Question Solved1 Answer Question 1 Find the area of the region that is bounded by the curve f(x) = x2 + 2x + 1 and the line g(x) = x + 1 over the interval [-2,0] . Enter your answer as an exact answer. . Provide your answer below: A= units? Question 2 Find the area of the region pictured below that is bounded by the functions f(x) = x2 - 6x + 8 and g(x) = 18 - 3x and the x-axis when integrating with respect to y. Enter an exact answer. 64 5 4 3 2 1 -7 -6 -5 1 3 5 -4-3-2-1 0 -1 -2 (3) 6 Provide your answer below: units III Question 3 Find the volume of the solid whose base is a triangle with vertices (0,0), (0, 3), and (2,0). Slices perpendicular to the xy-plane are semicircles. Enter answer using exact values. Provide your answer below: V= units

Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. Find the eigenvalues. (Enter your answers as a comma-separated list.) λ = Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes O No Need Help? Read It -/2 Points] DETAILS LARLINALG8 7.2.026. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable. -0 0 3-2 Find the eigenvalues. (Enter your answers as a comma-separated list.) A = Is there a sufficient number to guarantee that the matrix is diagonalizable? O Yes Activate Windows O No

The Quantum Numbers for electron(s) in the valence shell of thallium (81 Tl) are: Select one: a. (6,0,0,+1/2) (6.1.-1,72) O b. (6.1.-1,72) (6,1,0,72) (6.1.1,72) C. (6.1.-1,12) Clear my choice

Consider each situation described below. Identify the population and the sample, explain what the parameter \( p \) or \( \mu \) represents, and tell whether the methods of this chapter can be used to create a confidence interval. If so, find the interval. (a) The service department at a new car dealer checks for small dents in cars brought in for scheduled maintenance. It finds that 22 of 87 cars have a dent that can be removed easily. The service department wants to estimate the percentage of all cars with these easily repaired dents. (b) A survey of customers at a supermarket asks whether they found shopping at this market more pleasing than at a nearby store. Of the 2,500 forms distributed to customers, 325 were filled in and 250 of these said that the experience was more pleasing. (c) A poll asks visitors to a Web site for the number of hours spent Web surfing daily. The poll gets 223 responses one day. The average response is three hours per day with \( s=1.5 \). (d) A sample of 1,000 customers given loans during the past two years contains 2 who have defaulted.

Problem 5: Camels are atypical for mammals because are able to tolerate relatively large diurnal changes in body temperature. Humans must keep their temperature within one or two degrees, but a Camel's body temperature may vary between 32 °C and 40 °C. Other mammals can shed heat by sweating. How much water would the camel have to lose to dump the extra heat it can absorb when raising temperature from 32 °C to 40 °C? Lets say, a camel has a mass of about m= 400 kg. The specific heat of mammals is about c=3500 J kg='C-1. The heat of vaporization for water is about L=2.3x106 J/kg. How that strategy would help them survive in the desert environments?

Problem 3: Mister Fantastic of the Fantastic Four weighs 70 kg and is made of rubber a. By how much will his legs (assumed to be cylindrical, 90 cm long and 10 cm in diameter and made of rubber without bones) shorten when his body weight is entirely supported by them? b. What will it be for The Thing of the same Fantastic Four fame, if you assume that he is made of granite and weighs 400 kg. Assume further that his legs are 150 cm long and 25 cm in diameter. How much additional weight can he carry before his legs break under the stress? For these problems, look at compression only and ignore bending and buckling. Compressive braking stress for Granite is 1.45x108 [Pa) and its Young Modulus is 517x108 [Pa]; Young Modulus for rubber is 1x10° [Pa].

Describe completely the single transformation that maps (a) AA onto a B. (b) A onto AC AA onto AD (e) (d) State the coordinates of the vertices A is translated to AE by the vector ofΔΕ.