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- Suppose that you are climbing a hill whose shape is given by 2360 0.01122 - 0.009y2 where z is the elevation of the hill and , y, and z are measured in meters. You are standing at a point with coordinates axis points east and the positive y axis points north. P(20, 180, 2064) where the positive ax (a) From the point P(20, 180, 2064) you walk in the direction of 2, - 3) what is rate of change in elevation? Round your answer to three decimals. (b) Find a unit vector in the direction of maximum increase of z at point P(20, 180, 2064) Round your value(s) to three decimals (c) What is the maximum rate of change of z at the point P(20, 180, 2064) Round your answer to three decimals.Suppose you are climbing a hill whose shape is given by the equation z = 2000 - 0.005x² -0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1966). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend O descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? O ascend Odescend At what rate? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction. the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.) 0x 1. An object moves in a plane from the position r₁=(-1,-2) m to the position_r₂=(2,7) m and then to r3=(3,8 m. The time of the motion is At = 30 s. Find: (a) total displacement; (b) distance between the initial and final positions; (c) distance travelled (way length); d) average velocity and average speed. total €=30s displacement +
- The curve y=ax² +bx+c_passes through the point (1,2). The line y=2x+1 is tangent to the curve when x=0. What are the values of a, b and c? O a = 1, b = 2, c = 1 O a = 1, b = -2, c = 1 а%3D —1, b %3D2, с %3D -1 O a = -1, b = -2, c = 1 O a = -1, b = 2, c = 1Express the mathematical relationship between stress and strain in case of elastic material.in a reactangular field of 60 and 80m respectively two farmoers start moving from the same point and take same time i.e 30 minutes to reach diagonally opposites poont aling two different paths. find the velocity and the speed of both farmers
- The coordinates of the points O, A and B of the plane are (0, 0), (0, 12) and (108, 0), respectively. A point P=(x,y) is such that the area of triangle ΔPOA is twice the area of triangle ΔPOB. We can then say that the coordinates of P satisfy the relationship: Choose an option: a. x^(2)−81/4y^(2)=0 b. x^(2)−324y^(2)=0 c. x^(2)−81y^(2)=0 d. x^(2)−18y^(2)=0 e.x^(2)−54y^(2)=0The curve passes through the point (1,-11) and its gradient at any point is ax^2+b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the value of a and b ii) the equation of the curveThe cubic y = ax3 + bx2 + cx + d that passes through the points (-1, -10) and (1, -4) and tangent to the line 2x + y + 7 = 0 at (0, -7).
- The velocity function is v(t)=t^2−6t+8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-3,5]. A)Displacement= B)Distance Traveled=Find the point on the parabola that is closest to the point (0, -3). HINT: distance:=surd((x-x1)^2+9y-y1)^2,2); and parabola:=x+y^2=0; Isolate(x+y^2=0,x); Substitute the result obtained for x into your distance equation. Substitute the x and y ordinates (0 and -3) for x1 and y1 in your distance formula. Take the radicand (what’s under the radical of your new distance function) and differentiate that for y. Set this derivative to zero and solve for y. Substitute this y-value (select only the real number solution) into parabola equation to solve for x. You will now have both x and y ordinates.Which of the following sets contain functions that are linearly independent? А. (3х — 1, х + 2, 4x) В. (4, 2х — 3) O c. [3 e^(2x),4 e^(2x) ] ОD. [2 e (3x - 1), - 3 е^(3х — 1)1