You purchase a remote-controlled drone for d dollars. Your friend purchases a drone that costs $35 more than your drone. Your brother purchases a drone that costs three times as much as your friend's drone. Write and simplify an expression that represents the cost (in dollars) of your brother's drone. <img src="https://d2nchlq0f2u6vy.cloudfront.net/questions/q-a37dc8e07-0542-40f6-85f0-7f2c5c0594d1.png" style="transform: rotate(0deg)">
The height of a drone, in meters, above its launching platform that is 5 m above the ground, is modeled by $$ y = 0.1x^2 - 1.5x + 5, $$ where x is the time in seconds. The drone leaves the launch pad, flies down into a canyon, and then it flies back up again. a. What is the factored form of the equation for the height of the drone? b. After how many seconds will the drone be at ground level? c. After how many seconds will the drone come back to the height of its platform?
The use of drones, aircraft without onboard human pilots, is becoming more prevalent in the United States. According to a 2017 Pew Research Center report, 59 percent of American had seen a drone in action. Suppose 50 Americans are randomly selected. a. What is the probability that at least 25 had seen a drone? b. What is the probability that more than 30 had seen a drone? c. What is the probability that between 30 and 35 had seen a drone? d. What is the probability that more than 30 had not seen a drone?
A camera weighing 10 N falls from a small drone hovering 20 m overhead and enters free fall. What is the gravitational potential energy change of the camera from the drone to the ground if you take a reference point of (a) the ground being zero gravitational potential energy? (b) The drone being zero gravitational energy? What is the gravitational potential energy of the camera (c) before it falls from the drone and (d) after the camera lands on the ground if the reference point of zero gravitational potential energy is taken to be a second person looking out of a building 30 m from the ground?
Pretend that the starship Enterprise in the previous problem is somehow traveling at $c$ with respect to the Earth, and it fires a drone forward at speed $c$ with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to the Earth is still $c$.
The students in Kennedy High School's Energetic Engineering Club have created four drones for the National Robotics Competition. a. Drone A currently has an energy level of 3. The energy level affects how fast the drone moves forward. The students decide that the drone needs a greater energy level, so they have created EB4(energy boost 4) that will multiply any drone's energy by 4. If Drone A is given EB4, what is its resulting energy level? b. The Energetic Engineering Club also created Drone B with an energy level that affects two directions. Drone B's energy is given by the vector $\langle 1,7\rangle$, which combines for a total energy level of 8. The students have also developed EB4.2, which multiplies the drone's horizontal energy by 4 and vertical energy by 2. The energy boost EB4.2 is represented by the vector $\langle 4,2\rangle$. If frone B is given EB4.2, what is its new combined energy level? Give an answer that is a scalar, not a vector. c. Drone C's energy is given by the vector $\langle 3,5\rangle$, and EB2.6 multiplies it by the vector $\langle 2,6\rangle$. What is the value of $\langle 2,5\rangle \cdot\langle 2,6\rangle$? That is, what is Drone C's new combined energy level? d. Due to a design flaw, Drone D has an excessive amount of energy, so the students develop a "boost" that actually reduces the drone's energy. If Drone D's energy level is given by $\langle 25,22\rangle$ and the energy boost is represented by $\langle- 1,2\rangle$, what is the value of $\langle 25,22\rangle \cdot\langle- 1,2\rangle$? e. What you have been doing intuitively in this problem is formally called the dot product.
Krista pilots a drone from her house to the park. The relative locations are shown in the coordinate plane. What is the distance the drone flies? <center><img src="https://slader-solution-uploads.s3.amazonaws.com/964d4508-c397-4c01-9e78-a14d1d6db687-1676182904191229.jpeg" width="pixel"><br></center>