EBK CALCULUS & ITS APPLICATIONS
14th Edition
ISBN: 8220103679527
Author: Asmar
Publisher: YUZU
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Chapter 2, Problem 54RE
Find the minimum value of the function
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5. Using parentheses make sense of
the expression V · VXVV · Å where
Ả = Ã(x, y, z). Is the result a vector
or a scaler?
3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following
loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20
KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a
distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m.
Calculate the value of the reactions at A and D and hence draw the S.F. and B.M.
diagrams. What are the magnitude and position of the maximum B.M. on the beam?
[41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J
m,
3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at
a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A,
a second concentrated load of 20 KN at C, 3 m from D, and a uniformly
distributed load of 10 kN/m between C and D. Determine: (a) the values of the
reactions at B and 0, (6) the position and magnitude of the maximum bending
moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]
Chapter 2 Solutions
EBK CALCULUS & ITS APPLICATIONS
Ch. 2.1 - Does the slope of the curve in Fig. 17 increases...Ch. 2.1 - At which labelled point on the graph in Fig. 18 is...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Exercises 1-4 refer to graphs (a)-(f) in Fig.19...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Describe each of the following graphs. Your...
Ch. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Prob. 10ECh. 2.1 - Describe each of the following graphs. Your...Ch. 2.1 - Prob. 12ECh. 2.1 - Describe the way the slope changes as you move...Ch. 2.1 - Prob. 14ECh. 2.1 - Describe the way the slope changes on the graph in...Ch. 2.1 - Prob. 16ECh. 2.1 - Exercise 17 and 18 refer to the graph in Fig 20....Ch. 2.1 - Exercise 17 and 18 refer to the graph in Fig 20....Ch. 2.1 - Prob. 19ECh. 2.1 - In Exercises 19-22, draw the graph of a function...Ch. 2.1 - In Exercises 19-22, draw the graph of a function...Ch. 2.1 - Prob. 22ECh. 2.1 - Annual World Consumption of Oil The annual world...Ch. 2.1 - Prob. 24ECh. 2.1 - A Patients Temperature At noon, a childs...Ch. 2.1 - Prob. 26ECh. 2.1 - Blood Flow through the Brain One method of...Ch. 2.1 - Pollution Suppose that some organic waste products...Ch. 2.1 - Number of U.S. Farms Figure 22 gives to number of...Ch. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Let P(t) be the population of a bacteria culture...Ch. 2.1 - In Exercises 3336, sketch the graph of a function...Ch. 2.1 - In Exercises 3336, sketch the graph of a function...Ch. 2.1 - In Exercises 3336, sketch the graph of a function...Ch. 2.1 - In Exercises 3336, sketch the graph of a function...Ch. 2.1 - Consider a smooth curve with no undefined points....Ch. 2.1 - If the function f(x) has a relative minimum at x=a...Ch. 2.1 - Technology Exercises Graph the function...Ch. 2.1 - Prob. 40ECh. 2.1 - Technology Exercises Simultaneously graph the...Ch. 2.2 - Make a good sketch of the function f(x) near the...Ch. 2.2 - The graph of f(x)=x3 is shown in Fig. 15. Is the...Ch. 2.2 - The graph of y=f(x) is shown in Fig. 16. Explain...Ch. 2.2 - Exercises 14 refer to the functions whose graphs...Ch. 2.2 - Exercises 14 refer to the functions whose graphs...Ch. 2.2 - Exercises 14 refer to the functions whose graphs...Ch. 2.2 - Exercises 14 refer to the functions whose graphs...Ch. 2.2 - Which one of the graph in Fig. 18 could represent...Ch. 2.2 - Which one of the graphs in Fig. 18 could represent...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 712, sketch the graph of a function...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - In Exercises 1318, use the given information to...Ch. 2.2 - Refer to the graph in Fig. 19. Fill in each box of...Ch. 2.2 - The first and second derivatives of the function...Ch. 2.2 - Suppose that Fig. 20 contains the graph of y=s(t),...Ch. 2.2 - Suppose that Fig. 20 contains the graph of y=v(t),...Ch. 2.2 - 23. Refer to figure 21, Looking at the graph f(x),...Ch. 2.2 - In figure 22, the t axis represent the time in...Ch. 2.2 - 25. