aph of the velocity of a car accelerating from rest to a speed of 105 km/h over a period of 30 seconds is shown. v (km/h) 105 70 35 t (seconds) 10 20 30 s graph and a midpoint Riemann sum with six equal subintervals to estimate the distance traveled (in km) by the car during this time period. (Round your answer to two decimal places.) km

Q: Tea leaves are placed in a cup of hot water. Caffeine is infused into the water at a rate of…

A: Amount of caffeine in the  cup of water after tea.  leaves are removed:-  ∴Per minute,caffeine…

Q: *3. The following function is positive and negative on the given interval. f(x) = 9- x2; [0,4] a.…

A:

Q: function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b]…

A: In the given question, the concept of Riemann Sum is applied. Riemann Sum   To estimate ∫abfxdx,…

Q: The graph of the velocity of a braking car is shown. v (ft/s) 45 30 15 t (seconds) 4 Use this graph…

A: We need to find a midpoint Riemann sum with six equal intervals to estimate the distance traveled by…

Q: The following function is positive and negative on the given interval. f(x) = 2 – 2x2; [0,4] a.…

A: Given The given function is fx=2-2x2 and the interval is 0,4.

Q: a. Estimate R'(1.5). Indicate units of measure. b. Justify why there must be at least one time t,…

A: Solution for part a: t Rt 0 0 1 4 2 8 3 16 R'1.5≅R2-R12-1=8-41=4 Therefore, R'1.5≅4

Q: An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

A:

Q: The table shown shows the rate of water flow w(t) through a pipe, in gallons per hour from 0 <t < 12…

A: Use the riemann mid point rule to find the solution I have drawn the table and the following 3 sub…

Q: (a) Find the Riemann sum for f(x) = sin x,    0&lt;=x &lt;= 3 pie/2 , with six terms, taking the…

A: The formula of Riemann sum is Where,

Q: 9. On July 2, 2019, a total solar eclipse was observable over the South Pacific Ocean and parts of…

A:

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with a rope…

A:

Q: 止星期五由23:59编辑 得分 100 提較 外部工具 Question Given the graph of the function f(x) below, use a left Riemann…

A:

Q: 2. Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed,…

A: solution:-left end pointRiemann sumnumber of rectanglen=5∆t=10-05=2t0=0, t1=2,  t2=4,  t3=6,  t4=8,…

Q: The following function is positive and negative on the given interval. f(x) = 3 – 3x²; [0,4] a.…

A: Part (a) f(x) = 3 - 3x2 intersects x axis when f(x) = 0 i.e. 3 - 3x2 = 0 Or, x = -1, 1 Since we are…

Q: A cable that weighs 6 Ib/ft is used to lift 850 lb of coal up a mine shaft 350 ft deep. Find the…

A:

Q: 50 1 dx using a Riemann sum with n=50,000? In x What is the approximate value of

A: Step:-1 Since, we know ∫ab f(x)dx=limn→∞∑i=1n f(xi') ∆xHere, ∆x=b-an,  xi' =a+ ∆x i Step:-2 Now,…

Q: Approximate sin (x) dr 37 77 57 by Riemann sums with the partition P ={ 2 2}, using first the left…

A:

Q: The rate at which pollution escapes a scrubbing process at a manufacturing plant increases over time…

A: Consider the given information:

Q: A leaky 10-kg bucket is lifted from the ground to a height of 14 m at a constant speed with a rope…

A: Follow step 2 and 3 .

Q: The following function is positive and negative on the given interval. f(x) = 18 - 2x2; [0,4] a.…

A: I am going to solve the given problem by using some simple calcuus to get the required result.

Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = (13/x) on the…

A: The given questions are as follows

Q: Can i get help step by step with this problem?

A: Find the Riemann sum and the area under the curve [-1, 0].

Q: a) The rectangles in the graph below illustrate a x2 Riemann sum for f(x) 8 left endpoint on the…

A:

Q: Can i get help step by step with this problem?

A: Find the Riemann sum and the area under the curve [0, 1].

Q: Question Given the graph of the function f(x) below, use a right Riemann sum with 4 rectangles to…

A:

Q: Give an expression for the 11 cm volume of the slice used in a Riemann sum representing the total…

A: Consider the given figure. Given information Diameter of the cylinder is 8 cm Hence, radius of the…

Q: The following function is positive and negative on the given interval. f(x) = sin 2x; 元 4 म a.…

A: Solution :-

Q: Graph the function fix) =x -1 over the interval (0, 21 Partkion the interval into four subintervals…

A:

Q: 10. A heavy rope, 80 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 80 ft high. The…

A: ----------------------------------------------------------- All length dimensions are in feet. h =…

Q: Question A left Riemann sum with n = 4 subintervals is used to approximate the area under the curve…

A:

Q: An aquarium 4 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

A:

Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for - x2 + 2x on the…

A: Given that, A region is enclosed byfx=-x24+2xand the vertical lines,x=2 and x=6

Q: 3. DETAILS LARCALCET7 8.8.047. MY NOTES ASK YOUR TEACHER Determine whether the improper integral…

A: Answer and explanation is given below..

Q: 2) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4]…

A: There is no part 'd' in the given question. Moreover, we solve the first three questions as per the…

Q: 5. The table below shows the rate of water flow w(t) through a pipe, in gallons per hour from 0 sts…

A: Given that t(hours) 0 2 4 5 7 9 12 w(t) (gals/hr) 0 8 15 12 18 10 6 To find the total amount…

Q: a) The rectangles in the graph below illustrate a left endpoint x2 on the interval 4, 8]. 10 for…

A:

Q: biologist of frog has been studying Particelar a for many years and She used the data to cics し、 an…

A:

Q: Can i get help step by step with this problem?

A: The given function is,

Q: Answer both please.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The following function is positive and negative on the given interval. 5л 2 f(x) sin 2x; a. Sketch…

A: Choose the correct option for the given function.Part (a):

Q: Which of the following statements are true? A) If the number of terms in a Riemann sum increases…

A:

Q: Question Given the graph of the function f(x) below, use a left Riemann sum with 4 rectangles to…

A:

Q: 8e-17 A. Estimate the area under the graph of f(x) between 1 and 17 using L8, the Left-Endpoints…

A: b = 17, a = 1.  f(x) = 8e-x17

Q: A cable that weighs 4 Ib/ft is used to lift 650 lb of coal up a mine shaft 600 ft deep. Find the…

A:

Q: The following function is positive and negative on the given interval. f(x) = 8 – 2x2; [0,4] a.…

A: The following function is positive and negative on the given interval:fx=8-2x2aSketch the function…

Q: 3. (seconds) t 0.369 12 p(t) (feet) 3 5.5 7 13 17 whore ton of a particle, A, moving along the…

A: For (d), We need to show that there exists a value of c, for 0&lt;c&lt;12, such that p'(c) is equal…

Q: Calculator Active. Using a Left Hand Riemann Sum with 6 sub-intervals of equal width, approximate…

A: Given fx=9−x2, 0≤x≤3 Δx=b−an=3−06=12=0.5 Hence, Δx=0.5 Now, break the interval 0,3 into 6…

Q: t 0. 36 9 12 (seconds) p(t) (feet) 3 5.5 7 13 17 The position of a particle, A, moving along the…

A: Given table is,

Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = (15/x) on the…

A:

Q: ) We approximate the area under the graph of y = f(x), above the x-axis, over the interval [0, 4] by…

A: Given function is y=f(x) Divide the interval [0,4] into n rectangles . (a) Width of each rectangle…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.