thrown upward from a height of 960ft960⁢ft with an initial velocity of…

A: The equation for the object's height 'h' at time t seconds is given by h(t)=-16t2+V0t+h0 Where V0 is…

Q: Use differentials to approximate the change in the area of a square if the length of its side…

A: Area of a square with a side length of x cm is, Ax=x2 Here, x=5 cm & ∆x=5.32-5=0.32 cm Now…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: A man that is 5 feet tall is walking in a straight line at a rate of 3 ft / s towards a lamp post…

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Q: A car is moving at 60 mi/hr (88 ft/sec) on a straight road when the driver steps on the brake pedal…

A: Given  Initial speed of the car =60 mi/hr (88 ft/sec) deceleration =12 ft/sec^2  time =3 sec

Q: A 6-ft tall man is walking towards a 15-ft tall street lamp at the rate of 9 ft/sec. How fast is his…

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Q: The radius of a circle is increasing at a constant rate of 0.2 meter per second. What is the rate of…

A: Given Where r is radius. and

Q: A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground…

A: x2+y2=172=289Differentiate with respect to 't'2xdxdy+2ydydt=0   xdxdt+ydydt=0

Q: A 6ft tall man is walking away from a 15ft tall street lamp at the rate of 5 ft/sec. How fast is his…

A: topic - triangles and rate

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

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Q: A light is hung 7m above straight horizontal path. If a man 2meters tall is walking toward a light…

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Q: How fast is the tip of her shadow moving?

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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

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Q: How many kilometers can a train moving at an average velocity of 25 m/s southwest be displaced in 2…

A: Given, average velocity of train = 25 m/s 2 hours = 2x60x60 = 7200 seconds

Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

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Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

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Q: A rock is thrown from the top of a 120ft cliff with an initial velocity of 20 ft./sec  how 2…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: form a triangle with given information : let BC = x   dxdt=0.5 AB = y  dydt=-0.375  AC = z  dzdt=0…

Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: A 27 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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Q: A person is walking at a rate of 5 ft per hour toward the foot of a flag pole 60 feet high. At what…

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Q: A 25 -foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

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Q: A 15-foot ladder is slider down a wall at a rate of 3 ft/sec.  At what rate is the bottom of the…

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Q: a machinist is required to manufacture a square metal plate with the side length of 5cm.  if the…

A: The length of the metal plate is x=5cm. The machinist is allowed an error of 0.3 cm. The area of the…

Q: The base of a 20-foot ladder is sliding toward a wall at a rate of 1.5 feet per second. How fast is…

A: We solve the above problem.

Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…