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 26. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 27. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 28. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 29. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 30. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 31. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - Prob. 32ECh. 2.2 - 33. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 34. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - 35. Exercises 2536 refer to Fig. 23, which...Ch. 2.2 - Prob. 36ECh. 2.2 - 37. Level of Water from Melting Snow Melting snow...Ch. 2.2 - 38. Changes in Temperature T(t) is the temperature...Ch. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - 42. Match each observation (a)(e) with a...Ch. 2.2 - Prob. 43ECh. 2.2 - Drug Diffusion in the Bloodstream After a drug is...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.3 - Which of the curves in Fig.15 could possibly be...Ch. 2.3 - Which of the curves in Fig.16 could be the graph...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Each of the graphs of the functions in Exercises...Ch. 2.3 - Prob. 24ECh. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Sketch the following curves, indicating all...Ch. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Let a,b,c,d be fixed numbers with a0, and let...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - Prob. 36ECh. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - The graph of each function in Exercises 35 40 has...Ch. 2.3 - In Exercises 41 and 42, determine which function...Ch. 2.3 - In Exercises 41 and 42, determine which function...Ch. 2.3 - Consider the graph of g(x) in Fig. 17. a. If g(x)...Ch. 2.3 - U. S. Population The population (in millions) of...Ch. 2.3 - Index-Fund Fees When a mutual fund company charges...Ch. 2.3 - Prob. 46ECh. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.3 - Technology Exercises Draw the graph of...Ch. 2.4 - Determine whether each of the following functions...Ch. 2.4 - Prob. 2CYUCh. 2.4 - Prob. 3CYUCh. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Prob. 2ECh. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Prob. 4ECh. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Find the x intercepts of the given function....Ch. 2.4 - Show that the function f(x)=13x32x2+5x has no...Ch. 2.4 - Prob. 8ECh. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 14ECh. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 16ECh. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 18ECh. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Sketch the graphs of the following functions....Ch. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 24ECh. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 26ECh. 2.4 - Sketch the graphs of the following functions for...Ch. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Find the quadratic function f(x)=ax2+bx+c that...Ch. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Technology Exercises Height of Tropical Grass The...Ch. 2.5 - Volume A canvas wind shelter for the beach has a...Ch. 2.5 - Prob. 2CYUCh. 2.5 - For what x does the function g(x)=10+40xx2 have...Ch. 2.5 - Find the maximum value of the function f(x)=12xx2,...Ch. 2.5 - Find the minimum value of f(t)=t36t2+40, t0 and...Ch. 2.5 - For what t does the function f(t)=t2-24t have its...Ch. 2.5 - Optimization with Constraint Find the maximum of...Ch. 2.5 - Optimization with Constraint Find two positive...Ch. 2.5 - Optimization with Constraint Find the minimum of...Ch. 2.5 - In Exercise 7, can there be a maximum for Q=x2+y2...Ch. 2.5 - Minimizing a Sum Find the positive values of x and...Ch. 2.5 - Maximizing a Product Find the positive values of...Ch. 2.5 - Area There are 320 available to fence in a...Ch. 2.5 - Volume Figure 12 (b) shows an open rectangular box...Ch. 2.5 - Volume Postal requirements specify that parcels...Ch. 2.5 - Perimeter Consider the problem of finding the...Ch. 2.5 - Cost A rectangular garden of area 75 square feet...Ch. 2.5 - Cost A closed rectangular box with a square base...Ch. 2.5 - Surface Area Find the dimensions of the closed...Ch. 2.5 - Volume A canvas wind shelter for the beach has a...Ch. 2.5 - Area A farmer has 1500 available to build an...Ch. 2.5 - Area Find the dimensions of the rectangular garden...Ch. 2.5 - Maximizing a Product Find two positive numbers,...Ch. 2.5 - Minimizing a Sum Find two positive numbers, xandy,...Ch. 2.5 - Area Figure 140 (a) shows a Norman window, which...Ch. 2.5 - Surface Area A large soup can is to be designed so...Ch. 2.5 - In Example 3 we can solve the constraint equation...Ch. 2.5 - Cost A ship uses 5x2 dollars of fuel per hour when...Ch. 2.5 - Cost A cable is to be installed from one corner,...Ch. 2.5 - Area A rectangular page is to contain 50 square...Ch. 2.5 - Distance Find the point on the graph of y=x that...Ch. 2.5 - Prob. 30ECh. 2.5 - Distance Find the point on the line y=2x+5 that is...Ch. 2.5 - Technology Exercise Inscribed Rectangle of Maximum...Ch. 2.6 - In the inventory problem of Example 2, suppose...Ch. 2.6 - In the inventory problem Example 2, Suppose that...Ch. 2.6 - Inventory Problem Figure 6 shows the inventory...Ch. 2.6 - Refer to Fig. 6. Suppose that The ordering cost...Ch. 2.6 - Inventory Control A pharmacist wants to establish...Ch. 2.6 - Inventory Control A furniture store expects to...Ch. 2.6 - Inventory Control A California distributor of...Ch. 2.6 - Economic Lot Size The Great American Tire Co....Ch. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Area Starting with a 100-foot-long stone wall, a...Ch. 2.6 - Prob. 12ECh. 2.6 - Length A rectangular corral of 54 square meters is...Ch. 2.6 - Refer to Exercise 13. If the cost of the fencing...Ch. 2.6 - Revenue Shakespeares Pizza sells 1000 large vegi...Ch. 2.6 - Prob. 16ECh. 2.6 - Cost A storage shed is to be built in the shape of...Ch. 2.6 - Cost A supermarket is to be designed as a...Ch. 2.6 - Volume A certain airline requires that rectangular...Ch. 2.6 - Area An athletic field [Fig.8] consists of a...Ch. 2.6 - Volume An open rectangular box is to be...Ch. 2.6 - Volume A closed rectangular box is to be...Ch. 2.6 - Amount of Oxygen in a Lake Let f(t) be the amount...Ch. 2.6 - Prob. 24ECh. 2.6 - Area Consider a parabolic arch whose shape may be...Ch. 2.6 - Prob. 26ECh. 2.6 - Surface Area An open rectangular box of volume 400...Ch. 2.6 - If f(x) is defined on the interval 0x5 and f(x) is...Ch. 2.6 - Technology Exercises Volume A pizza box is formed...Ch. 2.6 - Technology Exercises Consumption of Coffee in the...Ch. 2.7 - Prob. 1CYUCh. 2.7 - Rework Example 4 under the condition that the...Ch. 2.7 - On a certain route, a regional airline carries...Ch. 2.7 - Minimizing Marginal Cost Given the cost function...Ch. 2.7 - Minimizing Marginal Cost If a total cost function...Ch. 2.7 - Maximizing Revenue Cost The revenue function for a...Ch. 2.7 - Maximizing Revenue The revenue function for a...Ch. 2.7 - Cost and Profit A one-product firm estimates that...Ch. 2.7 - Maximizing Profit A small tie shop sells ties for...Ch. 2.7 - Demand and Revenue The demand equation for a...Ch. 2.7 - Maximizing Revenue The demand equation for a...Ch. 2.7 - Profit Some years ago, it was estimated that the...Ch. 2.7 - Maximizing Area Consider a rectangle in the xy-...Ch. 2.7 - Demand, Revenue, and Profit Until recently...Ch. 2.7 - Demand and Revenue The average ticket price for a...Ch. 2.7 - Demand and Revenue An artist is planning to sell...Ch. 2.7 - Demand and Revenue A swimming club offers...Ch. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Price Setting The monthly demand equation for an...Ch. 2.7 - Taxes, Profit, and Revenue The demand equation for...Ch. 2.7 - Interest Rate A savings and loan association...Ch. 2.7 - Prob. 20ECh. 2.7 - Revenue The revenue for a manufacturer is R(x)...Ch. 2.7 - Prob. 22ECh. 2 - State as many terms used to describe graphs of...Ch. 2 - What is the difference between having a relative...Ch. 2 - Give three characterizations of what it means for...Ch. 2 - What does it mean to say that the graph of f(x)...Ch. 2 - Prob. 5CCECh. 