Numerade

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9. (10 points) Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 3x + 3y; R: The triangle cut from the first quadrant by the line x + y = 4

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Using the limits from part (d) and the expression from part (c), determine an expression for the magnitude of the electric field E at the stylus generated by the entire line of charged plastic.

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Which type of budget reflects a company's anticipated costs based on variations in activity levels? Multiple Choice None of these answers are correct. A static budget. A flexible budget. A standard budget and a flexible budget. A standard budget.

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2. Let $A = \begin{pmatrix} 3 & -2 & 0 \ 4 & 4 & 1 \ -5 & 1 & 7 \end{pmatrix}$. Find the adjoint of A. If det(A) = 5, find the value of each of the following properties of determinants: a. det(B) b. det(C)

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ANSWER ALL QUESTIONS PLS QUESTION 2: Consider the fall of a pole vaulter as a projectile once the pole is released. The pole has a length of 15.8 feet and once the athlete lets go of the pole, he will land on a cushion 2 feet high, 10 feet wide, and 16 feet long, which protects him in the fall. If an athlete lets go of the pole when he is 13.1 ft above the ground with a speed of 17.2 ft/s at an angle of 72 degrees, calculate the initial velocity component HORIZONTAL. Don't forget to include the units in the result. QUESTION 3: Consider the fall of a pole vaulter as a projectile once the pole is released. The pole has a length of 15.8 feet and once the athlete lets go of the pole, he will land on a cushion 2 feet high, 10 feet wide, and 16 feet long, which protects him in the fall. If an athlete lets go of the pole when he is 12.9 ft above the ground with a velocity of 18.9 ft/s at an angle of 52 degrees, calculate the initial velocity component VERTICAL. Don't forget to include the units in the result. QUESTION 4: Consider the fall of a pole vaulter as a projectile once the pole is released. The pole has a length of 15.8 feet and once the athlete lets go of the pole, he will land on a cushion 2 feet high, 10 feet wide, and 16 feet long, which protects him in the fall. If an athlete lets go of the pole when he is 12.9 ft above the ground with a speed of 14.7 ft/s at an angle of 51 degrees, calculate the MAXIMUM HEIGHT it can reach with the indicated conditions. Don't forget to include the units in the result. QUESTION 5: Consider the fall of a pole vaulter as a projectile once the pole is released. The pole has a length of 15.8 feet and once the athlete lets go of the pole, he will land on a cushion 2 feet high, 10 feet wide, and 16 feet long, which protects him in the fall. If an athlete lets go of the pole when he is 14.4 ft above the ground with a speed of 17.4 ft/s at an angle of 65 degrees, calculate the HORIZONTAL DISTANCE that the athlete will move with the indicated conditions. Don't forget to include the units in the result. Note: take into account the height of the mattress.

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Figure 4

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1. Given the following charts with isobars for the NORTHERN Hemisphere, show the directions of forces (please specify which forces) and wind vectors for: (12 pts) (a) upper level flow in geostrophic wind balance, (b) the surface wind, which includes friction, (c) an anticyclonic tornado in cyclostrophic balance. Hint: the potential forces include: pressure gradient force (PGF), Coriolis force (CoF), friction force (FF), and centrifugal force (CF). (a) (b) 530 mb 524 mb 1012 mb 1008 mb (c) 900 mb 800 mb

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A B D1 D2 0.45T C 0.3T d3 D3 F 0.25T l1 l2 l3 Stepped shaft shown in the figure is fixed at section A, and subjected to torques 0.45T, 0.3T, and 0.25T at sections B, C, F, respectively. If the allowable shear stress is 8000 N/cm², a) Draw the internal torque diagram (as a function of T), b) Determine the maximum torque T. c) For maximum torque, calculate the twist angle of sections B, C, and F. GIVEN: G = 0.8×10$^7$ N/cm$^2$, D? = 4 cm, D? = 3 cm, D? = 3 cm, d? = 2.2 cm, l? = 25 cm, l? = 20 cm, l? = 20 cm.

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A set of 20 bolts is to be used to provide a clamping force of 80000 lb between two components of a machine. The load is shared equally among the 4 bolts. Knowing that the grade of the material is SAE Grade 1, if each is to be stressed to 55 %of its proof strength. Determine a) the allowable stress of the bolts material; b) the required tensile stress area and c) Specify suitable bolts a. $A_t = 0.22 \text{ in}^2$ b. $A_t = 0.142 \text{ in}^2$ c. $\sigma_{all} = 15389 \text{ psi}$ d. $A_t = 0.173 \text{ in}^2$ e. 5/8-11 UNC f. 5-40 UNC g. $\sigma_{all} = 18150 \text{ psi}$

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4 Considering the disk with radius of r, constant rotational velocity of \omega, calculate the ratio between the velocity of point A respecting point B. Any method is acceptable.

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dana c.