Numerade

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What is the magnitude of the gravitational force acting on the earth due to the sun? Express your

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Evaluate the following definite integral: $ \int_{-1}^{1} 3x^2 (4x^3 - 1)^3 dx $ \nRound your answer to the nearest hundredth.

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The phenomenon wherein individuals cannot recall explicit memories from their first three years of life due to significant changes in the neural connections in their hippocampus and frontal lobes is called

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20.7 RL Circuits 7. A 12-V battery is connected in series with a switch, resistor and coil. If the circuit's time constant is $2.0 \times 10^{-4}$ s and the final steady current after the switch is closed becomes 1.0 A, what is the value of the inductance? a. 1.2 mH b. 2.4 mH c. 9.6 mH d. 48 mH 20.6 Self-Inductance 8. The current in a coil with a self-inductance of 1.5 mH increases from 0 to 1.0 A in a tenth of a second. What is the induced emf in the coil? a. 15 mV b. 30 mV c. 0.10 V d. 0.30 V

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The length and width of a rectangle are consecutive odd integers. The area of the rectangle is 255 square inches. Find the length and width of the rectangle.

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Present your solution with the illustration of the figure with correct labels and the equation necessary to answer the question. a) A searchlight is shaped like a parabola of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening be? b) The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet across and 90 feet high. Find an equation describing the door's shape. If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head? c) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 150 feet from the center of the bridge? d) An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus). How far is it from the deepest part of the dish? e) A radar antenna is constructed so that a cross section along its axis is parabola with the receiver at the focus. Find the height of the receiver if the antenna is 18 meters across and 6 meters deep.

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Find the acute angle between the lines. Round your answer to the nearest degree.\ $9x - y = 3$, $8x + y = 7$

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6. [0/4 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.5.047. MY NOTES Find the points on the lemniscate where the tangent is horizontal. (Order your answers from smallest to largest $x$, then from smallest to largest $y$). $2(x^2 + y^2)^2 = 81(x^2 - y^2)$ $(x, y) = \left(\frac{9}{2}, 0\right)$ $(x, y) = \left(\frac{9}{2}, 0\right)$ $(x, y) = \left(\frac{9}{2}, 0\right)$ $(x, y) = \left(\frac{9}{2}, 0\right)$

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1. For each of the following functions take the first derivative, and then take the second derivative. (a) (3 points) f(x) = 4x^2 - 10x - 20 (b) (3 points) f(x) = x^3 - 5x 2. (4 points) Find the maximum or minimum value for each of the functions in problem 1 . If there is no max or min, then briefly explain how you know this. If there is a max (or a min), then briefly explain how you know that it is a max (or a min ).

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2- For the common source amplifier circuit shown below: a) If the transistor has $V_t = 1 V$, and $k' = 2 mA/V^2$, verify that the bias circuit establishes $V_G = 2 V$, $I_D = 1 mA$ and $V_D = 7.5 V$. b) Find $g_m$, $r_o$ and $r$ if $V_A = 100 V$. c) Find voltage gain, $V_o/V_i$

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margarita r.