2 - Prob. 6CCECh. 2 - Prob. 7CCECh. 2 - Prob. 8CCECh. 2 - Prob. 9CCECh. 2 - Prob. 10CCECh. 2 - Prob. 11CCECh. 2 - Prob. 12CCECh. 2 - Prob. 13CCECh. 2 - Prob. 14CCECh. 2 - Outline the procedure for solving an optimization...Ch. 2 - Prob. 16CCECh. 2 - Figure (1) contains the graph of f(x), the...Ch. 2 - Figure (2) shows the graph of function f(x) and...Ch. 2 - In Exercise 36, draw the graph of a function f(x)...Ch. 2 - In Exercise 36, draw the graph of a function f(x)...Ch. 2 - In Exercise 36, draw the graph of a function f(x)...Ch. 2 - In Exercise 36, draw the graph of a function f(x)...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Exercise 712, refer to the graph in Fig. 3. List...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Properties of various functions are described...Ch. 2 - Prob. 20RECh. 2 - In Fig. 4 (a) and 4 (b), the t axis represents...Ch. 2 - U.S. Electric Energy United States electrical...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following parabolas. Include there x...Ch. 2 - Sketch the following curves. y=2x3+3x2+1Ch. 2 - Sketch the following curves. y=x332x26xCh. 2 - Sketch the following curves. y=x33x2+3x2Ch. 2 - Sketch the following curves. y=100+36x6x2x3Ch. 2 - Sketch the following curves. y=113+3xx213x3Ch. 2 - Sketch the following curves. y=x33x29x+7Ch. 2 - Sketch the following curves. y=13x32x25xCh. 2 - Sketch the following curves. y=x36x215x+50Ch. 2 - Sketch the following curves. y=x42x2Ch. 2 - Sketch the following curves. y=x44x3Ch. 2 - Sketch the following curves. y=x5+20x+3(x0)Ch. 2 - Sketch the following curves. y=12x+2x+1(x0)Ch. 2 - Let f(x)=(x2+2)3/2. Show that the graph of f(x)...Ch. 2 - Show that the function f(x)=(2x2+3)3/2 is...Ch. 2 - Let f(x) be a function whose derivative is...Ch. 2 - Let f(x) be a function whose derivative is...Ch. 2 - Position Velocity and Acceleration A car traveling...Ch. 2 - The water level in a reservoir varies during the...Ch. 2 - Population near New York City Let f(x) be the...Ch. 2 - For what x does the function f(x)=14x2x+2,0x8,...Ch. 2 - Find the maximum value of the function...Ch. 2 - Find the minimum value of the function...Ch. 2 - Surface Area An open rectangular box is to be 4...Ch. 2 - Volume A closed rectangular box with a square base...Ch. 2 - Volume A long rectangular sheet of metal 30 inches...Ch. 2 - Maximizing the Total Yield A small orchard yields...Ch. 2 - Inventory Control A publishing company sells...Ch. 2 - Profit if the demand equation for a monopolist is...Ch. 2 - Minimizing time Jane wants to drive her tractor...Ch. 2 - Maximizing Revenue A travel agency offers a boat...
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- 3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward3.11 (B). A beam, 12 m long, is to be simply supported at 2m from each end and to carry a U.d.l of 30kN/m together with a 30 KN point load at the right-hand end. For ease of transportation the beam is to be jointed in two places, one joint being Situated 5 m from the left-hand end. What load (to the nearest KN) must be applied to the left-hand end to ensure that there is no B.M. at the joint (i.e. the joint is to be a point of contraflexure)? What will then be the best position on the beam for the other joint? Determine the position and magnitude of the maximum B.M. present on the beam. [114 KN, 1.6 m from r.h. reaction; 4.7 m from 1.h. reaction; 43.35 KN m.]arrow_forward2. Using vector algebraic operations, if - Ả = 2ây – mây – C - B = mây tây – 2, C = ây + mây + 20, D = m x + mây tậ Z Find the value(s) of m such that (a) Ả is perpendicular to B (b) B is parallel to Carrow_forward
- 1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$arrow_forward3 Evaluate the double integral 10 y√x dy dx. First sketch the area of the integral involved, then carry out the integral in both ways, first over x and next over y, and vice versa.arrow_forwardQuestion 2. i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) = P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer. ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer.arrow_forward
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