13. x² + y? + 16x + 10y – 55 = 0 14. x2 + y? -16x + 9y – 8 = 0
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- Suppose that x14 + y14 = 2. What is y00 at the point (1, 1)?You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Based on this information, answer the following questions. 1. determine if it exists, the safe distance between the two hearing zones of the guards for you to pass through undetected? (Hint: use Pythagorean Theorem or distance formula) Distance between two red dots is:________________ . (5 pts) We know that the radius of the hearing zones are:…You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…
- You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape through a door located on the western wall. Guard 1 is located in a tower at the northeast corner of the yard and Guard 2 is located in the yard, in the southwest corner, as shown in the figure below. Guard 1 can hear you if anything more than 1/36 of the footstep sound energy reaches them; similarly Guard 2 can hear you if anything more than 1/16 of the footstep sound energy reaches them (Guard 1 can hear more due to his elevated height in the tower). Assume for now that both guards are fixed at these locations and cannot move unless they detect you. Now assume that Guard 2 is on patrol. He walks a straight patrol route up and down along the dotted line always remaining 3 m from the western wall. Determine the new maximum safe distance between the two hearing zones of the guards for you to pass undetected? (Hint: use Pythagorean Theorem or distance formula) Where is the Guard 2 located for…Suppose you go up a hill whose shape is given by the equationz = 1000 - 0.005x2 - 0.01y2, where x, y and z are measured in meters and you are at a point with coordinates (60,40,966). The positive x axis points east and the positive y axis points north. a) If you walk south, will you begin to ascend or descend? For what reason?b) If you walk northeast, will you begin to climb or descend? At what rate?c) In which direction is the slope greater? What is the rate of ascent in that direction?d) At what angle above the horizontal does the trajectory begin in that direction? Note: To solve take into account the topics partial derivatives, directional derivative and the gradient. Note: answer only subsection dWhat are the coordinates of the vertices of △A′B′C′ after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?
- What are the coordinates of the vertices of△A′B′C′after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of L?