An object moves along a line where its velocity function is as described by the graph. What is the total distance that it has traveled between [1, 6]? 8 O 4 O 2

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A: Write the formula for the volume of the sphere and take the derivative.

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A: This question is related to straight line. we will solve it using the condition of shortest distance…

Q: time (sec) velocity (ft/sec) 11 1 19 2 20 3 12 4 3 1 8 feet

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Q: Suppose that a particle moves along a straight line with velocity defined by v(t) =2t2 -t - 3, where…

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A: We will find the rate of change of volume of sphere at a given radius.

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A:

Q: 2. All edges x of a cube are expanding at a rate of 8 centimeters surface area changing when each…

A: To solve the following problem, we use the given formula if S is equal to surface area then S = 6x2…

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Q: A car is driving on a circular track with a radius of 1 (km). At the southernmost point of the…

A: Here the radius of track is R = 1 km. The distance between car and radar meter at a given time is  S…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: We have to find the rate of change of surface area.

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the volume…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.  Let the edge of a cube = x…

Q: Define a function, f, that determines the volume o: sphere in terms of the number of seconds, t,…

A: Given that r=4cm/sec

Q: Consider a closed rectangular box with dimensions ft by y ft by z ft. If is increasing at the rate…

A: Given:    dxdt=4 ft/min    dydt=-6 ft/min     dzdt=3 ft/min To find dDdt when x=18 ft, y=10 ft,z=4…

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

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Q: The volume of a cube is increasing at a rate of 10 cm/min. How fast is the surface area increasing…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y

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Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A: We will use the left endpoint approximation.

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Rate of increase of radius of a spherical ball,drdt= 2 cm/min Radius of the ball = 9 cm

Q: A toy rocket is launched at an initial velocity of 50 ft/s at an angl of 75° with the horizontal.…

A: Here, given that the initial velocity 50 ft/s and the angle is 75°

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A: Introduction: A definite integration of a single variable can be approximated using three different…

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A: To find the correct option

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Q: An object is rolling with a driving force that suddenly ceases. The object then rolls 10 meters in…

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Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: The radius of a circle is increasing at a constant rate of 0.3 meter per second. What is the rate of…

A:

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A:

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Given :radius of spherical ball is increasing at a rate of 2cm/minso, drdt=2cm/min

Q: A body above the surface of the earth is pulled toward the center of the earth. If the radius of the…

A:

Q: 1. Suppose oil spills from a ruptured tanker and spreads in a circu pattern. If the radius of the…

A: Given that

Q: 1)A man 7 ft tall walks at a speed of 5 ft/sec toward a street lamp which is 15 ft above the ground.…

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Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

A:

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: The radius of a sphere is decreasing at a rate of 14cm/s.The radius is 2cm.

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

A: Explanation of the answer is as follows

Q: According to Boyle's law, which graph shows the relationship between the pressure (æ) and volume (y)…

A: option c is correct.

Q: A ship leaves point A and sails north at the constant rate of 12 knots. Two hours later, a second…

A: lets assume speed of ship in north direction = dydt = 12 knots speed of sheep in east direction =…

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: AB=BC=5cm Let l=asinθ where a=6l=6sinθAlso given…

Q: Assume a circle is expanding with time where r=t+ 3. What is the formula for the rate of change of…

A: Given  r=t+3

Q: Suppose that the radius of a circular water pool is expanding at a rate of 2 meters per hour, when…

A: Given:

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A:

Q: A car starts moving at timet=0 and goes faster and faster. Its velocity is shown in the following…

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Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given : 1) Oil spills from a ruptured tanker and spreads in a circular pattern.             2)…

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

A:

Q: t that is only of the total distance she

A: Here, x is total distance.

Q: 1. An airliner passes over an airport at noon traveling 530 mi/hr due west. At 1:00 P.M., another…

A: We have to find the rate of change of distance between two planes at 2:30 PM. We will use…